Schedule-at-a-Glance
Schedule-at-a-Glance
Schedule-at-a-Glance
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1PRIMA 2013-Table of ContentsTable of ContentsWelcome………………………………………………………………………………………………………………….2Organiz<strong>at</strong>ion ................................................................................................................... 3Scientific Committee ............................................................................................... 3Local Organizing Committee ................................................................................... 3Local Advisory Committee ...................................................................................... 3Public Lecturers ....................................................................................................... 3Plenary Speakers ..................................................................................................... 4Special Sessions & Organizers ................................................................................. 4Sponsors .................................................................................................................. 6Useful Inform<strong>at</strong>ion ......................................................................................................... 7Congress Venues…………………………………………………………………………………………..…..7Hotel…………………………………………………………………………………………………………………7Transport<strong>at</strong>ion Directions ....................................................................................... 7Airports & Railway St<strong>at</strong>ions ............................................................................. 7Congress Bus .................................................................................................... 9Dining ...................................................................................................................... 9On-campus Dining ............................................................................................ 9Off-campus Dining……………………………………………………………………………………10Standard Audio/Visual Set-up…………………………………………………………………………..10Internet Access…………………………………………………………………………………………………10Get-togethers……………………………………………………………………………………………………10Book Display..……………………………………………………………………………………………………10Program…………………………………………………………………………………………………………………13<strong>Schedule</strong>-<strong>at</strong>-a-<strong>Glance</strong>……..………………………………………………………………………………..13Monday, June 24………………..…………………………………………………………………………..14Tuesday, June 25…….………………………………………………………………………………………23Wednesday, June 26…...……………………………………………………………………………………32Thursday, June 27...…..……………………………………………………………………………………33Friday, June 28….………………………………………………………………………………………………42Abstracts……………………………………………………………………………………………………Appendix 1Map from Airports to Hua Ting Hotel & Towers…………………..................... …Appendix 2Map of SJTU Xuhui Campus ........................................................................... Appendix 3Floor Plan of Engineering Hall ............................................................………….Appendix 4
2PRIMA 2013-WelcomeWelcomeDear Colleagues,It is a pleasure for me to write a few words of welcome on behalf of the scientificand organizing committees for the 2013 PRIMA Congress, which will take place <strong>at</strong>Shanghai Jiao Tong University in the vibrant city of Shanghai, China on June 24- 28,2013. PRIMA, the Pacific Rim M<strong>at</strong>hem<strong>at</strong>ical Associ<strong>at</strong>ion, was established in 2005 asan organiz<strong>at</strong>ion for promoting the development of m<strong>at</strong>hem<strong>at</strong>ical sciences in thePacific Rim region. Our most important activity is the PRIMA Congress, which is heldevery four years. Our inaugural event took place in Sydney, Australia in 2009.The 2013 PRIMA Congress promises to be an exciting event, with world-class plenarylectures and public speakers. In addition there will be 23 special sessions ormini-symposia in a broad array of topics in the m<strong>at</strong>hem<strong>at</strong>ical sciences, withparticipants from all over the Pacific Rim. Our host for this event is Shanghai JiaoTong University, and they have done a wonderful job with the local arrangements.Aside from the excellent scientific program, the Congress will be a uniqueopportunity for participants to establish contacts throughout the Pacific Rim. Wewould like to invite the m<strong>at</strong>hem<strong>at</strong>ical community to <strong>at</strong>tend this meeting and join usin celebr<strong>at</strong>ing the incredible vitality and intellectual richness of our region.We are looking forward to welcoming you to the 2013 PRIMA Congress in Shanghai!With best regards,Alejandro AdemDirector of PRIMAUniversity of British Columbia, Vancouver, Canada、
3PRIMA 2013-Organiz<strong>at</strong>ionOrganiz<strong>at</strong>ionScientific CommitteeAlejandro Adem,The University of British Columbia, CanadaFederico ArdilaSan Francisco St<strong>at</strong>e University, USAMarston ConderUniversity of Auckland, New ZealandDavid EisenbudUC Berkeley, USAYakov EliashbergStanford University, USANassif GhoussoubThe University of British Columbia, CanadaTony GuttmannUniversity of Melbourne, AustraliaLe Minh HaVietnam N<strong>at</strong>ional University, VietnamShi JinShanghai Jiao Tong University, China andUniversity of Wisconsin-Madison, USAAlejandro JofréUniversity of Chile, ChileYujiro Kawam<strong>at</strong>aThe University of Tokyo, JapanJong HaeKeumKorea Institute for Advanced Study, KoreaDoug LindUniversity of Washington, USAKyewonKoh ParkAjou University, KoreaShige PengShandong University, ChinaJose SeadeUniversidad Nacional Autónoma de México,MéxicoGang TianPrinceton University and Peking University,USA/ChinaT<strong>at</strong>iana ToroUniversity of Washington, USALocal Organizing Committee <strong>at</strong> SJTUShi Jin (Chair)David CaiDong HanJianguo HuangHongze LiYachun LiLihe WangWeike WangYa-Guang WangYaokun WuDongmei XiaoPu ZhangXiao-Dong ZhangXiaoqun ZhangLocal Advisory CommitteeKungching Chang, Peking UniversityWeinan E, Princeton University and PekingUniversityLei Guo, Chinese Academy of SciencesJiaxing Hong, Fudan UniversityPeiwen Ji, N<strong>at</strong>ional N<strong>at</strong>ural ScienceFound<strong>at</strong>ion of ChinaT<strong>at</strong>sien Li, Fudan UniversityYiming Long, Nankai UniversityZhongci Shi, Chinese Academy of SciencesJie Wang, N<strong>at</strong>ional N<strong>at</strong>ural ScienceFound<strong>at</strong>ion of ChinaJie Zhang, Shanghai Jiao Tong UniversityPublic LecturersRonald Graham, University of California, SanDiego, USACédric Villani, Université de Lyon and InstitutHenri Poincaré, France
4PRIMA 2013-Organiz<strong>at</strong>ionPlenary LecturersMartin Barlow, University of British Columbia,CanadaAndrea Bertozzi, University of California, LosAngeles, USAWeinan E, Princeton University, USA andPeking University, ChinaJun-Muk Hwang, Korea Institute for AdvancedStudy, KoreaVaughan Jones, University of California,Berkeley, USAZhi-Ming Ma, Chinese Academy of Sciences,ChinaM<strong>at</strong>ilde Marcolli, California Institute ofTechnology, USAArun Ram, University of Melbourne, AustraliaYongbin Ruan, University of Michigan, USAShuji Saito, Tokyo Institute of Technology,JapanWeiping Zhang, Nankai University, ChinaSpecial Sessions & Organizers1. A Glimpse of Stochastic DynamicsJinqiao Duan (University of California, LosAngeles & Illinois Institute of Technology,USA)Hongjun Gao (Nanjing Normal University,China)2. Algebraic and Complex GeometryYujiro Kawam<strong>at</strong>a (The University of Tokyo,Japan)JongHaeKeum (Korea Institute for AdvancedStudy, Korea)3. Algebraic Topology and Rel<strong>at</strong>ed TopicsAlejandro Adem (The University of BritishColumbia, Canada)Alan Jon<strong>at</strong>han Berrick (N<strong>at</strong>ional University ofSingapore, Singapore)Craig Westerland (University of Melbourne,Australia)4. Applic<strong>at</strong>ions of Harmonic Maps andSubmanifold TheoryYuxin Dong (Fudan University, China)Martin A. Guest (Waseda University, Japan)Wei Zhang (University of Science andTechnology of China, China)5. Combin<strong>at</strong>orics and Discrete M<strong>at</strong>hem<strong>at</strong>icsAndreas Dress (Chinese Academy of Sciences,China)Jing Huang (University of Victoria, Canada)Yaokun Wu (Shanghai Jiao Tong University,China)6. Geometric AnalysisJie Qing (University of California, Santa Cruz,USA)Gang Tian (Princeton University and PekingUniversity, USA/China)Xiaohua Zhu (Peking University, China)7. Geometric Aspects of Semilinear EllipticEqu<strong>at</strong>ions: Recent Advances & FuturePerspectivesNassif Ghoussoub (The University of BritishColumbia, Canada)Manuel del Pino (University of Chile, Chile)Juncheng Wei (The Chinese University ofHong Kong, Hong Kong)8. Hyperbolic Conserv<strong>at</strong>ion Laws and Rel<strong>at</strong>edApplic<strong>at</strong>ionsFeimin Huang (Chinese Academy of Sciences,China)Dehua Wang (University of Pittsburgh, USA)Ya-Guang Wang (Shanghai Jiao TongUniversity, China)9. Inverse ProblemsGuillaume Bal (Columbia University, USA)Jin Cheng (Fudan University, China)Gunther Uhlmann (University of Washington,USA)10. Kinetic Equ<strong>at</strong>ionsRadjesvarane Alexandre (Shanghai Jiao TongUniversity, China)Benoit Perthame (University of Pierre andMarie Curie, France)11. M<strong>at</strong>hem<strong>at</strong>ical Fluid Dynamics andRel<strong>at</strong>ed TopicsDongho Chae (Chung-Ang University, Korea)
5PRIMA 2013-Organiz<strong>at</strong>ionYoshikazu Giga (The University of Tokyo,Japan)Yasunori Maekawa (Kobe University, Japan)Tai-Peng Tsai (The University of BritishColumbia, Canada)12. M<strong>at</strong>hem<strong>at</strong>ics of String TheoryPeter Bouwknegt (Australian N<strong>at</strong>ionalUniversity, Australia)M<strong>at</strong>hai Varghese (The University of Adelaide,Australia)Siye Wu (Hong Kong University, Hong Kong)13. Measurable and Topological DynamicsAlejandro Maass (University of Chile, Chile)Hitoshi Nakada (Keio University, Japan)KyewonKoh Park (Ajou University, Korea)Xiangdong Ye (University of Science andTechnology of China, China)14. Multiscale Analysis and AlgorithmsWeinan E (Princeton University and PekingUniversity, USA/China)Carlos Garcia-Cervera (University of California,Santa Barbara, USA)Pingbing Ming (Chinese Academy of Sciences,China)15. Number Theory and Represent<strong>at</strong>ionTheoryClifton Cunningham (University of Calgary,Canada)Atsushi Ichino (Kyoto University, Japan)Vinayak V<strong>at</strong>sal (The University of BritishColumbia, Canada)16. Oper<strong>at</strong>or Algebras and Harmonic AnalysisAnthony Lau (University of Alberta, Canada)Zhong-Jin Ruan (University of Illinois <strong>at</strong>Urbana-Champaign, USA)17. Optimiz<strong>at</strong>ionRegina Burachik (University of South Australia,Australia)Xiaojun Chen (Hong Kong PolytechnicUniversity, Hong Kong)Alejandro Jofré (Center for M<strong>at</strong>hem<strong>at</strong>icalModeling, Chile)Hector Ramirez (Center for M<strong>at</strong>hem<strong>at</strong>icalModeling, Chile)18. ProbabilityShige Peng (Shandong University, China)Martin Barlow (The University of BritishColumbia, Canada)19. Represent<strong>at</strong>ion Theory andC<strong>at</strong>egorific<strong>at</strong>ionXuhua He (Hong Kong University of Scienceand Technology, Hong Kong)Joel Kamnitzer (University of Toronto,Canada)Tony Lic<strong>at</strong>a (Australian N<strong>at</strong>ional University,Australia)James Parkinson (University of Sydney,Australia)Arun Ram (University of Melbourne,Australia)20. Singularities in Geometry and TopologyGuangfeng Jiang (Peking University ofChemical Technology, China)Laurentiu Maxim (University ofWisconsin-Madison, USA)Mutsuo Oka (Tokyo University of Science,Japan)Jose Seade (Universidad NacionalAutonomade Mexico, Mexico)21. Symplectic Geometry and HamiltonianDynamicsYakovEliashberg (Stanford University, USA)Yiming Long (Nankai University, China)22. Symplectic Geometry and M<strong>at</strong>hem<strong>at</strong>icalPhysicsXiaobo Liu (University of Notre Dame andPeking University, USA/China)Huijun Fan (Peking University, China)23. Triangul<strong>at</strong>ed C<strong>at</strong>egories inRepresent<strong>at</strong>ion Theory of AlgebrasRagnar-Olaf Buchweitz (University of Toronto,Canada)Shiping Liu (University of Sherbrook, Canada)Claus Michael Ringel (Universitaet Bielefeld,Germany)Pu Zhang (Shanghai Jiao Tong University,China)
6PRIMA 2013-SponsorsFunding Agencies and SponsorsPRIMA and the organizing committee of the 2 nd PRIMA Congress wish to extend theirthanks and appreci<strong>at</strong>ion to the following agencies for their supports to this congress.
7PRIMA 2013-Useful Inform<strong>at</strong>ionUseful Inform<strong>at</strong>ionCongress VenuesOpening Ceremony /Public & Plenary Lectures, Wen Zhi Hall, SJTU Xuhui CampusSpecial Sessions & Contributed Talks, Engineering Hall, SJTU Xuhui CampusAddress: No. 1954, Hua Shan Road, Xuhui District, Shanghai, China( 上 海 交 通 大 学 徐 汇 校 区 地 址 : 上 海 市 徐 汇 区 华 山 路 1954 号 )The Second PRIMA Congress will be convened <strong>at</strong> the Xuhui Campus of Shanghai Jiao TongUniversity. SJTU, one of the top universities of China, boasts a long history of more than 117years. Xuhui Campus is loc<strong>at</strong>ed in Xujiahui, a shopping paradise and gourmet destin<strong>at</strong>ion. Thereare many large department stores within walking distance, such as Grand G<strong>at</strong>eway, OrientalDepartment Store, Pacific Plaza, Metro City and Huijin Department Store, etc. There are alsosome ancient buildings nearby, and many gre<strong>at</strong> cafes and restaurants are loc<strong>at</strong>ed in theneighborhood.Shanghai, as the largest city in China, has many tourist <strong>at</strong>tractions, such as the Bund, OrientalPearl Tower, Yu Garden, Chenghuang Temple and Longhua Temple etc.HotelHUA TING HOTEL & TOWERS ( 华 亭 宾 馆 )1200 North Cao Xi Road, Shanghai, China ( 上 海 市 徐 汇 区 漕 溪 北 路 1200 号 )Telephone: +8621 64391000Fax: +8621 6481 2070Hotel website: http://www.hu<strong>at</strong>ing.jinjianghotels.comTransport<strong>at</strong>ion Directions From Shanghai Pudong Airport (PVG) to the Xuhui Campus of SJTUMetro: Take Metro Line 2 to East Nanjing Road St<strong>at</strong>ion, then transfer to Metro Line 10 toShanghai Jiao Tong University St<strong>at</strong>ion; after th<strong>at</strong>, walk for around 10 minutes thenyou can arrive <strong>at</strong> the Xuhui Campus. The whole journey is around 47km and maytake you about 1 hour.Taxi: The whole journey is around 47km, which will take you around 35 minutes with 150Yuan.If you want to go directly from Pudong Airport to the Congress Venue, please givethe following message to the taxi driver:--- 请 载 我 到 徐 汇 区 华 山 路 1954 号 上 海 交 通 大 学 ( 近 广 元 西 路 )。---Please take me to No. 1954, Hua Shan Road, Xuhui District, SJTU Xuhui Campus. From Shanghai Hongqiao Airport (SHA) to SJTU Xuhui CampusMetro: Take Metro Line 10 to Shanghai Jiao Tong University St<strong>at</strong>ion; after th<strong>at</strong>, walk for
8PRIMA 2013-Useful Inform<strong>at</strong>ionTaxi:around 10 minutes then you can arrive <strong>at</strong> the Xuhui Campus. The whole journey isaround 10 km and may take you about 40 minutes.The whole journey is around 12 km, which will take you around 30 minuteswith 50 Yuan.If you want to go directly from Hongqiao Airport to the Congress Venue, please givethe following message to the taxi driver:--- 请 载 我 到 徐 汇 区 华 山 路 1954 号 上 海 交 通 大 学 。---Please take me to No. 1954, Hua Shan Road, Xuhui District, SJTU Xuhui Campus. From Shanghai Railway St<strong>at</strong>ion to the Xuhui Campus of SJTUMetro: Take Metro Line 1 to Xujiahui St<strong>at</strong>ion; after th<strong>at</strong>, walk north along Huashan Road foraround 10 minutes then you can arrive <strong>at</strong> the Xuhui Campus. The whole journey isaround 10 km and may take you about 30 minutes.Taxi: The whole journey is around 10 km, which will take you around 30 minutes with 50Yuan. From Hongqiao Railway St<strong>at</strong>ion to the Xuhui Campus of SJTUMetro: Take Metro Line 10 to Shanghai Jiao Tong University St<strong>at</strong>ion; after th<strong>at</strong>, walk foraround 10 minutes then you can arrive <strong>at</strong> Xuhui Campus. The whole journey is around10 km and may take you about 40 minutes.Taxi: The whole journey is around 12 km, which will take you around 30 minutes with 50Yuan. From Pudong Intern<strong>at</strong>ional Airport (PVG) to Hua Ting Hotel & TowersMetro: 1. Take Metro Line 2 to People Square St<strong>at</strong>ion and change to Metro Line 1 and get off<strong>at</strong> Shanghai Indoor Stadium and get out from Exit 7. 2. Take the Metro Line 2 andchange to Metro Line 4 <strong>at</strong> the Century Avenue St<strong>at</strong>ion, and take Metro Line 4 headingfor Xinzhuang and get off <strong>at</strong> Shanghai Indoor Stadium St<strong>at</strong>ion and get out from Exit 7.Bus: Take Airport Bus No. 7 and arrive <strong>at</strong> South Shanghai Railway St<strong>at</strong>ion and change toMetro Line 1 and get off <strong>at</strong> Shanghai Indoor Stadium St<strong>at</strong>ion, and get out from Exit 7.Taxi: Take taxi for about 50 minutes. Normal taxi charge is about RMB ¥ 175, plus 30% nightextra charge after 11:00 PM.If you want to go directly from Pudong Airport to the Hotel, please give the followingmessage to the taxi driver:--- 请 载 我 到 徐 汇 区 徐 汇 区 漕 溪 北 路 1200 号 华 亭 宾 馆 。宾 馆 前 台 电 话 :6439 1000--- Please take me to 1200 North Cao Xi Road, Hua Ting Hotel & Towers.Reception phone: 6439 1000 From Hongqiao Airport (SHA) to Hua Ting Hotel & TowersMetro: Take Metro Line 2 to People Square St<strong>at</strong>ion and change to Metro Line 1 and get off <strong>at</strong>Shanghai Indoor Stadium St<strong>at</strong>ion and get out from Exit 7.Bus: Take Airport Bus No. 938. Get in the bus <strong>at</strong> Hongqiao Airport St<strong>at</strong>ion and get off <strong>at</strong> thecross of Western Zhongshan Road and North Caoxi Road.
9PRIMA 2013-Useful Inform<strong>at</strong>ionTaxi:Normal taxi charge is about 60 RMB, plus 30% night extra charge if after 11:00 PM.If you want to go directly from Hongqiao Airport to the Hotel, please give thefollowing message to the taxi driver:--- 请 载 我 到 徐 汇 区 徐 汇 区 漕 溪 北 路 1200 号 华 亭 宾 馆 。宾 馆 前 台 电 话 :6439 1000---Please take me to 1200 North Cao Xi Road, Hua Ting Hotel & Towers. Receptionphone: 6439 1000Way-finding & Shuttle Bus <strong>at</strong> AirportsThe 2 nd PRIMA local organizing committee has arranged shuttle bus to bring the <strong>at</strong>tendees to theHua Ting Hotel & Towers on June 23. The shuttle bus will be available during 9:00-21:00 inPudong Airport (PVG), and it will leave PVG for Hua Ting Hotel & Towers every three hours (seethe below form for more details); the shuttle bus will be available during 12:00-20:00 inHongqiao Airport (SHA) and it will leave SHA for Hua Ting Hotel & Towers every two hours (seethe below form for more details). The <strong>at</strong>tendees may choose to take public transport<strong>at</strong>ions ortake the shuttle bus based on their own arrival time and needs. Volunteers will be in both PVGand SHA to guide the <strong>at</strong>tendees to the shuttle bus or help the <strong>at</strong>tendees to find the taxi or themetro st<strong>at</strong>ion. The volunteers will wear orange T-shirts with PRIMA and SJTU logos.Shuttle Bus <strong>at</strong> Airports ( June 23, Sunday)Airport 1 st 2 nd 3 rd 4 th 5 thPVG 9:00 12:00 15:00 18:00 21:00SHA 12:00 14:00 16:00 18:00 20:00Congress BusThere will be buses to pick up the <strong>at</strong>tendees <strong>at</strong> Hua Ting Hotel & Towers and send them to thecongress venue (the Xuhui Campus of SJTU) every morning from June 24 to June 28.Since there will be the congress banquet on Monday (June 24) evening so th<strong>at</strong> congress buseswill bring the <strong>at</strong>tendees back from SJTU Xuhui Campus to the Hua Ting Hotel & Towers. However,in the l<strong>at</strong>er days (June 25-June 28) there will be no buses to bring the <strong>at</strong>tendees back to the hotelafter the meeting and they need to go back to the hotel by themselves.
10PRIMA 2013-Useful Inform<strong>at</strong>ionCongress Bus <strong>Schedule</strong>D<strong>at</strong>eDepartureTimeFromTo2013.06.248:00-8:30 Hua Ting Hotel & Towers SJTU Xuhui Campus17:45 SJTU Xuhui Campus Banquet2013.06.25 7:30-8:00 Hua Ting Hotel & Towers SJTU Xuhui Campus2013.06.26 7:30-8:00 Hua Ting Hotel & Towers SJTU Xuhui Campus2013.06.27 7:30-8:00 Hua Ting Hotel & Towers SJTU Xuhui CampusDining2013.06.28 7:30-8:00 Hua Ting Hotel & Towers SJTU Xuhui CampusLunch on Campus1/F, 2/F, University Canteen (Xuhui Campus). The <strong>at</strong>tendees can buy Lunch Tickets from theregistr<strong>at</strong>ion desk.Off-campus DiningOutside the campus is the center of the Xuhui District, which is a certified food paradise. Thestreet outside of the g<strong>at</strong>e <strong>at</strong> Panyu Road is lined with small e<strong>at</strong>eries offering traditionalShanghainese food and Yunnan rice noodle. Be ready to pay <strong>at</strong> least 25 yuan for a decent meal.Further down the road is a Sihaiyoulong ( 四 海 游 龙 ), a Taiwanese Fried Dumpling chainrestaurant, where meals cost 30 yuan or so. By the g<strong>at</strong>e <strong>at</strong> West Guang Yuan Road are variouschain restaurants such as Yonghe King, Sukiya, etc.. Be ready to shell out 15 to 25 yuan per meal.The Hunan and Northeastern restaurants on Panyu Road are good choices for get-togethers withfriends and for a taste of Chinese food. Average expenditure per person is 40 to 60 yuan(excluding alcoholic drinks). You can also consider Ajisen Ramen on Huashan Road (40 yuan perperson), sushi-go-round restaurant Sushi Express in MetroCity (6 yuan per pl<strong>at</strong>e), and Pizza Hutin MetroCity. If you are feeling a little ritzy, try Charme and South Memory. Your taste buds aresure to be s<strong>at</strong>isfied, but be prepared to get out th<strong>at</strong> hundred-yuan bill!Standard Audio/Visual Set-up in Meeting RoomsAll meeting rooms for PRIMA 2013 will be equipped with one computer, one blackboard, andone overhead projector.Speakers should load their talks to the computer before their speaking sessions.Internet AccessWireless internet access is available in all meeting rooms.The user names are: m<strong>at</strong>h1; m<strong>at</strong>h2; m<strong>at</strong>h3; m<strong>at</strong>h4; m<strong>at</strong>h5; m<strong>at</strong>h6; m<strong>at</strong>h7; m<strong>at</strong>h8; m<strong>at</strong>h9;
11PRIMA 2013-Useful Inform<strong>at</strong>ionm<strong>at</strong>h10The password is: PLMN3148Attendees staying <strong>at</strong> the hotel will be able to use the cable line to access to the internet or beprovided with a password upon check-in for using the wireless connection.Registr<strong>at</strong>ion Fee Includes Printed scientific program Welcome reception Coffee breaks dailyGet-togethers Welcome reception <strong>at</strong> the Hua Ting Hotel & TowersSunday, June 2318:00-19:30 Banquet (self-paid) <strong>at</strong> the Hua Ting Hotel & TowersMonday, June 2418:00-20:00Book DisplaySix publishing houses will be present in the Second PRIMA Congress, and they are: OxfordUniversity Press, Science Press, Springer, Advances in M<strong>at</strong>hem<strong>at</strong>ics (China), Acta M<strong>at</strong>hem<strong>at</strong>icaSinica, and Higher Educ<strong>at</strong>ion Press. A large variety of books in m<strong>at</strong>hem<strong>at</strong>ical science will be ondisplay.Medical ServiceThe University Campus Hospital will provide medical service to the congress <strong>at</strong>tendees duringJune 24-28.Special Medical Service Room for PRIMA: Room 105, Campus Hospital, 8:30-17:30, June 24-28Emergency Call: 13788942692 (Mr. Liu)If the <strong>at</strong>tendees need medical assistance in any other time or need emergency service, directlydial the n<strong>at</strong>ional ambulance number: 120Please NotePRIMA 2013 is not responsible for the safety and security of <strong>at</strong>tendees’ computers. Do not leaveyour laptop computers un<strong>at</strong>tended. Please remember to turn off your cell phones during alltalks.
12PRIMA 2013-Useful Inform<strong>at</strong>ionRecording of Present<strong>at</strong>ionsAudio and video recording of present<strong>at</strong>ions <strong>at</strong> PRIMA 2013 meetings is prohibited without thewritten permission of the presenter and PRIMA.Useful Links• Shanghai Jiao Tong Universityhttp://en.sjtu.edu.cn/• Department of M<strong>at</strong>hem<strong>at</strong>ics, SJTUhttp://www.m<strong>at</strong>h.sjtu.edu.cn/• PRIMA 2013 Websitehttp://meeting.healife.com/prima2013• Institute of N<strong>at</strong>ural Sciences, SJTUhttp://ins.sjtu.edu.cn/• Pacific Rim M<strong>at</strong>hem<strong>at</strong>ical Associ<strong>at</strong>ionhttp://www.m<strong>at</strong>h.sjtu.edu.cn/Conference/prima/index.htm• Shanghai Todayhttp://www.shanghai-today.com/• Shanghai Airlinehttp://en.ceair.com/
13PRIMA 2013 Program-<strong>Schedule</strong>-<strong>at</strong>-a-<strong>Glance</strong><strong>Schedule</strong>-<strong>at</strong>-a-<strong>Glance</strong><strong>Schedule</strong>-<strong>at</strong>-a-<strong>Glance</strong>On-site Registr<strong>at</strong>ion:Sunday, June 23 13:00-21:00, Hua Ting Hotel & Towers (1/F)Monday-Friday (June 24-28), 8:00-16:30, Room 114, Engineering Hall, SJTU Xuhui CampusCongress Venues:Opening Ceremony /Public & Plenary Lectures, Wen Zhi Hall, SJTU Xuhui CampusSpecial Sessions & Contributed Talks, Engineering Hall, SJTU Xuhui CampusTimeSundayJune 23MondayJune 24TuesdayJune 25WednesdayJune 26ThursdayJune 27FridayJune 288:309:00-9:30OpeningCeremonyPlenary LectureYongbin RuanPublic LectureRonald GrahamPlenary LectureMartin BarlowPlenary LectureVaughan Jones9:30-Public LecturePlenary LecturePlenary LecturePlenary LecturePlenary Lecture10:20Cédric VillaniShuji SaitoWeinan EArun RamM<strong>at</strong>lide Marcolli10:30-11:00Coffee Break11:00-Plenary LecturePlenary LecturePlenary LecturePlenary LectureSpecial Sessions &11:50Zhi-Ming MaAndrea BertozziWeiping ZhangJun-Muk HwangContributed Talks12:00-14:00Lunch14:00-16:00Special Sessions & Contributed TalksSpecial Sessions & Contributed Talks16:00-16:30Registr<strong>at</strong>ionCoffee BreakFree AfternoonCoffee Break16:30-17:30Special Sessions & Contributed TalksSpecial Sessions& ContributedTalks18:00-19:30WelcomeReceptionBanquetWelcome Reception: Sunday, June 23, 18:00-19:30, Hua Ting Hotel & TowersBanquet: Monday, June 24, 18:00-20:00, Hua Ting Hotel & TowersLunch: University Canteen/Faculty Club
14PRIMA 2013 Program-Monday, June 24Monday, June 24Morning Lectures: <strong>at</strong> Wen Zhi Hall9:00-9:30Opening Ceremony9:30-10:20Public Lecture, Cédric Villani, Université deLyon and Institut Henri Poincaré, FranceOf Triangles, Gas, Prices and MenChair: Jie Zhang, Shanghai Jiao Tong University,China10:30-11:00Coffee BreakXu Sun, Huazhong University of Science andTechnology, ChinaFokker-Planck Equ<strong>at</strong>ions for NonlinearDynamical Systems Driven by Non-GaussianLévy Processes15:00-15:30Huijie Qiao, Southeast University, ChinaSome Results for Discontinuous RandomDynamical Systems15:30-16:00Jinqiao Duan, Institute for Pure and AppliedM<strong>at</strong>hem<strong>at</strong>ics, USAPerspectives in Stochastic Dynamics—Modeling,Analysis and Comput<strong>at</strong>ion11:00-11:50Plenary Lecture, Zhi-Ming Ma, Academy ofM<strong>at</strong>hem<strong>at</strong>ics and Systems Science, CAS, ChinaWeb Markov Skeleton Processes and TheirApplic<strong>at</strong>ionsChair: Alejandro Adem, University of BritishColumbia, Canada12:00-14:00LunchVenue: University CanteenAfternoon sessions: <strong>at</strong>Engineering Hall14:00-16:00Session 1: A Glimpse of Stochastic Dynamics(Room: 208)Organizers: Jinqiao Duan, Hongjun Gao14:00-14:30Samuel Kou, Harvard University, USAFast Analysis of Dynamic Systems via GaussianEmul<strong>at</strong>or14:30-15:00Session 2: Algebraic and Complex Geometry(Room: 207)Organizers: Yujiro Kawam<strong>at</strong>a, JongHae Keum14:00-14:50Jun Li, Stanford University, USAC<strong>at</strong>egorific<strong>at</strong>ion of Donaldson-ThomasInvariants and Gopakumar-Vafa Invariants15:00-15:50Colin Ingalls, University of New Brunswick,CanadaDivision Algebras of Transcendence DegreeTwoSession 3: Algebraic Topology and Rel<strong>at</strong>edTopics (Room: 229)Organizers: Alejandro Adem, Alan Jon<strong>at</strong>hanBerrick, Craig Westerland14:00-14:30Vigleik Angeltveit, Australian N<strong>at</strong>ionalUniversity, AustraliaThe Topological Hochschild Homology of ThomSpectra as Cyclotomic Spectra14:30-15:00Ryan Budney, University of Victoria, CanadaUniversal Constructions on Spaces of Knots
15PRIMA 2013 Program-Monday, June 2415:00-15:30Haibao Duan, Institute of M<strong>at</strong>hem<strong>at</strong>ics, ChineseAcademy of Sciences, ChinaCircle Actions on 5-ManifoldsSession 4: Applic<strong>at</strong>ions of Harmonic Maps andSubmanifold Theory (Room: 224)Organizers: Yuxin Dong, Martin A. Guest, WeiZhang14:00-14:40Reiko Miyaoka, Tohoku University, JapanTBA14:45-15:25Peng Wang, Tongji University, ChinaWillmore Surfaces by Using Geometric Methodsand Loop Group Theory15:30-16:10Erxiao Wang, Hong Kong University ofScience and Technology, ChinaDefinite Affine Spheres by the DPW MethodSession 5: Combin<strong>at</strong>orics and DiscreteM<strong>at</strong>hem<strong>at</strong>ics (Room: 202)Organizers: Andreas Dress, Jing Huang,Yaokun Wu14:00-14:30Pavol Hell , Simon Fraser University, CanadaM<strong>at</strong>rix Partitions14:30-15:00Jan Kr<strong>at</strong>ochvil, Charles University in Prague,Czech RepublicGeometric Represent<strong>at</strong>ions of Graphs15:00-15:30Moshe Rosenfeld, University of Washington,Tacoma, USAHamiltonian Cycles in Prisms15:30-16:00Jack Koolen, University of Science andTechnology of China, China and PohangUniversity of Science and Technology, KoreaOn m-Walk-regular Graphs, a Generaliz<strong>at</strong>ion ofDistance-regular GraphsSession 6: Geometric Analysis (Room: 226)Organizers: Jie Qing, Gang Tian, Xiaohua Zhu14:00-14:30Albert Chau, The University of BritishColumbia, CanadaTBA14:30-15:00Yalong Shi, Nanjing University, ChinaBergman Kernel of a Polarized Kähler ALEManifold15:00-15:30Yuji Odaka, Kyoto University, JapanK-stability of Fano Varieties and AlphaInvariant15:30-16:00Xi Zhang, University of Science andTechnology of China, ChinaThe Limit of the Yang-Mills-Higgs Flow onSemi-stable Higgs BundlesSession 7: Geometric Aspects of SemilinearElliptic Equ<strong>at</strong>ions: Recent Advances & FuturePerspectives (Room: 218)Organizers: Nassif Ghoussoub, Manuel delPino,Juncheng Wei14:00-14:30Fang-Hua Lin, Courant Institute, NYU, USATBA14:30-15:00Zhi-Qiang Wang, Nankai University, China andUtah St<strong>at</strong>e University, USASynchronized and Segreg<strong>at</strong>ed Solutions forCoupled Nonlinear Schrödinger Equ<strong>at</strong>ions15:00-15:30J.-M. Roquejoffre, University Toulouse, FranceTBA15:30-16:00Daomin Cao, Chinese Academy of Sciences,ChinaRegulariz<strong>at</strong>ion of Point Vortex Solution forEuler Equ<strong>at</strong>ion
16PRIMA 2013 Program-Monday, June 24Session 8: Hyperbolic Conserv<strong>at</strong>ion Laws andRel<strong>at</strong>ed Applic<strong>at</strong>ions (Room: 100)Organizers: Feimin Huang, Dehua Wang,Ya-Guang Wang14:00-14:30Alberto Bressan, Pennsylvania St<strong>at</strong>e University,USASome Counterexamples in the Theory ofConserv<strong>at</strong>ion Laws14:30-15:00Shuxing Chen, Fudan University, ChinaNonlinear Mixed Type Equ<strong>at</strong>ions Arisen inMach Reflection15:00-15:30John K. Hunter, University of California <strong>at</strong>Davis, USANormal Forms and a Burgers-Hilbert Equ<strong>at</strong>ion15:30-16:00Eun Heui Kim, California St<strong>at</strong>e UniversityLong Beach, USAGlobal Solutions for Transonic Self-similarTwo-dimensional Riemann ProblemsSession 10: Kinetic Equ<strong>at</strong>ions (Room: 220)Organizers: Radjesvarane Alexandre, BenoitPerthame14:00-14:30Kazuo Aoki, Kyoto University, JapanTBA14:30-15:00Nicolas Vauchelet, University of Pierre andMarie Curie, FranceKinetic Description of Bacterial Motion byChemotaxis and Asymptotics15:00-15:30Xuguang Lu, Tsinghua University, ChinaCondens<strong>at</strong>ion and Regularity for BosonBoltzmann Equ<strong>at</strong>ion15:30-16:00Peter Markowich, King Abdullah University ofScience and Technology, Kingdom of SaudiArabiaHamiltonian Propag<strong>at</strong>ion of Mono-kineticMeasures with Rough Initial ProfilesSession 11: M<strong>at</strong>hem<strong>at</strong>ical Fluid Dynamics andRel<strong>at</strong>ed Topics (Room: 228)Organizers: Dongho Chae, Yoshikazu Giga,Yasunori Maekawa Tai-Peng Tsai14:00-14:50Chun Liu, Pennsylvania St<strong>at</strong>e University, USASome New Advances on Modeling andAlgorithms Development of Multiphase ComplexFluid System Using the Phase Field Method15:00-15:50Maria Schonbek, University of California,Santa Cruz, USAAsymptotic Stability of Mild Solutions to theNavier-Stokes Equ<strong>at</strong>ionsSession 12: M<strong>at</strong>hem<strong>at</strong>ics of String Theory(Room: 234)Organizers: Peter Bouwknegt, M<strong>at</strong>hai Varghese,Siye Wu14:00-15:00Ugo Bruzzo, Intern<strong>at</strong>ional School for AdvancedStudies (SISSA), ItalyStacky Resolutions of the Moduli Spaces ofInstantons on ALE Spaces15:00-15:30Jarah Evslin, Institute of High Energy Physics,CAS, ChinaTopology Change from Heterotic NarainT-Duality15:30-16:00Hisham S<strong>at</strong>i , University of Pittsburgh, USAM-branes and Higher BundlesSession 13: Measurable and TopologicalDynamics (Room: 104)Organizers: Alejandro Maass, Hitoshi Nakada,KyewonKoh Park, Xiangdong Ye14:00-14:30Anthony Dooley, University of B<strong>at</strong>h, UKRandom Dynamical Systems14:30-15:00Mas<strong>at</strong>o Tsujii, Kyushu University, JapanThe Semi-classical Zeta Function for ContactAnosov Flow
17PRIMA 2013 Program-Monday, June 2415:00-15:30Uijin Jung, Ajou University, KoreaDecomposition Problems in Symbolic Dynamics15:30-16:00Song Shao, University of Science andTechnology of China, ChinaHigher Order Bohr Problem and Rel<strong>at</strong>ed TopicsSession 15: Number Theory andRepresent<strong>at</strong>ion Theory (Room: 105)Organizers: Clifton Cunningham, AtsushiIchino, Vinayak V<strong>at</strong>sal14:00-14:30Noriyuki Abe, Hokkaido University, JapanOn a Classific<strong>at</strong>ion of Irreducible Modulo pRepresent<strong>at</strong>ions of p-adic Groups14:30-15:00Pramod N. Achar, Louisiana St<strong>at</strong>e University,USAParity Sheaves on the Affine Grassmannian andthe Mirkovic-Vilonen Conjecture15:00-15:30Julia Gordon, University of British Columbia,CanadaUniform in p Estim<strong>at</strong>es for Orbital Integrals15:30-16:00Masoud Kamgarpour, University ofQueensland, AustraliaOn the Center of Lie AlgebrasSession 16: Oper<strong>at</strong>or Algebras and HarmonicAnalysis (Room: 106)Organizers: Anthony Lau, Zhong-Jin Ruan14:00-14:30Liming Ge, University of New Hampshire, USAUncertainty Principles for Infinite AbelianGroups14:30-15:00Narutaka Ozawa, Kyoto University, JapanQuantum Correl<strong>at</strong>ions and Tsirelson's Problem15:00-15:30Chunlan Jiang, Hebei Normal University,ChinaComplex Geometry and Similarity ofCowen-Douglas Oper<strong>at</strong>ors15:30-16:00Zhiguo Hu, University of Windsor, CanadaConvolution Algebras Associ<strong>at</strong>ed with LocallyCompact Quantum GroupsSession 17: Optimiz<strong>at</strong>ion (Room: 110)Organizers: Regina Burachik, Xiaojun Chen,Alejandro Jofré, Hector Ramirez14:00-14:40Xiaojun Chen, The Hong Kong PolytechnicUniversity, Hong Kong, ChinaExpected Residual Minimiz<strong>at</strong>ion for StochasticVari<strong>at</strong>ional Inequalities14:40-15:20Gui-Hua Lin, Shanghai University, ChinaSolving M<strong>at</strong>hem<strong>at</strong>ical Programs withEquilibrium Constraints as ConstrainedEqu<strong>at</strong>ions15:20-16:00Rafael Correa, Universidad de Chile, ChileExistence of Minimizers on DropsSession 18: Probability (Room: 103)Organizers: Shige Peng, Martin Barlow14:00-14:30Xin Guo, University of California, Berkeley,USAMartingale Problem under Non-linearExpect<strong>at</strong>ions14:30-15:00Rainer Buckdahn, Université de BretagneOccidentale, FranceTBA15:00-15:30Feng-Yu Wang, Beijing Normal University,ChinaBismut Formula and Gradient Estim<strong>at</strong>es forSDEs Driven by Multiplic<strong>at</strong>ive Levy Noise15:30-16:00Louis Chen, N<strong>at</strong>ional University of Singapore,SingaporeMultivari<strong>at</strong>e Normal Approxim<strong>at</strong>ion by Stein's
18PRIMA 2013 Program-Monday, June 24Method: The Concentr<strong>at</strong>ion Inequality ApproachSession 19: Represent<strong>at</strong>ion Theory andC<strong>at</strong>egorific<strong>at</strong>ion (Room:107)Organizers: Xuhua He, Joel Kamnitzer, TonyLic<strong>at</strong>a, James Parkinson, Arun Ram14:00-15:00Anthony Henderson, University of Sydney,AustraliaThe Modular Generalized SpringerCorrespondence15:00-15:30Haibao Duan, Institute of M<strong>at</strong>hem<strong>at</strong>ics, ChineseAcademy of Sciences, ChinaSchubert Calculus and Cohomology of LieGroups15:30-16:00Hiroyuki Ochiai, Kyushu University, JapanOn Orbits in Double Flag Varieties forSymmetric PairsSession 21: Symplectic Geometry andHamiltonian Dynamics (Room: 216)Organizers: Yakov Eliashberg, Yiming Long14:00-14:50Yongbin Ruan, University of Michigan, AnnArbor, USAWitten Equ<strong>at</strong>ion and the Geometry of LG-model15:00-15:50Sheila Sandon, Université de Nantes, FranceTransl<strong>at</strong>ed Points and Contact Rigidity15:25-15:55Osamu Iyama, Nagoya University, JapanGeigle-Lenzing Spaces and Canonical Algebrasin Dimension d (II)Contributed Talks Group 3: DiscreteM<strong>at</strong>hem<strong>at</strong>ics (Room: 219)Chair: Eiichi Bannai, Shanghai Jiao TongUniversity, China14:00-14:20Xiao-Dong Zhang, Shanghai Jiao TongUniversity, ChinaThe Number of Subtrees of a Tree14:20-14:40Jiyou Li, Shanghai Jiao Tong University, ChinaThe Subsets Counting Problems and TheirApplic<strong>at</strong>ions14:40-15:00Liangxia Wan, Beijing Jiaotong University,ChinaUnimodality of Genus Distribution of Ladders15:00-15:20Lemin Gu, Tongji University, ChinaGeneraliz<strong>at</strong>ion of Legendre Polynomials Theory15:20-15:40Peng Li, Shanghai Jiao Tong University, ChinaP<strong>at</strong>hs and Cycles of Interval Graphs15:40-16:00Ziqing Xiang, Shanghai Jiao Tong University,ChinaThe Lit-onlyσ-GameSession 23: Triangul<strong>at</strong>ed C<strong>at</strong>egories inRepresent<strong>at</strong>ion Theory of Algebras (Room: 214)Organizers: Ragnar-Olaf Buchweitz , ShipingLiu, Claus Michael Ringel, Pu Zhang14:00-14:45Idun Reiten, Norwegian University of Scienceand Technology, NorwayTriangul<strong>at</strong>ed C<strong>at</strong>egories and Tau-tilting Theory14:50 -15:20Martin Herschend, Nagoya University, JapanGeigle-Lenzing Spaces and Canonical Algebrasin Dimension d (I)Contributed Talks Group 4: Comput<strong>at</strong>ionalM<strong>at</strong>hem<strong>at</strong>ics & Optimiz<strong>at</strong>ion (Room: 221)Chair: Wenjun Ying, Shanghai Jiao TongUniversity, China14:00-14:20Jianguo Huang, Shanghai Jiao Tong University,ChinaAn Uzawa Method for Solving SteadyNavier-Stokes Equ<strong>at</strong>ions Discretized by MixedElement Methods14:20-14:40Qin Li, University of Wisconsin-Madison, USA
19PRIMA 2013 Program-Monday, June 24Semi-classical Limit for the SchroedingerEqu<strong>at</strong>ion with L<strong>at</strong>tice Potential, andBand-crossing14:40-15:00AbdurRashid, Gomal University, PakistanLegendre Pseudospectral Method for SolvingThree-dimensional Non-Linear HyperbolicPartial Differential Equ<strong>at</strong>ions15:00-15:20Xingzhong Shi, Wenzhou-Kean University,ChinaM<strong>at</strong>h and Gaming15:20-15:40Congmin Wu, Xiamen University, ChinaMD Simul<strong>at</strong>ions for Motions of Evapor<strong>at</strong>iveDroplets Driven by Thermal Gradients15:40-16:00Hongyu Zhu, University of Texas <strong>at</strong> Austin,USAInversion of Geothermal He<strong>at</strong> Flux in aThermomechanically Coupled Stokes Ice SheetModelContributed Talks Group 6: Probability andSt<strong>at</strong>istics (Room: 222)Chair: Dong Han, Shanghai Jiao TongUniversity, China14:00-14:20Jielin Zhu, University of British Columbia,CanadaAsymptotic Analysis for Tipping Points Problems14:20-14:40Yanyan He, Florida St<strong>at</strong>e University, USAD<strong>at</strong>a Fusion Based on Evidence Theory14:40-15:00Xiang Zhou, City University of Hong Kong,Hong Kong, ChinaExplicit Cross Entropy Scheme for Mixture15:00-15:20Xiaoming Fan, Southwest Jiao Tong Universityand Beijing Normal University, ChinaEstim<strong>at</strong>es of Ito Integral and Applic<strong>at</strong>ions toRandom Dynamical Systems15:20-15:40Elena Karachanskaya, Pacific N<strong>at</strong>ionalUniversity, RussiaThe Generalized Ito-Wentzell Formula for Ito'sProcess and the Stochastic First Integral16:00-16:30Coffee Break16:30-17:30Session 1: A Glimpse of Stochastic Dynamics(Room: 208)Organizers: Jinqiao Duan, Hongjun Gao16:30-17:00Dong Zhao, Academy of M<strong>at</strong>hem<strong>at</strong>ics &Systems Science, CAS, ChinaMalliavin M<strong>at</strong>rix of Degener<strong>at</strong>e PDE andGradient Estim<strong>at</strong>es17:00-17:30Wei Wang, Nanjing University, ChinaSelf-similarity for Some SPDEsSession 2: Algebraic and Complex Geometry(Room: 207)Organizers: Yujiro Kawam<strong>at</strong>a, JongHae Keum16:30-17:20Amnon Neeman, The Australian N<strong>at</strong>ionalUniversity, AustraliaCompactsSession 3: Algebraic Topology and Rel<strong>at</strong>edTopics (Room: 229)Organizers: Alejandro Adem, Alan Jon<strong>at</strong>hanBerrick, Craig Westerland16:30-17:00Soren Gal<strong>at</strong>ius, Stanford University, USACohomology of Moduli Spaces of Manifolds17:00-17:30Daniel Juan Pineda, N<strong>at</strong>ional AutonomousUniversity of Mexico, MexicoBraid Groups of Surfaces and Their LowerAlgebraic K-theory
20PRIMA 2013 Program-Monday, June 24Session 4: Applic<strong>at</strong>ions of Harmonic Maps 17:00-17:30and Submanifold Theory (Room: 224)Masaharu Taniguchi, Okayama University,Organizers: Yuxin Dong, Martin A. Guest, Wei JapanZhangMulti-dimensional Traveling Fronts in Bistable16:40-17:20Reaction-diffusion Equ<strong>at</strong>ionsYoshihiro Ohnita, Osaka City University andOCAMI, JapanSession 8: Hyperbolic Conserv<strong>at</strong>ion Laws andGeometry of Lagrangian Submanifolds Rel<strong>at</strong>ed Rel<strong>at</strong>ed Applic<strong>at</strong>ions (Room: 100)to Isoparametric HypersurfacesOrganizers: Feimin Huang, Dehua Wang,Ya-Guang WangSession 5: Combin<strong>at</strong>orics and Discrete16:30-17:00M<strong>at</strong>hem<strong>at</strong>ics (Room: 202)Zhouping Xin, The Chinese University of HongOrganizers: Andreas Dress, Jing Huang,Kong, Hong Kong, ChinaYaokun WuOn the Existence of Meyer Type Transonic16:30-17:00Flows and a Degener<strong>at</strong>e Change Type Equ<strong>at</strong>ionBruce Reed, McGill University, Canada17:00-17:30The Structure of a Typical H-free GraphMikhail Feldman, University of17:00-17:30Wisconsin-Madison, USASang-il Oum, Korea Advanced Institute of Shock Reflection and Von Neumann ConjecturesScience and Technology, KoreaUnavoidable Vertex-minors in Large Prime Session 10: Kinetic Equ<strong>at</strong>ions (Room: 220)GraphsOrganizers: Radjesvarane Alexandre, BenoitPerthameSession 6: Geometric Analysis (Room: 226) 16:30-17:00Organizers: Jie Qing, Gang Tian, Xiaohua Zhu Benoit Perthame, University of Pierre and16:30-17:00Marie Curie and Institut Universitaire de France,Bing Wang, University of Wisconsin-Madison, FranceUSAScalar Conserv<strong>at</strong>ion Laws and KineticThe Regularity of Limit SpaceFormul<strong>at</strong>ion17:00-17:3017:00-17:30Jihun Park, Institute for Basic Science & Lingbing He, Tsinghua University, ChinaPohang University of Science and Technology, On the Sp<strong>at</strong>ially Homogeneous Boltzmann andKoreaLandau Equ<strong>at</strong>ionsα-Functions of Smooth del Pezzo SurfacesSession 11: M<strong>at</strong>hem<strong>at</strong>ical Fluid DynamicsSession 7: Geometric Aspects of Semilinear and Rel<strong>at</strong>ed Topics (Room: 228)Elliptic Equ<strong>at</strong>ions: Recent Advances & Future Organizers: Dongho Chae, Yoshikazu Giga,Perspectives (Room: 218)Yasunori Maekawa Tai-Peng TsaiOrganizers: Nassif Ghoussoub, Manuel del 16:30-16:55Pino, Juncheng WeiTsuyoshi Yoneda, Hokkaido University, Japan16:30-17:00Topological Instability of Laminar Flows for theMonica Musso, Universidad C<strong>at</strong>ólica de Chile, Two-dimensional Navier-Stokes Equ<strong>at</strong>ion withChileCircular Arc No-slip Boundary ConditionsCritical Trudinger Moser Equ<strong>at</strong>ion in R 2 17:00-17:25
21PRIMA 2013 Program-Monday, June 24Dong Li, University of British Columbia,CanadaTBASession 12: M<strong>at</strong>hem<strong>at</strong>ics of String Theory(Room: 234)Organizers: Peter Bouwknegt, M<strong>at</strong>hai Varghese,Siye Wu16:30-17:00M<strong>at</strong>hai Varghese, The University of Adelaide,AustraliaT-Duality for Circle Bundles viaNoncommut<strong>at</strong>ive Geometry17:00-17:30M<strong>at</strong>ilde Marcolli, California Institute ofTechnology, USAA Motivic Approach to Potts ModelsSession 13: Measurable and TopologicalDynamics (Room: 104)Organizers: Alejandro Maass, Hitoshi Nakada,KyewonKoh Park, Xiangdong Ye16:30-17:00Hiroki Sumi , Osaka University, JapanNeg<strong>at</strong>ivity of Lyapunov Exponents in GenericRandom Dynamical Systems of ComplexPolynomials17:00-17:30Ercai Chen, Nanjing Normal University, ChinaTBASession 15: Number Theory andRepresent<strong>at</strong>ion Theory (Room: 105)Organizers: Clifton Cunningham, AtsushiIchino, Vinayak V<strong>at</strong>sal16:30-17:00Syu K<strong>at</strong>o, Kyoto University, JapanA homological study of Green polynomials17:00-17:30David Roe, University of Calgary, CanadaGeometrizing Characters of ToriSession 16: Oper<strong>at</strong>or Algebras and HarmonicAnalysis (Room: 106)Organizers: Anthony Lau, Zhong-Jin Ruan16:30-17:00Volker Runde, University of Alberta, CanadaErgodic Theory over Locally Compact QuantumGroups17:00-17:30Yong Zhang, University of Manitoba, CanadaAmenability Properties of Weighted GroupAlgebrasSession 17: Optimiz<strong>at</strong>ion (Room: 110)Organizers: Regina Burachik, Xiaojun Chen,Alejandro Jofré, Hector Ramirez16:30-17:00Juan Peypouquet, Universidad TecnicaFederico Santa Marıa, ChileA Dynamical Approach to an InertialForward-backward Algorithm for ConvexMinimiz<strong>at</strong>ion17:00-17:30Felipe Alvarez, Universidad de Chile, ChileRegularized Interior Proximal Altern<strong>at</strong>ingDirections MethodSession 18: Probability (Room: 103)Organizers: Shige Peng, Martin Barlow16:30-17:00Yongsheng Song, Chinese Academy of Sciences,ChinaBackward Stochastic Differential Equ<strong>at</strong>ionsDriven by G-Brownian Motion17:00-17:30Jianfeng Zhang, University of SouthernCalifornia, USAViscosity Solutions of P<strong>at</strong>h Dependent PDEsSession 19: Represent<strong>at</strong>ion Theory andC<strong>at</strong>egorific<strong>at</strong>ion (Room: 107)Organizers: Xuhua He, Joel Kamnitzer, TonyLic<strong>at</strong>a, James Parkinson, Arun Ram16:30-17:00Hiraku Nakajima, Kyoto University, JapanCluster Algebras and Singular Supports ofPerverse Sheaves
22PRIMA 2013 Program-Monday, June 24Session 21: Symplectic Geometry andHamiltonian Dynamics (Room: 216)Organizers: Yakov Eliashberg, Yiming Long16:30-17:20Mei-Lin Yau, N<strong>at</strong>ional Central University,TaiwanIsotopy of Lagrangian Tori RevisitedContributed Talks Group 3: DiscreteM<strong>at</strong>hem<strong>at</strong>ics (Room: 219)Chair: Xiao-Dong Zhang, Shanghai Jiao TongUniversity, China16:30-16:50Aaron Dutle, University of South Carolina,USARealiz<strong>at</strong>ions of Joint Degree M<strong>at</strong>rices16:50-17:10Trent G. Marbach, The University OfQueensland, AustraliaThe Spectrum of 3-Way k-Homogeneous L<strong>at</strong>inTrades17:10-17:30David Cariolaro, Xi'an Jiaotong-LiverpoolUniversity, ChinaEdge Colouring Graphs with Bounded ColourClassesLu Zong, Xi’an Jiaotong -Liverpool University,ChinaModelling of Temper<strong>at</strong>ure and Pricing We<strong>at</strong>herDeriv<strong>at</strong>ives: a Comparison for Mainland China17:10-17:30Cheng Wang, University of MassachusettsDartmouth, USALinear Numerical Schemes for Epitaxial ThinFilm Growth Model with Energy Stability18:00-20:00BanquetVenue: Hua Ting Hotel & TowersContributed Talks Group 4: Comput<strong>at</strong>ionalM<strong>at</strong>hem<strong>at</strong>ics & Optimiz<strong>at</strong>ion (Room: 221)Chair: Jinyan Fan, Shanghai Jiao TongUniversity, China16:30-16:50Julian Romero Barbosa, University of LosAndes, ColombiaA Semidefinite Approxim<strong>at</strong>ion for SymmetricTravelling Salesman Polytopes16:50-17:10
23PRIMA 2013 Program-Tuesday, June 25Tuesday, June 25Morning Lectures: <strong>at</strong> Wen Zhi Hall8:30-9:20Plenary Lecture, Yongbin Ruan, Universityof Michigan, USASearching the Quantum SymmetryChair: Gang Tian, Princeton University, USAand Peking University, China9:30-10:20Plenary Lecture, Shuji Saito, TokyoInstitute of Technology, JapanGeometric Class Field Theory and ExistenceConjecture of Smooth l-adic Sheaves onVarieties over Finite FieldsChair: Gang Tian, Princeton University, USAand Peking University, China10:30-11:00Coffee Break11:00-11:50Plenary Lecture, Andrea Bertozzi,University of California, Los Angeles, USAThe M<strong>at</strong>hem<strong>at</strong>ics of CrimeChair: Weinan E, Princeton University, USAand Peking University, China12:00-14:00LunchAfternoon sessions: <strong>at</strong>Engineering Hall14:00-16:00Session 1: A Glimpse of Stochastic Dynamics(Room: 208)Organizers: Jinqiao Duan, Hongjun Gao14:00-14:30Shanjian Tang, Fudan University, ChinaP<strong>at</strong>h-Dependent Optimal Stochastic Control andViscosity Solution of Associ<strong>at</strong>ed BellmanEqu<strong>at</strong>ions14:30-15:00Guangyue Han , University of Hong Kong,Hong Kong, ChinaRefinements of the Shannon-McMillan-BreimanTheorem15:00-15:30Xiaoying Han, Auburn University, USAConvergent Analysis of Methods for Non-linearFiltering Problems15:30-16:00Hongjun Gao, Nanjing Normal University,ChinaLarge Devi<strong>at</strong>ions for the StochasticTwo-component b-Family SystemSession 2: Algebraic and Complex Geometry(Room: 207)Organizers: Yujiro Kawam<strong>at</strong>a, JongHae Keum14:00-14:50Junkai Chen, N<strong>at</strong>ional Taiwan University,TaiwanPluricanonical Maps and Minimal Models ofThreefolds15:00-15:50De-Qi Zhang, N<strong>at</strong>ional University of Singapore,SingaporePositivity of Log Canonical Divisors andMori/Brody HyperbolicitySession 3: Algebraic Topology and Rel<strong>at</strong>edTopics (Room: 229)Organizers: Alejandro Adem, Alan Jon<strong>at</strong>hanBerrick, Craig Westerland14:00-14:30Fengchun Lei, Dalian University of Technology,China
24PRIMA 2013 Program-Tuesday, June 25TBA14:30-15:00Zhi Lü, Fudan University, ChinaEquivariant Chern Numbers and the Number ofFixed Points for Unitary Torus Manifolds15:00-15:30Ernesto Lupercio, Center for Research andAdvanced Studies of the N<strong>at</strong>ional PolytechnicInstitute, MexicoVirtual Orbifold Cohomology15:30-16:00Alejandro Adem, University of BritishColumbia, CanadaHomotopy Colimits and Commut<strong>at</strong>ive Elementsin Lie GroupsSession 4: Applic<strong>at</strong>ions of Harmonic Mapsand Submanifold Theory (Room: 224)Organizers: Yuxin Dong, Martin A. Guest, WeiZhang14:00-14:40Ting-Hui Chang, Academia Sinica, TaiwanThe Liouville Property for PseudoharmonicMaps with Finite Dirichlet Energy14:45-15:25Hezi Lin, Fujian Normal University, ChinaA Rigidity Theorem for Self-shrinkers of theMean Curv<strong>at</strong>ure Flow15:30-16:10Chen-Yu Chi, N<strong>at</strong>ional Taiwan University,TaiwanOn the Toda Systems of VHS TypeSession 5: Combin<strong>at</strong>orics and DiscreteM<strong>at</strong>hem<strong>at</strong>ics (Room: 202)Organizers: Andreas Dress, Jing Huang,Yaokun Wu14:00-14:30Jaroslav Nešetřil, Charles University, CzechRepublicStructural Limits in Logical and AnalyticContext14:30-15:00L. Sunil Chandran, Indian Institute of Science,Bangalore, IndiaBoxicity and Cubicity of Graphs15:00-15:30Andreas Brandstädt, University of Rostock,GermanyOn the Efficient Solution of Some Packing andCovering Problems in Graphs15:30-16:00Jayme Luiz Szwarcfiter, Federal University ofRio de Janeiro, BrazilOn the Comput<strong>at</strong>ion of the Radon Number inSome Graph ConvexitiesSession 6: Geometric Analysis (Room: 226)Organizers: Jie Qing, Gang Tian, Xiaohua Zhu14:00-14:30Xiaodong Cao, Cornell University, USACurv<strong>at</strong>ure Behavior <strong>at</strong> Singularity Time of RicciFlow14:30-15:00Xiaoli Han, Tsinghua University, ChinaSymplectic Mean Curv<strong>at</strong>ure CP 215:00-15:30Shucheng Chang, N<strong>at</strong>ional Taiwan University,TaiwanComplete Pseudohermitian Manifolds withPositive Spectrum15:30-16:00Haozhao Li, University of Science andTechnology of China, ChinaConvergence of Calabi Flow with Small InitialD<strong>at</strong>aSession 7: Geometric Aspects of SemilinearElliptic Equ<strong>at</strong>ions: Recent Advances & FuturePerspectives (Room: 218)Organizers: Nassif Ghoussoub, Manuel delPino,Juncheng Wei14:00-14:30Changfeng Gui, University of Connecticut,USATBA14:30-15:00
25PRIMA 2013 Program-Tuesday, June 25Mike Kowalczyk, Universidad de Chile, ChileTBA15:00-15:30Juan Davila, Universidad de Chile, ChileNonlocal Minimal Surfaces15:30-16:00Shusen Yan, The University of New England,AustraliaBubbling Solutions for the Chern-Simons ModelSession 8: Hyperbolic Conserv<strong>at</strong>ion Laws andRel<strong>at</strong>ed Applic<strong>at</strong>ions (Room: 100)Organizers: Feimin Huang, Dehua Wang,Ya-Guang Wang14:00-14:30Song Jiang, Institute of Applied Physics andComput<strong>at</strong>ional M<strong>at</strong>hem<strong>at</strong>ics, ChinaIncompressible Limit of the Non-isentropic IdealMagnetohydrodynamic Equ<strong>at</strong>ions14:30-15:00Volker Elling, University of Michigan, AnnArbor, USASelf-similar Vortex Spiral Solutions of the 2dIncompressible Euler Equ<strong>at</strong>ions15:00-15:30Yongqian Zhang, Fudan University, ChinaWeakly Nonlinear Geometric Optics forHyperbolic Systems of Conserv<strong>at</strong>ion Laws15:30-16:00Tong Li, University of Iowa, USATraveling Waves of Chemotaxis ModelsSession 9: Inverse Problems (Room: 219)Organizers: Guillaume Bal, Jin Cheng, GuntherUhlmann14:00-14:30Gang Bao, Zhejiang University, China andMichigan St<strong>at</strong>e University, USAInverse Sc<strong>at</strong>tering Problems in WavePropag<strong>at</strong>ion14:30-15:00Otmar Scherzer, University of Vienna, AustriaTBA15:00-15:30Michael Lamoureux, University of Calgary,CanadaMulti-scale Full Waveform Inversion for SeismicImaging15:30-16:00Kui Ren, University of Texas <strong>at</strong> Austin, USAInverse Problems to Elliptic Systems inQuantit<strong>at</strong>ive (Fluorescence) PhotoacousticTomographySession 10: Kinetic Equ<strong>at</strong>ions (Room: 220)Organizers: Radjesvarane Alexandre, BenoitPerthame14:00-14:30Cédric Villani, Université de Lyon and InstitutHenri Poincaré, FranceTBA14:30-15:00Irene Gamba, University of Texas-Austin, USAAngular Averaging, Propag<strong>at</strong>ion of ExponentialTails and Grazing Collisions for Solutions of theBoltzmann Equ<strong>at</strong>ion15:00-15:30Shih-Hsien Yu, N<strong>at</strong>ional University ofSingapore, SingaporeViscous Wave Propag<strong>at</strong>ion <strong>at</strong> Interface15:30-16:00Giuseppe Toscani, University of Pavia, ItalyTBASession 11: M<strong>at</strong>hem<strong>at</strong>ical Fluid Dynamicsand Rel<strong>at</strong>ed Topics (Room: 228)Organizers: Dongho Chae, Yoshikazu Giga,Yasunori Maekawa Tai-Peng Tsai14:00-14:50Zhouping Xin, The Chinese University of HongKong, Hong Kong, ChinaOn Vanishing Viscosity Limit for 3-DimensionalIncompressible Navier-Stokes Equ<strong>at</strong>ions with aSlip Boundary Condition15:00-15:50Seung-Yeal Ha, Seoul N<strong>at</strong>ional University,Korea
26PRIMA 2013 Program-Tuesday, June 25Well-posedness of Coupled Kinetic-fluid Modelsfor FlockingSession 12: M<strong>at</strong>hem<strong>at</strong>ics of String Theory(Room:234)Organizers: Peter Bouwknegt, M<strong>at</strong>hai Varghese,Siye Wu14:00-14:30Pedram Hekm<strong>at</strong>i , University of Adelaide,AustraliaT-duality Commutes with Reduction14:30-15:00Fei Han, N<strong>at</strong>ional University of Singapore,SingaporeEquivariant Cohomology and Bismut-ChernCharacter in the Stolz-Teichner Program15:00-15:30David Ridout, The Australian N<strong>at</strong>ionalUniversity, AustraliaThe Wess-Zumino-Witten Model on SL (2;R)Session 13: Measurable and TopologicalDynamics (Room: 104)Organizers: Alejandro Maass, Hitoshi Nakada,KyewonKoh Park, Xiangdong Ye14:00-14:30Shigeki Akiyama, University of Tsukuba, JapanHeight Reducing Problem14:30-15:00Jeong-Yup Lee, Kwandong University, KoreaOverlap and Strong Coincidences onSubstitution Tilings15:00-15:30Juan Rivera-Letelier, Pontificia C<strong>at</strong>holicUniversity, ChileTBA15:30-16:00Dou Dou, Nanjing University, ChinaLocal Entropy Dimension for a Measure and aVari<strong>at</strong>ional PrincipleSession 14: Multiscale Analysis andAlgorithms (Room: 102)Organizers: Weinan E, Carlos Garcia-Cervera,Pingbing Ming14:00-14:30Christof Schutte, Max Planck Institute forMolecular Genetics, GermanyTBA14:30-15:00Tiejun Li, Peking University,ChinaTBA15:00-15:30Di Liu, Michigan St<strong>at</strong>e University, USAMultiscale Modeling and Comput<strong>at</strong>ion of NanoOptical Responses15:30-16:00Zhijian Yang, Wuhan University, ChinaGeneralized Irving-Kirkwood Formula for theCalcul<strong>at</strong>ion of Continuum Quantities inMolecular Dynamics ModelsSession 15: Number Theory andRepresent<strong>at</strong>ion Theory (Room: 105)Organizers: Clifton Cunningham, AtsushiIchino, Vinayak V<strong>at</strong>sal14:00-14:30Jianshu Li, Hong Kong University of Scienceand Technology, Hong Kong, ChinaOn the First Betti Number of HyperbolicArithmetic Manifolds14:30-15:00Wen-Wei Li, Chinese Academy of Sciences,ChinaOn the Elliptic Part of the Trace Formula forSp(2n)15:00-15:30Paul Mezo, Carleton University, CanadaTwisted Spectral Transfer for Real Groups15:30-16:00Yoichi Mieda, Kyoto University, JapanZelevinsky Involution and l-adic Cohomology ofRapoport-Zink SpacesSession 16: Oper<strong>at</strong>or Algebras and HarmonicAnalysis (Room: 106)Organizers: Anthony Lau, Zhong-Jin Ruan14:00-14:30
28PRIMA 2013 Program-Tuesday, June 2514:00-14:50Kaoru Ono, RIMS, Kyoto University, JapanAnti-symplectic Involution and Floer Theory15:00-15:50An-min Li, Sichuan University, ChinaThe Extremal Kahler Metrics on Toric ManifoldsSession 22: Symplectic Geometry andM<strong>at</strong>hem<strong>at</strong>ical Physics (Room: 222)Organizers: Xiaobo Liu, Huijun Fan14:00-14:45Ludmil K<strong>at</strong>zarkov, University of Miami, USAand University of Vienna, AustriaC<strong>at</strong>egories and Dynamical Systems14:50-15:35Bohui Chen, Sichuan University, ChinaVirtual Neighborhood Techniques inGromov-Witten Theory15:35-16:20Hiroshi Iritani, Kyoto University, JapanFock Sheaf of Givental Quantiz<strong>at</strong>ionSession 1: A Glimpse of Stochastic Dynamics(Room: 208)Organizers: Jinqiao Duan, Hongjun Gao16:30-17:00Yong Liu, Peking University, ChinaOn Time Regularity of SPDE Driven by LevyNoise in Hilbert Spaces17:00-17:30Qi Zhang, Fudan University, ChinaBackward Stochastic Partial DifferentialEqu<strong>at</strong>ions and Their Applic<strong>at</strong>ion to StochasticBlack-Scholes FormulaSession 2: Algebraic and Complex Geometry(Room: 207)Organizers: Yujiro Kawam<strong>at</strong>a, JongHae Keum16:30-17:20Keiji Oguiso, Osaka University, Japan andKorea Institute for Advanced Study, KoreaSmooth Quartic K3 Surfaces and CremonaTransform<strong>at</strong>ionsSession 23: Triangul<strong>at</strong>ed C<strong>at</strong>egories inRepresent<strong>at</strong>ion Theory of Algebras(Room: 214)Organizers: Ragnar-Olaf Buchweitz, ShipingLiu, Claus Michael Ringel, Pu Zhang14:00-14:45Luchezar L. Avramov, University ofNebraska-Lincoln, USATBA14:50-15:20Ryo Takahashi, Nagoya University,JapanExact C<strong>at</strong>egories over Cohen-Macaulay Rings15:25-15:55Changchang Xi, Capital Normal University,ChinaRigid Morphisms, Exact Pairs and Applic<strong>at</strong>ions16:00-16:30Coffee Break16:30-17:30Session 3: Algebraic Topology and Rel<strong>at</strong>edTopics (Room: 229)Organizers: Alejandro Adem, Alan Jon<strong>at</strong>hanBerrick, Craig Westerland16:30-17:00Dev P. Sinha, University of Oregon, USACohomology of Symmetric andAltern<strong>at</strong>ing Groups17:00-17:30Dong Youp Suh, Korea Advanced Institute ofScience and Technology, KoreaClassific<strong>at</strong>ion of Complex Projective Towers Upto Dimension 8 and Cohomological RigiditySession 4: Applic<strong>at</strong>ions of Harmonic Mapsand Submanifold Theory (Room: 224)Organizers: Yuxin Dong, Martin A. Guest, WeiZhang16:40-17:20ShihShu Walter Wei, University of Oklahoma,USATBA
29PRIMA 2013 Program-Tuesday, June 25Session 5: Combin<strong>at</strong>orics and DiscreteM<strong>at</strong>hem<strong>at</strong>ics (Room: 202)Organizers: Andreas Dress, Jing Huang,Yaokun Wu16:30-17:00Xuding Zhu, Zhejiang Normal University,ChinaOn-line List Colouring of Graphs17:00-17:30Pinar Heggernes, University of Bergen,NorwayEnumer<strong>at</strong>ion in Graph ClassesSession 6: Geometric Analysis (Room: 226)Organizers: Jie Qing, Gang Tian, Xiaohua Zhu16:30-17:00Ivan Cheltsov, University of Edinburgh, UKAffine Cones over Smooth del Pezzo Surfaces17:00-17:30Hong Huang, Beijing Normal University, ChinaRicci Flow and 4-Manifolds with PositiveIsotropic Curv<strong>at</strong>ureSession 7: Geometric Aspects of SemilinearElliptic Equ<strong>at</strong>ions: Recent Advances & FuturePerspectives (Room: 218)Organizers: Nassif Ghoussoub, Manuel delPino,Juncheng Wei16:30-17:00Yong Liu, North China Electric PowerUniversity, ChinaSingly Periodic Solutions to the Allen-CahnEqu<strong>at</strong>ion and the Toda L<strong>at</strong>tice17:00-17:30Kelei Wang, Wuhan Institute of Physics andM<strong>at</strong>hem<strong>at</strong>ics, Chinese Academy of Sciences,ChinaMonotonicity Formula and Liouville Theoremsfor Stable Solutions of Some Elliptic ProblemsSession 8: Hyperbolic Conserv<strong>at</strong>ion Laws andRel<strong>at</strong>ed Applic<strong>at</strong>ions (Room: 100)Organizers: Feimin Huang, Dehua Wang,Ya-Guang Wang16:30-17:00Ronghua Pan, Georgia Institute of Technology,USACompressible Navier-Stokes Equ<strong>at</strong>ions withChapman Dissip<strong>at</strong>ion17:00-17:30Daoyuan Fang, Zhejiang University, ChinaSome Results about Compressible Oldroyd-BSession 10: Kinetic Equ<strong>at</strong>ions (Room: 220)Organizers: Radjesvarane Alexandre, BenoitPerthame16:30-17:00Seung-Yeal Ha, Seoul N<strong>at</strong>ional University,KoreaL p -sc<strong>at</strong>tering and Uniform Stability of KineticEqu<strong>at</strong>ions17:00-17:30Pierre-Emmanuel Jabin, University ofMaryland, USANew Regularity Estim<strong>at</strong>es for TransportEqu<strong>at</strong>ions17:30-18:00Radjesvarane Alexandre, French NavalAcademy, France and Shanghai Jiao TongUniversity, ChinaOn Some Kinetic Models for Bose EinsteinCondens<strong>at</strong>ionSession 11: M<strong>at</strong>hem<strong>at</strong>ical Fluid Dynamicsand Rel<strong>at</strong>ed Topics (Room: 228)Organizers: Dongho Chae, Yoshikazu Giga,Yasunori Maekawa, Tai-Peng Tsai16:30-16:55Ting Zhang, Zhejiang University, ChinaGlobal Strong Solution for Equ<strong>at</strong>ions Rel<strong>at</strong>ed tothe Incompressible Viscoelastic Fluids17:00-17:25Xiangdi Huang, Academy of M<strong>at</strong>hem<strong>at</strong>ics andSystem Sciences, CAS, ChinaGlobal Classical and Weak Solutions to the 3DFully Compressible Navier-Stokes-FourierSystem
30PRIMA 2013 Program-Tuesday, June 25Session 13: Measurable and TopologicalDynamics (Room: 104)Organizers: Alejandro Maass, Hitoshi Nakada,KyewonKoh Park, Xiangdong Ye16:30-17:00Seonhee Lim, Seoul N<strong>at</strong>ional University, KoreaSubword Complexity and Sturmian Colorings ofTrees17:00-17:30Xiongping Dai, Nanjing University, ChinaChaotic Dynamics of Continuous-timeTopological Semiflow on Polish SpaceSession 14: Multiscale Analysis andAlgorithms (Room: 102)Organizers: Weinan E, Carlos Garcia-Cervera,Pingbing Ming16:30-17:00Mitchell Luskin, University of Minnesota, USATBA17:00-17:30Xiantao Li, Pennsylvania St<strong>at</strong>e University, USAAtomic Level Interpret<strong>at</strong>ion of Fracture CriteriaSession 15: Number Theory andRepresent<strong>at</strong>ion Theory (Room: 105)Organizers: Clifton Cunningham, AtsushiIchino, Vinayak V<strong>at</strong>sal16:30-17:00Moshe Adrian, University of Utah, USARectifiers and the Local LanglandsCorrespondence17:00-17:30Chung Pang Mok, McMaster University,CanadaEndoscopic Classific<strong>at</strong>ion of AutomorphicRepresent<strong>at</strong>ions of Classical GroupsSession 16: Oper<strong>at</strong>or Algebras and HarmonicAnalysis (Room: 106)Organizers: Anthony Lau, Zhong-Jin Ruan16:30-17:00Michael Lamoureux, University of Calgary,CanadaMinimum Phase Oper<strong>at</strong>ors and the Polya-SchurProblemSession 17: Optimiz<strong>at</strong>ion (Room: 110)Organizers: Regina Burachik, Xiaojun Chen,Alejandro Jofré, Hector Ramirez16:30-17:00Huifu Xu, City University of London, UKAsymptotic Convergence Analysis forDistributional Robust Optimiz<strong>at</strong>ion andEquilibrium Problems17:00-17:30Alejandro Jofré, Universidad de Chile, ChileThe Robust Stability of Every Equilibrium inEconomic Models of ExchangeSession 18: Probability (Room: 103)Organizers: Shige Peng, Martin Barlow16:30-17:00Takashi Kumagai, Kyoto University, JapanQuenched Invariance Principles for RandomWalks and Random Divergence Forms inRandom Media with a Boundary17:00-17:30Ryoki Fukushima, Kyoto University, JapanBrownian Motion in a Heavy Tailed PoissonianPotentialSession 19: Represent<strong>at</strong>ion Theory andC<strong>at</strong>egorific<strong>at</strong>ion (Room:107)Organizers: Xuhua He, Joel Kamnitzer, TonyLic<strong>at</strong>a, James Parkinson, Arun Ram16:30-17:00Julia Pevtsova, University of Washington, USAElementary Subalgebras of Modular LieAlgebras17:00-17:30Stephen Griffeth, Universidad de Talca, ChileVanishing Properties of Jack PolynomialsSession 20: Singularities in Geometry andTopology (Room: 221)Organizers: Guangfeng Jiang, Laurentiu Maxim,Mutsuo Oka, Jose Seade
31PRIMA 2013 Program-Tuesday, June 2516:30 -17:20Ricardo Uribe-Vargas, Université deBourgogne, FranceCharacteristic Points, Fundamental CubicForm and Euler Characteristic of ProjectiveSurfacesSession 21: Symplectic Geometry andHamiltonian Dynamics (Room: 216)Organizers: Yakov Eliashberg, Yiming Long16:30-17:20Yong-Geun Oh, University ofWisconsin-Madison, USA & IBS-Center forGeometry and Physics, KoreaCanonical Connection and Analysis of ContactCauchy-Riemann Equ<strong>at</strong>ionSession 22: Symplectic Geometry andM<strong>at</strong>hem<strong>at</strong>ical Physics (Room: 222)Organizers: Xiaobo Liu, Huijun Fan16:30-17:15Yakov Eliashberg, Stanford University, USAAlgebra of Legendrian SurgerySession 23: Triangul<strong>at</strong>ed C<strong>at</strong>egories inRepresent<strong>at</strong>ion Theory of Algebras(Room: 214)Organizers: Ragnar-Olaf Buchweitz, ShipingLiu, Claus Michael Ringel, Pu Zhang16:30-17:15Pierre-Guy Plamondon, University ofParis-Sud, FranceCluster C<strong>at</strong>egories and Independence Results forExchange Graphs17:25-17:55Claus Michael Ringel, Bielefeld University,Germany and Shanghai Jiao Tong University,ChinaFrom Submodule C<strong>at</strong>egories to PreprojectiveAlgebrasUniversity, China16:30-16:50Ju Zhou, Kutztown University of Pennsylvania,USAPancyclicity of 4-Connected〔K 1,3, Z 8 〕-freeGraphs16:50-17:10Congpei An, Jinan University, ChinaNumerical Verific<strong>at</strong>ion Method for WellConditioned Spherical t-Designs17:10-17:30Suhadi Wido Saputro, Institut TeknologiBandung, IndonesiaOn the Fractional Metric Dimension of TreeGraphsContributed Talks Group 5: DifferentialEqu<strong>at</strong>ions (Room: 229)Chair: Lei Zhang, Shanghai Jiao TongUniversity, China16:30-16:50Beixiang Fang, Shanghai Jiao Tong University,ChinaGlobal Stability of E-H Type Regular Refractionof Shocks on the Interface between Two Media16:50-17:10Fang Yu, Shanghai Jiao Tong University, ChinaStability of Supersonic Contact Discontinuitiesfor Three Dimensional Compressible SteadyEuler Flows17:10-17:30Qin Wang, Shanghai Jiao Tong University,ChinaThe Regularity of Semi-hyperbolic P<strong>at</strong>ches <strong>at</strong>Sonic Lines for the Pressure Gradient Equ<strong>at</strong>ionin Gas DynamicsContributed Talks Group 3: DiscreteM<strong>at</strong>hem<strong>at</strong>ics (Room: 219)Chair: Xiao-Dong Zhang, Shanghai Jiao Tong
32PRIMA 2013 Program-Wednesday, June 26Wednesday, June 26Morning Lectures: <strong>at</strong> Wen Zhi Hall8:30-9:20Public Lecture, Ronald Graham, University of California, San Diego, USAComputers and M<strong>at</strong>hem<strong>at</strong>ics: Problems and ProspectsChair: Shige Peng, Shandong University, China9:30-10:20Plenary Lecture, Weinan E, Peking University, China and Princeton University, USAThe Exact Renormaliz<strong>at</strong>ion Group FlowChair: Shige Peng, Shandong University, China10:30-11:00Coffee Break11:00-11:50Plenary Lecture, Weiping Zhang, Nankai University, ChinaGeometric Quantiz<strong>at</strong>ion Formulas on Symplectic ManifoldsChair: Yakov Eliashberg, Stanford University, USA12:00-14:00Lunch14:00-17:30Free afternoon
33PRIMA 2013 Program-Thursday, June 27Thursday, June 27Morning Lectures: <strong>at</strong> Wen Zhi Hall8:30-9:20Plenary Lecture, Martin BarlowUniversity of British Columbia, CanadaRandom Walks and Percol<strong>at</strong>ionChair: Doug Lind, University of Washington,USA9:30-10:20Plenary Lecture, Arun Ram, University ofMelbourne, AustraliaCombin<strong>at</strong>orics, Represent<strong>at</strong>ions,Homogeneous Spaces and EllipticCohomologyChair: Doug Lind, University of Washington,USA10:30-11:00Coffee Break11:00-11:50Plenary Lecture, Jun-Muk Hwang, KoreaInstitute for Advanced Study, KoreaSphere Packings, Symplectic L<strong>at</strong>tices andRiemann SurfacesChair: JongHae Keum, Korea Institute forAdvanced Study, Korea14:00-14:30Yong XuNorthwestern Polytechnical University, ChinaThe Availability of Logical Oper<strong>at</strong>ion Inducedby Dichotomous Noise for a Nonlinear BistableSystem14:30-15:00Guillaume Bal, Columbia University, USATBA15:00-15:30Hassan Allouba, Kent St<strong>at</strong>e University, USATBA15:30-16:00Mickael Chekroun, University of Hawaii, USATBASession 2: Algebraic and Complex Geometry(Room: 207)Organizers: Yujiro Kawam<strong>at</strong>a, JongHae Keum14:00-14:50Sijong Kwak, Korea Advanced Institute ofScience and Technology, KoreaGeometry and Syzygies in the First LinearStrand15:00-15:50Takehiko Yasuda, Osaka University, JapanThe Hilbert Scheme of Points and Extensions ofLocal Fields12:00-14:00LunchAfternoon Sessions: <strong>at</strong>Engineering Hall14:00-16:00Session 1: A Glimpse of Stochastic Dynamics(Room: 208)Organizers: Jinqiao Duan, Hongjun GaoSession 3: Algebraic Topology and Rel<strong>at</strong>edTopics (Room: 229)Organizers: Alejandro Adem, Alan Jon<strong>at</strong>hanBerrick, Craig Westerland14:30-15:00Jie Wu, N<strong>at</strong>ional University of Singapore,SingaporeOn Simplicial Resolutions of Framed Links15:00-15:30Shengkui Ye, University of Oxford, UKRigidity of M<strong>at</strong>rix Groups
34PRIMA 2013 Program- Thursday, June 2715:30-16:00Craig Westerland, University of Melbourne,AustraliaHomology of Hurwitz Spaces and theCohen-Lenstra HeuristicsSession 5: Combin<strong>at</strong>orics and DiscreteM<strong>at</strong>hem<strong>at</strong>ics (Room: 202)Organizers: Andreas Dress, Jing Huang,Yaokun Wu14:00-14:30Brendan McKay, Australian N<strong>at</strong>ionalUniversity, AustraliaThe Practice of Graph Isomorphism14:30-15:00Ryuhei Uehara, Japan Advanced Institute ofScience and Technology, JapanThe Graph Isomorphism Problem on GeometricGraphs15:00-15:30Nikolai Dolbilin, Steklov M<strong>at</strong>hem<strong>at</strong>ics Instituteof the Russian Academy of Sciences, RussiaParallelohedra: From Minkowski and Voronoi tothe Present Day15:30-16:00Eiichi Bannai, Shanghai Jiao Tong University,ChinaOn Tight Rel<strong>at</strong>ive t-DesignsZhou Zhang, University of Sydney, AustraliaRicci Curv<strong>at</strong>ure in Kahler-Ricci FlowSession 7: Geometric Aspects of SemilinearElliptic Equ<strong>at</strong>ions: Recent Advances & FuturePerspectives (Room: 218)Organizers: Nassif Ghoussoub, Manuel delPino,Juncheng Wei14:00-14:30Yoshihiro Tonegawa, Hokkaido University,JapanExistence and Regularity of Mean Curv<strong>at</strong>ureFlow with Transport Term14:30-15:00Congming Li, Shanghai Jiao Tong University,China and University of Colorado <strong>at</strong> Boulder,USAExistence and Non-existence of PositiveSolutions on the Hardy-Littlewood-Sobolev TypeSystems15:00-15:30Yong Yu, The Chinese University of HongKong, Hong Kong, ChinaGamma Convergence for Maxwell-Chern-Simons-Higgs Energy15:30-16:00Yiming Long, Nankai University, ChinaTBASession 6: Geometric Analysis (Room: 226)Organizers: Jie Qing, Gang Tian, Xiaohua Zhu14:00-14:30Zizhou Tang, Beijing Normal University, ChinaThe First Eigenvalue of Minimal Submanifoldsin a Unit Sphere14:30-15:00Sergio Almaraz, Universidade FederalFluminense, BrazilConvergence of Scalar-fl<strong>at</strong> Metrics on Manifoldswith Boundary under the Yamabe Flow15:00-15:30Bin Zhou, Peking University, ChinaA Class of Weingarten Curv<strong>at</strong>ure Measures15:30-16:00Session 8: Hyperbolic Conserv<strong>at</strong>ion Laws andRel<strong>at</strong>ed Applic<strong>at</strong>ions (Room: 100)Organizers: Feimin Huang, Dehua Wang,Ya-Guang Wang14:00-14:30Hai-Liang Li, Capital Normal University, ChinaLong Time Behaviors ofVlasov-Poisson-Boltzmann Equ<strong>at</strong>ions14:30-15:00Yue-Jun Peng, Université BlaisePascal, Clermont-Ferrand, FranceStability of Steady St<strong>at</strong>e Solutions forEuler-Maxwell Equ<strong>at</strong>ions15:00-15:30Yi Wang, Chinese Academy of Sciences, China
35PRIMA 2013 Program- Thursday, June 27TBA15:30-16:00Ming Mei, Champlain College Saint-Lambertand McGill University, CanadaAsymptotic Behavior of Solutions toEuler-Poisson Equ<strong>at</strong>ions for BipolarHydrodynamic Model of SemiconductorsSession 9: Inverse Problems (Room: 219)Organizers: Guillaume Bal, Jin Cheng, GuntherUhlmann14:00-14:30M<strong>at</strong>ti Lassas, University of Helsinki, FinlandTBA14:30-15:00Axel Osses, University of Chile, ChileA He<strong>at</strong> Source Reconstruction Formula fromSingle Internal Measurements Using a Family ofNull Controls15:00-15:30Hongyu Liu, University of North Carolina,USATBA15:30-16:00Ting Zhou, Massachusetts Institute ofTechnology, USATBASession 11: M<strong>at</strong>hem<strong>at</strong>ical Fluid Dynamicsand Rel<strong>at</strong>ed Topics (Room: 228)Organizers: Dongho Chae, Yoshikazu Giga,Yasunori Maekawa Tai-Peng Tsai14:00-14:50Tastuo Iguchi, Keio University, JapanSolvability of the Initial Value Problem to aModel System for W<strong>at</strong>er Waves15:00-15:50Stephen Gustafson, University of BritishColumbia, CanadaGlobal Solutions of the Equivariant He<strong>at</strong>-flowSession 13: Measurable and TopologicalDynamics (Room: 104)Organizers: Alejandro Maass, Hitoshi Nakada,KyewonKoh Park, Xiangdong Ye14:00-14:30Piotr Oprocha, AGH University of Science andTechnology, PolandShadowing Properties with Average Tracing ofPseudo-orbits14:30-15:00Yong Moo Chung, Hiroshima University, JapanLarge Devi<strong>at</strong>ion Principle for ChaoticDynamical Systems15:00-16:00Guohua Zhang, Fudan University, ChinaLocal Weak Mixing in Dynamical SystemsSession 14: Multiscale Analysis andAlgorithms (Room: 102)Organizers: Weinan E, Carlos Garcia-Cervera,Pingbing Ming14:00-14:30Claude Le Bris, École des Ponts ParisTech,FranceTBA14:30-15:00Xu Yang, University of California, SantaBarbara, USAA P<strong>at</strong>h Way Based Mean Field Model for E. coliChemotaxis15:00-15:30Olof Runborg, KTH Royal Institute ofTechnology, SwedenMultiscale Methods for Wave Propag<strong>at</strong>ionProblems15:30-16:00Ruo Li, Peking Univeristy, ChinaFrom Discrete Velocity Model to MomentMethodSession 15: Number Theory andRepresent<strong>at</strong>ion Theory (Room: 105)Organizers: Clifton Cunningham, AtsushiIchino, Vinayak V<strong>at</strong>sal14:00-14:30Shunsuke Yamana, Kyushu University, JapanL-functions and Theta Correspondence
36PRIMA 2013 Program- Thursday, June 2714:30-15:00Loren Spice, Texas Christian University, USAStability and Sign Changes in p-adic HarmonicAnalysis15:00-15:30Binyong Sun, Academy of M<strong>at</strong>hem<strong>at</strong>ics andSystems Science, CAS, ChinaConserv<strong>at</strong>ion Rel<strong>at</strong>ions for Local ThetaCorrespondence15:30-16:00Mas<strong>at</strong>o Kurihara, Keio University, JapanOn the Structure of Selmer GroupsSession 16: Oper<strong>at</strong>or Algebras and HarmonicAnalysis (Room: 106)Organizers: Anthony Lau, Zhong-Jin Ruan14:00-14:30Huaxin Lin, University of Oregon, USAKishimoto's Conjugacy Theorems in SimpleC*-algebras of Tracial Rank One14:30-15:00Ngai-Ching Wong, N<strong>at</strong>ional Sun Y<strong>at</strong>-senUniversity, TaiwanZero Products and Norm PreservingOrthogonally Additive HomogeneousPolynomials on C*-algebras15:00-15:30Chi-Keung Ng, Nankai University, ChinaSpectral Gap Actions and Invariant St<strong>at</strong>es15:30-16:00Ebrahim Samei, University of Sask<strong>at</strong>chewan,CanadaExtending Deriv<strong>at</strong>ions to Dual Banach AlgebrasSession 17: Optimiz<strong>at</strong>ion (Room: 110)Organizers: Regina Burachik, Xiaojun Chen,Alejandro Jofré, Hector Ramirez14:00-14:40Zhiping Chen, Xi'an Jiaotong University, ChinaStability of Two-stage Stochastic Programs withQuadr<strong>at</strong>ic Continuous Recourse14:40-15:20Vera Roshchina, University of Ballar<strong>at</strong>,AustraliaFacially Exposed Cones Are Not Always Nice15:00-16:00Miguel Carrasco, Universidad de los Andes,ChileDesign of Robust Truss Structures for MinimumWeight Using the Sequential ConvexApproxim<strong>at</strong>ion MethodSession 18: Probability (Room: 103)Organizers: Shige Peng, Martin Barlow14:00-14:30Dayue Chen, Peking University, ChinaThe Motion of a Tagged Particle in the SimpleExclusion Process14:30-15:00Jaime San Martin, University of Chile, ChileUltrametric Potentials15:00-15:30Qi-Man Shao, The Chinese University of HongKong, Hong Kong, ChinaFrom Stein's Method to Self-normalizedModer<strong>at</strong>e Devi<strong>at</strong>ions15:30-16:00Panki Kim, Seoul N<strong>at</strong>ional University, KoreaParabolic Littlewood-Paley Inequality for-type Oper<strong>at</strong>ors and Applic<strong>at</strong>ions toStochastic Integro-differential Equ<strong>at</strong>ionsSession 19: Represent<strong>at</strong>ion Theory andC<strong>at</strong>egorific<strong>at</strong>ion (Room:107)Organizers: Xuhua He, Joel Kamnitzer, TonyLic<strong>at</strong>a, James Parkinson, Arun Ram14:00-15:00Weiqiang Wang, University of Virginia, USAGlobalizing Crystal Basis for QuantumSuperalgebras15:00-15:30Alexander Molev, University of Sydney,AustraliaCenter <strong>at</strong> the Critical Level and Commut<strong>at</strong>iveSubalgebras15:30-16:00Paul Sobaje, University of Melbourne, Australia
37PRIMA 2013 Program- Thursday, June 27Support Varieties for Reductive GroupsSession 20: Singularities in Geometry andTopology (Room: 221)Organizers: Guangfeng Jiang, Laurentiu Maxim,Mutsuo Oka, Jose Seade14:00-14:25Osamu Saeki, Kyushu University, JapanBroken Lefschetz Fibr<strong>at</strong>ions and Their Moves14:30-14:55Masahiko Yoshinaga, Hokkaido University,JapanMilnor Fibers of Real Line Arrangements15:00-15:25Vu The Khoi, Hanoi Institute of M<strong>at</strong>hem<strong>at</strong>ics,VietnamTBA15:30-15:55Kiyoshi Takeuchi, University of Tsukuba,JapanGeometry of Non-tame Polynomial MapsSession 21: Symplectic Geometry andHamiltonian Dynamics (Room: 216)Organizers: Yakov Eliashberg, Yiming Long14:00-14:50ViktorGinzburg, University of California,Santa Cruz, USAMean Euler Characteristic: the Degener<strong>at</strong>eCase15:00-15:50Xijun Hu, Shandong University, ChinaThe Hill-type Formula and Krein-type TraceFormulaSession 22: Symplectic Geometry andM<strong>at</strong>hem<strong>at</strong>ical Physics (Room: 222)Organizers: Xiaobo Liu, Huijun Fan14:00-14:45Alejandro Adem, University of BritishColumbia, CanadaA Classifying Space for Commut<strong>at</strong>ivity15:00-15:45Paul Norbury, University of Melbourne,AustraliaOrbifold Hurwitz Numbers and Eynard-OrantinInvariantsSession 23: Triangul<strong>at</strong>ed C<strong>at</strong>egories inRepresent<strong>at</strong>ion Theory of Algebras(Room: 214)Organizers: Ragnar-Olaf Buchweitz, ShipingLiu, Claus Michael Ringel, Pu Zhang14:00-14:45Henning Krause, Bielefeld University,GermanyCohomological Length Functions14:50-15:20Christof Geiss, Universidad NacionalAutónoma de México, MéxicoThe Represent<strong>at</strong>ion Type of Non-degener<strong>at</strong>e QPs15:25-15:55Thomas Bruestle, Bishops’s University andUniversité de Sherbrooke, CanadaThe Decor<strong>at</strong>ed Mapping Class Group of aMarked SurfaceContributed Talks Group 1: Geometry andAnalysis (Room:224)Chair: Deliang Xu, Shanghai Jiao TongUniversity, China14:00-14:20Feng Rong, Shanghai Jiao Tong University,ChinaOn Automorphism Groups of Hua Domains14:20-14:40Peng Wu, Cornell University, USAOn the Potential Function of Gradient SteadyRicci Solitons14:40-15:00Paul Tupper, Simon Fraser University, CanadaDiversities and the Geometry of Hypergraphs15:00-15:20Yuan-Jen Chiang, University of MaryWashington, USADevelopments of Harmonic Maps intoBiharmonic Maps15:20-15:40
38PRIMA 2013 Program- Thursday, June 27Xiangjin Xu, Binghamton University, USANew He<strong>at</strong> Kernel Estim<strong>at</strong>es on Manifolds withNeg<strong>at</strong>ive Ricci Curv<strong>at</strong>ure Lower Bound15:40-16:00Rui Liu, Nankai University, ChinaCb-frames and the Completely BoundedApproxim<strong>at</strong>ion Property for Oper<strong>at</strong>or SpacesContributed Talks Group 2: Algebra andNumber Theory (Room: 220)Chair: Hongze Li, Shanghai Jiao TongUniversity, China14:00-14:20Yuehui Zhang, Shanghai Jiao Tong University,ChinaTriangul<strong>at</strong>ed C<strong>at</strong>egories from C<strong>at</strong>egories ofSpecial Exact Sequences14:20-14:40Liping Li, University of California, Riverside,USAA Generalized Koszul Theory14:40-15:00Shuvra Gupta, University of Iowa, USARealising Galois Groups via GaloisRepresent<strong>at</strong>ions15:00-15:20Yeansu Kim, Purdue University, USAL-functions from Langlands-Shahidi Method forGSpin Groups and the Generic Arthur L-packetConjecture15:20-15:40Igor Bakovic, University of Warsaw, PolandC<strong>at</strong>egorific<strong>at</strong>ion in Topology, Geometry andCombin<strong>at</strong>orics15:40-16:00Hirotaka Koga, University of Tsukuba, JapanDerived Equivalences and GorensteinDimensionContributed Talks Group 5: DifferentialEqu<strong>at</strong>ions (Room: 229)Chair: Chunjing Xie, Shanghai Jiao TongUniversity, China14:00-14:20Min Ding, Shanghai Jiao Tong University,ChinaSome Piston Problems in Fluid Dynamics14:20-14:40Cheng-Jie Liu, Shanghai Jiao Tong University,ChinaStability of Boundary Layers for theNon-isentropic Compressible CircularlySymmetric 2D Flow14:40-15:00Wei Yan, Institute of Applied Physics andComput<strong>at</strong>ional M<strong>at</strong>hem<strong>at</strong>ics, ChinaBlowup of Classical Solutions to theCompressible Navier-Stokes Equ<strong>at</strong>ions15:00-15:20Fengquan Li, Dalian University of Technology,ChinaOverdetermined Boundary Value Problems withStrongly Nonlinear Elliptic PDE15:20-15:40Yun-Ho Kim, Sangmyung University, KoreaOn Quasilinear Elliptic Equ<strong>at</strong>ions with VariableExponents15:40-16:00Linglong Du, N<strong>at</strong>ional University of Singapore,SingaporeOver-compressive Shock Profile Associ<strong>at</strong>ed witha Simplified System from MHD16:00-16:30Coffee Break16:30-17:30Session 2: Algebraic and Complex Geometry(Room: 207)Organizers: Yujiro Kawam<strong>at</strong>a, JongHae Keum16:30-17:20Meng Chen, Fudan University, ChinaSome Bir<strong>at</strong>ionality Criteria on 3-folds with p g >1
39PRIMA 2013 Program- Thursday, June 27Session 5: Combin<strong>at</strong>orics and DiscreteM<strong>at</strong>hem<strong>at</strong>ics (Room: 202)Organizers: Andreas Dress, Jing Huang,Yaokun Wu16:30-17:00Jing Huang, University of Victoria, CanadaThe Lexicographic Method17:00-17:30Michel Habib, University Paris Diderot - ParisVII, FranceNew Trends for Graph SearchesSession 7: Geometric Aspects of SemilinearElliptic Equ<strong>at</strong>ions: Recent Advances & FuturePerspectives (Room: 218)Organizers: Nassif Ghoussoub, Manuel delPino,Juncheng Wei16:30-17:00Hsin-Yuan Huang, N<strong>at</strong>ional Sun Y<strong>at</strong>-senUniversity, TaiwanOn the Entire Radial Solutions Arising inChern-Simons Equ<strong>at</strong>ions17:00-17:30Ignacio Guerra, Universidad de Santiago deChile, ChileSolutions for a Semilinear Elliptic Equ<strong>at</strong>ion inDimension Two with Supercritical GrowthSession 8: Hyperbolic Conserv<strong>at</strong>ion Laws andRel<strong>at</strong>ed Applic<strong>at</strong>ions (Room: 100)Organizers: Feimin Huang, Dehua Wang,Ya-Guang Wang16:30-17:00Wen Shen, Pennsylvania St<strong>at</strong>e University, USATraveling Waves for Slow Erosion17:00-17:30Quansen Jiu, Capital Normal University, ChinaThe Cauchy Problem to the Kazhikhov-VaigantModel in Compressible FlowSession 9: Inverse Problems (Room: 219)Organizers: Guillaume Bal, Jin Cheng, GuntherUhlmann16:30-17:00Lassi Paivarinta, University of Helsinki,FinlandTBA17:00-17:30Jun Zou, The Chinese University of Hong Kong,Hong Kong, ChinaSome Efficient Domain Decomposition Methodsfor a Class of Inverse ProblemsSession 11: M<strong>at</strong>hem<strong>at</strong>ical Fluid Dynamicsand Rel<strong>at</strong>ed Topics (Room: 228)Organizers: Dongho Chae, Yoshikazu Giga,Yasunori Maekawa Tai-Peng Tsai16:30-16:55S<strong>at</strong>oshi Masaki, Hiroshima University, JapanClassical Limit of Some Quantum EulerEqu<strong>at</strong>ionsSession 14: Multiscale Analysis andAlgorithms (Room: 102)Organizers: Weinan E, Carlos Garcia-Cervera,Pingbing Ming16:30-17:00Weiguo Gao, Fudan University, ChinaSolving Nonlinear Eigenvalue Problem inResonant Tunneling Diodes17:00-17:30Jianfeng Lu, Duke University, USAConvergence of Force-basedAtomistic-to-continuum MethodsSession 15: Number Theory andRepresent<strong>at</strong>ion Theory (Room: 105)Organizers: Clifton Cunningham, AtsushiIchino, Vinayak V<strong>at</strong>sal16:30-17:00Gordan Savin, University of Utah, USATwisted Bhargava CubesSession 19: Represent<strong>at</strong>ion Theory andC<strong>at</strong>egorific<strong>at</strong>ion (Room: 107)Organizers: Xuhua He, Joel Kamnitzer, TonyLic<strong>at</strong>a, James Parkinson, Arun Ram16:30-17:30
40PRIMA 2013 Program- Thursday, June 27Aaron Lauda, University of SouthernCalifornia, USAKnot Invariants and Their C<strong>at</strong>egorific<strong>at</strong>ions viaHowe DualitySession 20: Singularities in Geometry andTopology (Room: 221)Organizers: Guangfeng Jiang, Laurentiu Maxim,Mutsuo Oka, Jose Seade16:30-16:55José Luis Cisneros-Molina, UniversidadNacional Autónoma de México, MéxicoOn the Topology of Real Analytic Maps17:00-17:25Donghe PeiNortheast Normal University, ChinaSingularities of Several Geometric ObjectsRel<strong>at</strong>ed to Null Curves in Minkowski 3-spaceSession 21: Symplectic Geometry andHamiltonian Dynamics (Room: 216)Organizers: Yakov Eliashberg, Yiming Long16:30-17:20Urs Frauenfelder, Seoul N<strong>at</strong>ional University,KoreaContacting the MoonSession 22: Symplectic Geometry andM<strong>at</strong>hem<strong>at</strong>ical Physics (Room: 222)Organizers: Xiaobo Liu, Huijun Fan16:30-17:15Todor Milanov, Kavli Institute for the Physicsand M<strong>at</strong>hem<strong>at</strong>ics of the Universe, JapanThe Eynard-Orantin Recursion in SingularityTheorySession 23: Triangul<strong>at</strong>ed C<strong>at</strong>egories inRepresent<strong>at</strong>ion Theory of Algebras(Room: 214)Organizers: Ragnar-Olaf Buchweitz, ShipingLiu, Claus Michael Ringel, Pu Zhang16:30-17:15Helmut Lenzing, Paderborn University,GermanyInvariant Flags for Nilpotent Oper<strong>at</strong>ors, andWeighted Projective Lines17:20-17:50Bin Zhu, Tsinghua University, ChinaT-structures and Torsion Pairs in a2-Calabi-Yau Triangul<strong>at</strong>ed C<strong>at</strong>egoryContributed Talks Group 1: Geometry andAnalysis (Room: 224)Chair: Lihe Wang, Shanghai Jiao TongUniversity, China16:30-16:50Ming Shen, Fuzhou University, ChinaVariable Equ<strong>at</strong>ion of St<strong>at</strong>e for a Dark EnergyModel with Linearly Varying Deceler<strong>at</strong>ionParameter16:50-17:10Shengda Hu, Wilfrid Laurier University,CanadaHamiltonian Group of Self Product17:10-17:30Yi Huang, The University of Melbourne,AustraliaA McShane-type Identity for Closed SurfacesContributed Talks Group 2: Algebra andNumber Theory (Room: 220))Chair: Mikhail Tyaglov, Shanghai Jiao TongUniversity, China16:30-16:50N<strong>at</strong>ella Antonyan, Techologico de Monterrey,CCM, MexicoUniversal Objects for Free G-spaces16:50-17:10Jongyook Park, University of Science andTechnology of China, ChinaOn Symmetric Associ<strong>at</strong>ion Scheme with k 1 =3and m i =3Contributed Talks Group 5: DifferentialEqu<strong>at</strong>ions (Room 229)Chair: Beixiang Fang, Shanghai Jiao TongUniversity, China16:30-16:50
41PRIMA 2013 Program- Thursday, June 27Fang Wang, Princeton University, USAOn the Radi<strong>at</strong>ion Field for Wave Equ<strong>at</strong>ions16:50-17:10Tsing-San Hsu, Chang Gung University,TaiwanMultiplicity of Positive Solutions for ap-q-Laplacian Equ<strong>at</strong>ion with CriticalNonlinearities17:10-17:30Lei Yu, SISSA, ItalyGlobal Structure of Admissible BV Solutions toStrictly Hyperbolic Conserv<strong>at</strong>ion Laws in OneSpace Dimension
42PRIMA 2013 Program- Friday, June 28Friday, June 28Morning Lectures: <strong>at</strong> Wen Zhi Hall8:30-9:20Plenary Lecture, Vaughan Jones,Vanderbilt University, USAThe Classific<strong>at</strong>ion of Subfactors of SmallIndexChair: Yujiro Kawam<strong>at</strong>a, University of Tokyo,Japan9:30-10:20Plenary Lecture, M<strong>at</strong>lide Marcolli,California Institute of Technology, USAModuli Spaces and the Field with OneElementChair: Yujiro Kawam<strong>at</strong>a, University of Tokyo,Japan10:30-11:00Coffee BreakFriday Morning Talks: <strong>at</strong>Engineering Hall11:00-12:00Pingbing Ming11:00-11:30Xiao-Ping Wang, Hong Kong University ofScience and Technology, Hong Kong, ChinaModeling and Simul<strong>at</strong>ion of Three-componentFlows on Solid Surface11:30-12:00Weiqing Ren, N<strong>at</strong>ional University of Singaporeand Institute of High Performance Computing,SingaporeThe Growing String Method for Saddle PointSearchSession 20: Singularities in Geometry andTopology (Room: 221)Organizers: Guangfeng Jiang, Laurentiu Maxim,Mutsuo Oka, Jose Seade11:00-11:25Laurentiu Paunescu, The University of Sydney,AustraliaNewton-Puiseux Analysis11:30-11:55Mutsuo Oka, Tokyo University of Science,JapanIntersection Theory on Mixed CurvesSession 9: Inverse Problems (Room: 219)Organizers: Guillaume Bal, Jin Cheng, GuntherUhlmann11:00-11:30Plamen Stefanov, Purdue University, USALocal Lens Rigidity11:30-12:00Jin Kenn Seo, Yongsei University, KoreaRecent Progress in Electrical Tissue PropertyMRISession 14: Multiscale Analysis andAlgorithms (Room: 102)Organizers: Weinan E, Carlos Garcia-Cervera,Session 22: Symplectic Geometry andM<strong>at</strong>hem<strong>at</strong>ical Physics (Room: 222)Organizers: Xiaobo Liu, Huijun Fan11:00-12:00Jian Zhou, Tsinghua University, ChinaGopakumar-Vafa Invariants of LocalCalabi-Yau 3-FoldsSession 23: Triangul<strong>at</strong>ed C<strong>at</strong>egories inRepresent<strong>at</strong>ion Theory of Algebras(Room: 214)Organizers: Ragnar-Olaf Buchweitz, ShipingLiu, Claus Michael Ringel, Pu Zhang11:00-11:30
43PRIMA 2013 Program- Friday, June 28Quanshui Wu, Fudan University, ChinaSome Results Rel<strong>at</strong>ed to Poisson (co)Homology11:30-12:00Jiaqun Wei, Nanjing Normal University, ChinaToward Repetitive EquivalencesContributed Talks Group 1: Geometry andAnalysis (Room: 224)Chair: Yihu Yang, Shanghai Jiao TongUniversity, China11:00-11:20Jagjit Singh M<strong>at</strong>haru, Guru Nanak DevUniversity, IndiaSome Inequalities for Unitarily Invariant Norms11:20 -11:40Luis Manuel Tovar Sanchez, InstitutoPolitecnico Nacional, MexicoWeighted Harmonic Spaces11:40-12:00Massoud Amini, Institute for Research inFundamental Sciences, IranBounded Oper<strong>at</strong>ors on Hilbert C * -modulesContributed Talks Group 4: Comput<strong>at</strong>ionalM<strong>at</strong>hem<strong>at</strong>ics & Optimiz<strong>at</strong>ion (Room: 216)Chair: Xiaoqun Zhang, Shanghai Jiao TongUniversity, China11:00-11:20Wei Weng, Waseda University, JapanApplic<strong>at</strong>ion of MILP to Solve ComplexScheduling Problems11:20-11:40Pablo Zafra, Kean University, U.S.A.Calcul<strong>at</strong>ing Areas and Volumes with Rot<strong>at</strong>edAxis11:40-12:00Chang Yang, Université Claude Bernard Lyon 1,FranceEfficient Numerical Method for BoundaryConditions of Kinetic Equ<strong>at</strong>ionsContributed Talks Group 5: DifferentialEqu<strong>at</strong>ions (Room:229)Chair: Yachun Li, Shanghai Jiao TongUniversity, China11:00-11:20Jianzhong Su, University of Texas <strong>at</strong> Arlington,USADynamics in Immune Reactions during WoundHealing Processes11:20-11:40Bin Cheng, University of Surrey, UKAnalysis of Some Nonlinear PDEs fromMulti-scale Geophysical Applic<strong>at</strong>ions11:40-12:00Aimin Huang, Indiana University, USAThe Linear Hyperbolic Initial Boundary ValueProblems in a Domain with Corners12:00-14:00LunchAfternoon Sessions: <strong>at</strong>Engineering Hall14:00-16:00Session 5: Combin<strong>at</strong>orics and DiscreteM<strong>at</strong>hem<strong>at</strong>ics (Room: 202)Organizers: Andreas Dress, Jing Huang,Yaokun Wu14:00-14:30Mikhail Tyaglov, Shanghai Jiao TongUniversity, ChinaA Class of Periodic Continued Fractions andFactoriz<strong>at</strong>ion in Modular Group14:30-15:00David Bryant, University of Otago, NewZealand and Simon Fraser University, CanadaFrom Metrics to Diversities15:00-15:30Stefan Grünewald, CAS-MPG Partner Instituteand Key Lab for Comput<strong>at</strong>ional Biology (PICB),ChinaSlim Systems of Binary Phylogenetic Trees15:30-16:00
44PRIMA 2013 Program- Friday, June 28Andreas Dress, CAS-MPG Partner Institute andKey Lab for Comput<strong>at</strong>ional Biology (PICB),ChinaWh<strong>at</strong> is and to Which End Does One StudyPhylogenetic Combin<strong>at</strong>orics?Session 7: Geometric Aspects of SemilinearElliptic Equ<strong>at</strong>ions: Recent Advances & FuturePerspectives (Room: 218)Organizers: Nassif Ghoussoub, Manuel delPino, Juncheng Wei14:00-14:30Shin-Hwa Wang, N<strong>at</strong>ional Tsing HuaUniversity, TaiwanGlobal Bifurc<strong>at</strong>ion Diagrams and ExactMultiplicity of Positive Solutions for aOne-dimensional Prescribed Mean Curv<strong>at</strong>ureProblem Arising in MEMS14:30-15:00Qiuping LiuTBASession 9: Inverse Problems (Room: 219)Organizers: Guillaume Bal, Jin Cheng, GuntherUhlmann14:00-14:30Xu Zhang, Sichuan University, ChinaStochastic Controllability15:00-15:30Lingyun Qiu, Purdue University, USAInverse Boundary Value Problems forTime-harmonic Acoustic Waves:Conditional Stability and Iter<strong>at</strong>iveReconstruction15:30-16:00Shuai Lu, Fudan University, ChinaOn the Inverse Problems for the CoupledContinuum Pipe Flow Model for Flows in KarstAquifers16:30-17:00Jin Cheng, Fudan University, ChinaTBASession 14: Multiscale Analysis andAlgorithms (Room: 102)Organizers: Weinan E, Carlos Garcia-Cervera,Pingbing Ming14:00-14:30Pingbing Ming, Institute of Comput<strong>at</strong>ionalM<strong>at</strong>hem<strong>at</strong>ics, CAS, ChinaGhost Forces for Multiscale Coupling Methodsin Solids14:30-15:00Carlos J. García-Cervera, University ofCalifornia, Santa Barbara, USAQuantum, Kinetic and HydrodynamicDescriptions on Spin Transfer Torque15:00-15:30Wei Cai, University of North Carolina <strong>at</strong>Charlotte, USA and Shanghai Jiao TongUniversity, ChinaA Hybrid Method for Solving Laplace Equ<strong>at</strong>ionswith Dirichlet D<strong>at</strong>a Using Local BoundaryIntegral Equ<strong>at</strong>ions and Random WalksSession 20: Singularities in Geometry andTopology (Room: 221)Organizers: Guangfeng Jiang, Laurentiu Maxim,Mutsuo Oka, Jose Seade14:00-14:25Haydée AguilarCabrera, N<strong>at</strong>ionalAotonomous University of Mexico, MexicoThe Topology of Real Suspension Singularitiesof Type14:30-14:55Laurentiu Maxim, University ofWisconsin-Madison, USACharacteristic Classes of Singular ToricVarieties15:00-15:25Rong Du,East China Normal University, ChinaOn Griffiths Numbers for Higher DimensionalIsol<strong>at</strong>ed Singularities15:25 -15:55Terence Gaffney, Northeastern University,USAEquisingularity and Integral Closure of Idealsand Modules: Two Partners in a Dance
45PRIMA 2013 Program- Friday, June 28Session 22: Symplectic Geometry andM<strong>at</strong>hem<strong>at</strong>ical Physics (Room: 222)Organizers: Xiaobo Liu, Huijun Fan14:00-14:45Bumsig Kim, Korea Institute for AdvancedStudy, KoreaQuasimap Invariants and Mirror Maps15:00-16:00Youjin Zhang, Tsinghua University, ChinaOn a Certain Generaliz<strong>at</strong>ion of VirasoroConstraints for Frobenius ManifoldsSession 23: Triangul<strong>at</strong>ed C<strong>at</strong>egories inRepresent<strong>at</strong>ion Theory of Algebras(Room: 214)Organizers: Ragnar-Olaf Buchweitz, ShipingLiu, Claus Michael Ringel, Pu Zhang14:00-14:30Lidia Angeleri Huegel, University of Verona,ItalyDerived Simple Algebras14:35-15:05Xiao-Wu Chen, University of Science andTechnology of China, ChinaSingular Equivalences with Examples15:10-15:55Ragnar-Olaf Buchweitz, University of TorontoScarborough, CanadaAutoequi valences under Derived EquivalencesContributed Talks Group 1: Geometry andAnalysis (Room: 224)Chair: Chunqin Zhou, Shanghai Jiao TongUniversity, China14:00-14:20Xiaobin Li, Southwest Jiaotong University,ChinaA New Gluing Recursive Rel<strong>at</strong>ion for LinearSigma Model of P 1 -orbifold14:20-14:40Sergey Antonyan, N<strong>at</strong>ional University ofMexico, MexicoGromov-Hausdorff Hyperspaces of R nContributed Talks Group 4: Comput<strong>at</strong>ionalM<strong>at</strong>hem<strong>at</strong>ics & Optimiz<strong>at</strong>ion (Room: 216)Chair: Min Tang, Shanghai Jiao TongUniversity, China14:00-14:20Pengtao Sun, University of Nevada Las Vegas,USAFull Eulerian Finite Element Methods forFluid-structure Interaction Problem in FictitiousDomain and Phase Field Approaches14:20-14:40Jintao Cui, University of Arkansas <strong>at</strong> LittleRock, USAAn Analysis of HDG Methods for the HelmholtzEqu<strong>at</strong>ion14:40-15:00Ning Ruan, University of Ballar<strong>at</strong>, AustraliaEfficient Duality Method to a Class of GlobalOptimiz<strong>at</strong>ions Problems with NonconvexObjective FunctionContributed Talks Group 5: DifferentialEqu<strong>at</strong>ions (Room: 229)Chair: Shijin Deng, Shanghai Jiao TongUniversity, China14:00-14:20Ying Wang, University of Minnesota, USAThe Half Line versus Finite Domain Problems ofthe Modified Buckley-Leverett Equ<strong>at</strong>ion14:20-14:40XinAn Wang, Shanghai Jiao Tong University,ChinaConstructing Global Lyapunov Function forComplex Systems14:40-15:00Larry Wang, Southern Polytechnic St<strong>at</strong>eUniversity, USARel<strong>at</strong>ionship between Omega-limit Sets andMinimal Sets15:20-15:40Baili Chen, Gustavus Adolphus College, USANonlinear Impulsive Differential Equ<strong>at</strong>ionsArising from Chemotherapeutic Tre<strong>at</strong>ment
1 PRIMA 2013 AbstractsContents1 Public Lectures 22 Plenary Lectures 23 Special Sessions 4Special Session 1A Glimpse of Stochastic Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Special Session 2Algebraic and Complex Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Special Session 3Algebraic Topology and Rel<strong>at</strong>ed Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Special Session 4Applic<strong>at</strong>ions of Harmonic Maps and Submanifold Theory . . . . . . . . . . . . . . . . . . . 8Special Session 5Combin<strong>at</strong>orics and Discrete M<strong>at</strong>hem<strong>at</strong>ics . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Special Session 6Geometric Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Special Session 7Geometric Aspects of Semilinear Elliptic Equ<strong>at</strong>ions: Recent Advances & Future Perspectives 15Special Session 8Hyperbolic Conserv<strong>at</strong>ion Laws and Rel<strong>at</strong>ed Applic<strong>at</strong>ions . . . . . . . . . . . . . . . . . . . 17Special Session 9Inverse Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Special Session 10Kinetic Equ<strong>at</strong>ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Special Session 11M<strong>at</strong>hem<strong>at</strong>ical Fluid Dynamics and Rel<strong>at</strong>ed Topics . . . . . . . . . . . . . . . . . . . . . . 22Special Session 12M<strong>at</strong>hem<strong>at</strong>ics of String Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Special Session 13Measurable and Topological Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Special Session 14Multiscale Analysis and Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Special Session 15Number Theory and Represent<strong>at</strong>ion Theory . . . . . . . . . . . . . . . . . . . . . . . . . 29Special Session 16Oper<strong>at</strong>or Algebras and Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 31Special Session 17Optimiz<strong>at</strong>ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Special Session 18Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Special Session 19Represent<strong>at</strong>ion Theory and C<strong>at</strong>egorific<strong>at</strong>ion . . . . . . . . . . . . . . . . . . . . . . . . . 38Special Session 20Singularities in Geometry and Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Special Session 21Symplectic Geometry and Hamiltonian Dynamics . . . . . . . . . . . . . . . . . . . . . . 42Special Session 22Symplectic Geometry and M<strong>at</strong>hem<strong>at</strong>ical Physics . . . . . . . . . . . . . . . . . . . . . . . 43Special Session 23Triangul<strong>at</strong>ed C<strong>at</strong>egories in Represent<strong>at</strong>ion Theory of Algebras . . . . . . . . . . . . . . . . 454 Contributed Talks 47Contributed Talks Group 1Geometry and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Contributed Talks Group 2Algebra and Number Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Contributed Talks Group 3Discrete M<strong>at</strong>hem<strong>at</strong>ics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Contributed Talks Group 4Comput<strong>at</strong>ional M<strong>at</strong>hem<strong>at</strong>ics & Optimiz<strong>at</strong>ion . . . . . . . . . . . . . . . . . . . . . . . . . 53Contributed Talks Group 5Differential Equ<strong>at</strong>ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Contributed Talks Group 6Probability and St<strong>at</strong>istics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2 PRIMA 2013 Abstracts1 Public LecturesComputers and m<strong>at</strong>hem<strong>at</strong>ics:prospectsRon GrahamUniversity of California, San Diego, USAgraham@ucsd.eduproblems andThere is no question th<strong>at</strong> the recent advent of the moderncomputer has had a dram<strong>at</strong>ic impact on wh<strong>at</strong> m<strong>at</strong>hem<strong>at</strong>iciansdo and on how they do it. However, there is increasingevidence th<strong>at</strong> many apparently simple problemsmay in fact be forever beyond any conceivable computer<strong>at</strong>tack. In this talk, I will describe a variety of m<strong>at</strong>hem<strong>at</strong>icalproblems in which computers have had, may have orwill probably never have a significant role in their solutions.Of triangles, gas, prices and menCédric VillaniUniversité de Lyon and Institut Henri Poincaré, Francevillani@ihp.frThe story of m<strong>at</strong>hem<strong>at</strong>ical progress coming from the accidentalencounter of three different fields which seemedto have hardly anything in common.2 Plenary LecturesRandom walks and percol<strong>at</strong>ionMartin BarlowUniversity of British Columbia, Canadabarlow@m<strong>at</strong>h.ubc.caAround 1960 de Giorgi, Moser and Nash proved regularityfor the he<strong>at</strong> equ<strong>at</strong>ion associ<strong>at</strong>ed with divergence formPDE:∂u∂t = Lu, u = u(x, t), x ∈ Rd , t > 0. (1)Here L = ∇a∇, where a = a ij (x) is uniformly elliptic. Inthe special case when a = ρ(x)I, (1) describes he<strong>at</strong> flowin a medium of varying conductivity ρ, and uniformlyelliptic means th<strong>at</strong> ρ is bounded away from 0. If on theother hand Z = {x : ρ(x) = 0} ̸= ∅, then the zero regionscan form barriers, and the behaviour of solutions to (1)will depend on the detailed geometry of Z.As an approach to problems of this kind, one can considerdiscrete approxim<strong>at</strong>ions to (1). One such is percol<strong>at</strong>ionon the Euclidean l<strong>at</strong>tice Z d , which was introduced byBroadbent and Hammersley in 1957. Let p be a fixedprobability between 0 and 1. Each bond in Z d is retainedwith probability p, and removed with probability 1 − p,independently of all the others. If p is larger than somecritical value p = p c(d) then the resulting graph has aunique infinite connected component C. De Gennes in1976 called the random walk on C the ‘the ant in thelabyrinth’. The problem is rel<strong>at</strong>ed to the he<strong>at</strong> equ<strong>at</strong>ion,since if p(n, x, y) is the probability th<strong>at</strong> a random walker(‘the ant’), starting <strong>at</strong> x, is <strong>at</strong> y <strong>at</strong> time n, then p s<strong>at</strong>isfiesa discrete version of (1).The PDE techniques of Nash and Moser have proved veryuseful in these contexts. I will discuss recent progress onthese models, and in particular will discuss the proof ofGaussian bounds for p n, and a central limit theorem forthe (rescaled) random walk.The M<strong>at</strong>hem<strong>at</strong>ics of CrimeAndrea BertozziUniversity of California, Los Angeles, USAbertozzi@m<strong>at</strong>h.ucla.eduThere is an extensive applied m<strong>at</strong>hem<strong>at</strong>ics liter<strong>at</strong>ure developedfor problems in the biological and physical sciences.Our understanding of social science problems froma m<strong>at</strong>hem<strong>at</strong>ical standpoint is less developed, but alsopresents some very interesting problems. This lectureuses crime as a case study for using applied m<strong>at</strong>hem<strong>at</strong>icaltechniques in a social science applic<strong>at</strong>ion and coversa variety of m<strong>at</strong>hem<strong>at</strong>ical methods th<strong>at</strong> are applicable tosuch problems. We will review recent work on agent basedmodels, methods in linear and nonlinear partial differentialequ<strong>at</strong>ions, vari<strong>at</strong>ional methods for inverse problemsand st<strong>at</strong>istical point process models. From an applic<strong>at</strong>ionstandpoint we will look <strong>at</strong> problems in residentialburglaries and gang crimes. Examples will consider bothbottom up and top down approaches to understandingthe m<strong>at</strong>hem<strong>at</strong>ics of crime, and how the two approachescould converge to a unifying theory.The exact renormaliz<strong>at</strong>ion group flowWeinan EPeking University, China and Princeton University, USAweinan@m<strong>at</strong>h.princeton.eduRenormaliz<strong>at</strong>ion and renormaliz<strong>at</strong>ion group is the mostimportant theoretical advance in the second half of thelast centrury in physics. At its heart is a m<strong>at</strong>hem<strong>at</strong>icaltool for handling singularities, infinities and complexsystems involving multiple scales. Yet <strong>at</strong> the m<strong>at</strong>hem<strong>at</strong>icallevel, it still remains to be somewh<strong>at</strong> of a mysterious,ad hoc and even dubious procedure. We will discussour effort to develop the m<strong>at</strong>hem<strong>at</strong>ical found<strong>at</strong>ionof the exact renormaliz<strong>at</strong>ion group flow. We will startwith some simple examples (central limit theorem, extremest<strong>at</strong>istics, homogeniz<strong>at</strong>ion) and then discuss applic<strong>at</strong>ionsto stochastic PDEs, quantum field theory andturbulent transport. This is joint work with Hao Shen,Yajun Zhou and Qingyun Sun.Sphere packings, symplectic l<strong>at</strong>tices and RiemannsurfacesJun-Muk HwangKorea Institute for Advanced Study, Koreajmhwang@kias.re.krSymplectic l<strong>at</strong>tices are l<strong>at</strong>tices in Euclidean space withcertain extra-symmetries associ<strong>at</strong>ed to Hermitian forms.They correspond to principally polarized abelian varietiesin algebraic geometry. Classical examples are given by periodl<strong>at</strong>tices of compact Riemann surfaces.Our theme is the density of sphere packing for symplecticl<strong>at</strong>tices. In their seminal work in 1994, Buser andSarnak showed th<strong>at</strong> peorid l<strong>at</strong>tices of compact Riemannsurfaces give remarkably poor sphere packing. FollowingBuser-Sarnak’s work, many interesting rel<strong>at</strong>ions betweenthe density of sphere packing for symplectic l<strong>at</strong>tices andalgebro-geometric properties of corresponding abelian varietieshave been discovered. We will give an overview ofthis subject with a report on a recent work on period l<strong>at</strong>ticesof Prym varieties, another important class of symplecticl<strong>at</strong>tices arising from algebraic geometry.The classific<strong>at</strong>ion of subfactors of small indexVaughan JonesVanderbilt University, USAvfr@m<strong>at</strong>h.berkeley.eduStarting with the definition of a von Neumann algebra Iwill survey old and new developments in the index theory
3 PRIMA 2013 Abstractsof subfactors which suggest th<strong>at</strong> a complete classific<strong>at</strong>ionof "nice" subfactors may be possible up to index 6. Atindex 6 certain wild phenomena begin even for the nicesubfactors.Web Markov skeleton processes and their applic<strong>at</strong>ionsZhi-Ming MaAcademy of M<strong>at</strong>hem<strong>at</strong>ics and Systems Science, CAS,Chinamazm@amt.ac.cnRecently a new class of stochastic processes, Web MarkovSkeleton Processes (WMSP), has been found to be veryuseful in the study of inform<strong>at</strong>ion retrieval on the Web.In our research we found th<strong>at</strong> the framework of WMSPenjoys also many interesting theoretical properties by itsown. In this talk I shall briefly review some of our workin this research direction. I shall introduce the notion ofWMSP, compare it with the previous notion of Markovskeleton processes introduced and studied by Hou el.al.,discuss the rel<strong>at</strong>ion between WMSP and multivari<strong>at</strong>epoint processes, discuss in detail the properties of mirrorsemi-Markov processes, a new class of processes inWMSP family. At the end of my talk I shall briefly explorethe applic<strong>at</strong>ions of WMSP in modeling user browsingbehaviour on the web.Moduli spaces and the field with one elementM<strong>at</strong>ilde MarcolliCalifornia Institute of Technology, USAm<strong>at</strong>ilde@caltech.eduThis lecture is based on joint work with Yuri Manin(arXiv:1302.6526). Using a point of view on geometryover the “field with one element" based on torific<strong>at</strong>ions,developed by López-Peña and Lorscheid, we describe anotion of constructible sets over F 1 , given in terms of suitabledifferences of torific<strong>at</strong>ions with a positivity conditionon the class in the Grothendieck ring. We then show th<strong>at</strong>the operad of moduli spaces of genus zero curves withmarked points can be endowed with descent d<strong>at</strong>a to F 1 .We show th<strong>at</strong> other moduli spaces generalizing the caseof genus zero curves also give rise to operads defined overF 1 .Combin<strong>at</strong>orics, represent<strong>at</strong>ions, homogeneousspaces and elliptic cohomologyArun RamUniversity of Melbourne, Australiaaram@unimelb.edu.auThis talk will give an elementary survey of recent developmentsin combin<strong>at</strong>orial represent<strong>at</strong>ion theory, whereinput from stable homotopy theory and algebraic topologyenters. The theory of p-compact groups founded byDwyer and Wilkerson gives rise to homogeneous spacesth<strong>at</strong> generalize the combin<strong>at</strong>orics of Lie theory, and theframework of generalized cohomology theories (elliptic cohomologyand cobordism) provides new insight into classicalintersection theory comput<strong>at</strong>ions for Grassmanniansand flag varieties. In both cases, the study of possible generaliz<strong>at</strong>ionsof the Weyl character formula, and their rel<strong>at</strong>ionto Atiyah-Bott localiz<strong>at</strong>ion formulas provides usefulmotiv<strong>at</strong>ion and insight. The combin<strong>at</strong>orial aspect providespowerful elementary models for all of these objects.During last thirty years, there has been a gre<strong>at</strong> deal ofinteractions between m<strong>at</strong>hem<strong>at</strong>ics and physics. Duringthese interactions, m<strong>at</strong>hem<strong>at</strong>ician are often impressed bythe magic formula and conjectures physicists can comeup. At the same time, it is frustr<strong>at</strong>ing th<strong>at</strong> we can notcome up the similar formula and conjecture by our own.In the talk, I will illustr<strong>at</strong>e how to apply a simple physicalprincipal (quantiz<strong>at</strong>ion principal) to discover several newarea of m<strong>at</strong>hem<strong>at</strong>ics.Geometric class field theory and existenceconjecture of smooth l-adic sheaves on varietiesover finite fieldsShuji SaitoTokyo Institute of Technology, Japansshuji@msb.biglobe.ne.jpA main result of this talk is a proof of the rank one caseof an existence conjecture for smooth l-adic sheaves on asmooth variety X over a finite field due to Deligne andDrinfeld. The conjecture says th<strong>at</strong> a comp<strong>at</strong>ible systemof smooth l-adic sheaves on the curves on X, s<strong>at</strong>isfying acertain boundedness condition for ramific<strong>at</strong>ion <strong>at</strong> infinity,should arise from a smooth l-adic sheaf on X. It may beviewed as an arithmetic analogue of a well-known fact intopology th<strong>at</strong> the fundamental group of a CW complex isdetermined by its 2-skeleton. The problem is transl<strong>at</strong>edinto the language of geometric class field theory, whichdescribes the abelian fundamental group of X by Chowgroups of zero cycles with modulus.To give a more precise st<strong>at</strong>ement, let S r(X) be the set ofsmooth l-adic sheaves on X of rank r up to isomorphismand up to semi-simplific<strong>at</strong>ion. Let Cu(X) be the set ofnormaliz<strong>at</strong>ions of integral curves on X. Let Sk r(X) bethe set of systems (V Z ) Z∈Cu(X) with V Z ∈ S r(Z) suchth<strong>at</strong>(V Z ) |Z×X Z ′ =(V Z ′) |Z× X Z ′ for Z, Z′ ∈Cu(X).Such a system is called a skeleton sheaf on X (closedpoints and curves on X are viewed as 1-skeleton and 2-skeleton of X respectively). The question is how to determinethe image of the restriction mapS r(X) → Sk r(X),i.e. when a skeleton sheaf on X glues to a smooth l-adic sheaf on X. We explain a conjecture of Deligne(motiv<strong>at</strong>ed by work of Drinfeld) on the problem whichdescribes the image in terms of a ramific<strong>at</strong>ion condition<strong>at</strong> infinity and prove the conjecture in case r = 1 usinggeometric class field theory.Geometric quantiz<strong>at</strong>ion formulas on symplecticmanifoldsWeiping ZhangNankai University, Chinaweiping@nankai.edu.cnWe describe the theme of “Quantiz<strong>at</strong>ion commutes withreduction" on symplectic manifolds admitting a Hamiltonnianaction of a compact Lie group, which on compactmanifolds concerns the Guillemin-Sternberg conjectureand on noncompact manifolds concerns a conjectureof Vergne.Searching the quantum symmetryYongbin RuanUniversity of Michigan, Ann Arbor, USAruan@umich.edu
4 PRIMA 2013 Abstracts3 Special SessionsSpecial Session 1A Glimpse of Stochastic DynamicsPerspectives in stochastic dynamics — modeling,analysis and comput<strong>at</strong>ionJinqiao DuanInstitute for Pure and Applied M<strong>at</strong>hem<strong>at</strong>ics, USAjduan@ipam.ucla.eduDynamical systems arising in engineering and science areoften subject to random influences. The noisy processesmay be Gaussian or non-Gaussian, which are modeledby Brownian motion or stable Levy motion, respectively.Non-Gaussianity of the noise manifests as nonlocality <strong>at</strong>a "macroscopic" level. Stochastic partial/ordinary differentialequ<strong>at</strong>ions with Brownian motion or Levy motionare appropri<strong>at</strong>e models for these systems.To understand dynamics under uncertainty, topological,geometric and analytical approaches are taken to examinethe quantities th<strong>at</strong> carry dynamical inform<strong>at</strong>ion and thestructures th<strong>at</strong> act as dynamical skeletons. In particular,within the analytical approaches, a quantity called scapeprobability is investig<strong>at</strong>ed and computed in order to describetransitions between dynamical regimes. This leadsto consider<strong>at</strong>ion of a deterministic nonlocal partial differentialequ<strong>at</strong>ion. Moreover, the non-Gaussianity index inLevy motion is estim<strong>at</strong>ed by solving an inverse problemfor this nonlocal partial differential equ<strong>at</strong>ion, with the observ<strong>at</strong>ionon escape probability.The speaker will fist present an overview of available theoreticaland numerical techniques for investig<strong>at</strong>ing stochasticdynamical systems, highlighting some delic<strong>at</strong>e andprofound impact of noise on dynamics. Then, he will focuson understanding stochastic dynamics by examining“escape probability in the context of prototypical examplesin biophysical and physical settings.Large devi<strong>at</strong>ions for the stochastic twocomponentb-family systemHongjun GaoNanjing Normal University, Chinagaohj@njnu.edu.cnA Wentzell-Freidlin type large devi<strong>at</strong>ion principle is establishedfor the stochastic two-component b-family systemperturbed by a multiplic<strong>at</strong>ive noise. Firstly, the localwell-posedness of the stochastic two-component b-familysystem is proved by regulariz<strong>at</strong>ion. Then, the large devi<strong>at</strong>ionprinciple is obtained by weak convergence method.Refinements of the Shannon-McMillan-Breiman theoremGuangyue HanUniversity of Hong Kong, Hong Kong, Chinaghan@hku.hkIn this talk, under mild assumptions, we derive a lawof large numbers, a central limit theorem with an errorestim<strong>at</strong>e, an almost sure invariance principle and a variantof the Chernoff bound in finite-st<strong>at</strong>e hidden Markovmodels. These limit theorems, which can be refinementsof the celebr<strong>at</strong>ed Shannon-McMillan-Breiman theorem,are of interest in certain areas of inform<strong>at</strong>ion theory andst<strong>at</strong>istics. Particularly, in inform<strong>at</strong>ion theory, these limittheorems can be used to calcul<strong>at</strong>e the capacity of a classof finite-st<strong>at</strong>e channels, and in st<strong>at</strong>istics, they can used toderive the r<strong>at</strong>e of convergence of the maximum likelihoodestim<strong>at</strong>or in finite-st<strong>at</strong>e hidden Markov models.Convergent analysis of methods for non-linearfiltering problemsXiaoying HanAuburn University, USAxzh0003@auburn.eduOptimal filtering problems are important in signal processingand rel<strong>at</strong>ed fields. Most of the time the optimalfilter does not admit a closed-form expression, and variousnumerical methods are developed to solve the filteringproblem. Among these methods, particle filter is awidely used tool for numerical prediction of complex systemswhen observ<strong>at</strong>ion d<strong>at</strong>a are available. In this talkI will first give a brief introduction on particle filteringand present error analysis on the numerical formul<strong>at</strong>ionof particle filter. Then I will introduce an implicit filteringmethod, along with its convergence results.Fast analysis of dynamic systems via Gaussianemul<strong>at</strong>orSamuel KouHarvard University, USAkou@st<strong>at</strong>.harvard.eduDynamic systems are used in modeling diverse behaviorsin a wide variety of scientific areas. Current methodsfor estim<strong>at</strong>ing parameters in dynamic systems from noisyd<strong>at</strong>a are comput<strong>at</strong>ionally intensive (for example, relyingheavily on the numerical solutions of underlying differentialequ<strong>at</strong>ions). We propose a new inference method bycre<strong>at</strong>ing a system driven by a Gaussian process to mirrorthe dynamic system. Auxiliary variables are introducedto connect this Gaussian system to the real dynamic system;and a sampling scheme is introduced to minimizethe "distance" between these two systems iter<strong>at</strong>ively. Thenew inference method also covers the partially observedcase in which only certain components of the dynamicsystem are observed. The method offers a drastic savingof comput<strong>at</strong>ional time and fast convergence while still retaininghigh estim<strong>at</strong>ion accuracy. We will illustr<strong>at</strong>e themethod by numerical examples.On time regularity of SPDE driven by Levynoise in Hilbert spacesYong LiuPeking University, Chinaliuyong@m<strong>at</strong>h.pku.edu.cnIn this talk, we will present some new progresses onthe time regulaity of generalized Ornstein-Uhlenbeck processesdriven by Levy processes in Hilbert spaces. Thistalk is based on the following articles:1. Brzezniak, Z., Goldys, B., Imkeller, P., Pesz<strong>at</strong>, S.,Priola, E., Zabczyk, J. Time irregularity of generalizedOrnstein-Uhlenbeck processes, C. R. Acad. Sci. Paris,Ser. I 348(2010).2. Liu, Y., Zhai, J.L. A note on time regularity of generalizedOrnstein-Uhlenbeck processes with cylindrical stablenoise, C. R. Acad. Sci. Paris, Ser. I 350(2012).3. Pesz<strong>at</strong>, S., Zabczyk, J.Time regularity of solutions tolinear equ<strong>at</strong>ions with Levy noise in infinite dimensions,Stochastic Processes and their Applic<strong>at</strong>ions, 123(3), 2013.4. Liu, Y., Zhai, J.L. On time regularity of SPDE inHilbert spaces, 2013. Preprint.Some results for discontinuous random dynamicalsystemsHuijie QiaoSoutheast University, Chinahjqiaogean@seu.edu.cnIn the talk, first of all, discontinuous random dynamicalsystems are introduced. Next, escape probability,asymptotic methods, Lyapunov exponents and topologicalequivalence, which are rel<strong>at</strong>ed with discontinuous randomdynamical systems, are presented.Fokker-Planck equ<strong>at</strong>ions for nonlinear dynamicalsystems driven by non-Gaussian Lévy
5 PRIMA 2013 AbstractsprocessesXu SunHuazhong University of Science and Technology, Chinaxsun15@gmail.com; xsun@hust.edu.cnThe Fokker-Planck equ<strong>at</strong>ions describe time evolution ofprobability densities of stochastic dynamical systems andare thus widely used to quantify random phenomenasuch as uncertainty propag<strong>at</strong>ion. For dynamical systemsdriven by non-Gaussian Lévy processes, however, it is difficultto obtain explicit forms of Fokker-Planck equ<strong>at</strong>ions.In the present paper, Fokker-Planck equ<strong>at</strong>ions are derivedfor nonlinear stochastic differential equ<strong>at</strong>ions withnon-Gaussian Lévy processes. The stochastic differentialequ<strong>at</strong>ions are considered in sense of both Ito and Marcus.A few examples are presented to illustr<strong>at</strong>e the method.P<strong>at</strong>h-dependent optimal stochastic controland viscosity solution of associ<strong>at</strong>ed Bellmanequ<strong>at</strong>ionsShanjian Tang & Fu ZhangFudan University, Chinasjtang@fudan.edu.cnAbstract In this paper we study the optimal stochasticcontrol problem for a p<strong>at</strong>h-dependent stochastic systemunder a recursive p<strong>at</strong>h-dependent cost functional, whoseassoci<strong>at</strong>ed Bellman equ<strong>at</strong>ion from dynamic programmingprinciple is a p<strong>at</strong>h-dependent fully nonlinear partial differentialequ<strong>at</strong>ion of second order. A novel notion of viscositysolutions is introduced by restricting the semi-jetson an α -Hölder space C α for α ∈ (0, 1 ). Using Dupire’s2functional Itô calculus, we prove th<strong>at</strong> the value functionalof the optimal stochastic control problem is a viscositysolution to the associ<strong>at</strong>ed p<strong>at</strong>h-dependent Bellman equ<strong>at</strong>ion.We expect th<strong>at</strong> our viscosity solution is the valuefunctional in a fairly general situ<strong>at</strong>ion.Self-similarity for some SPDEsWei WangNanjing University, Chinawangweinju@yahoo.com.cnThis talk discusses self-similarity in distribution, whichis called stochastic self-similarity, for some SPDEs. Twotypes of noise are considered, one is additive noise and theother is of some multiplic<strong>at</strong>ive noise. The existence of aself-similar solution is implied by the existence of a st<strong>at</strong>ionarysolution under self-similar variables. We furthershow the <strong>at</strong>tracting property of a self-similar solution.For the case additive noise, different <strong>at</strong>traction is consideredby different approach. For the case of multiplic<strong>at</strong>ivenoise, a diffusion approxim<strong>at</strong>ion approach is applied.The availability of logical oper<strong>at</strong>ion inducedby dichotomous noise for a nonlinear bistablesystemYong Xu, Xiaoqin Jin, Huiqing Zhang & Tingting YangNorthwestern Polytechnical University, Chinahsux3@nwpu.edu.cnąąInstead of a continuous system driven by Gaussian whitenoise, logical stochastic resonance will be investig<strong>at</strong>ed ina nonlinear bistable system with two thresholds drivenby dichotomous noise, which shows a phenomenon differentfrom Gaussian white noise. We can realize twoparallel logical oper<strong>at</strong>ions by simply adjusting the valuesof these two thresholds. Besides, to quantify the reliabilityof obtaining the correct logic output, we numericallycalcul<strong>at</strong>e the success probability, and effects of dichotomousnoise on the success probability are observed, theseobserv<strong>at</strong>ions show th<strong>at</strong> the reliability of realizing logicaloper<strong>at</strong>ion in the bistable system can be improved throughoptimizing parameters of dichotomous noise.Backward stochastic partial differential equ<strong>at</strong>ionsand their applic<strong>at</strong>ion to stochasticBlack-Scholes formulaQi ZhangFudan University, Chinaqzh@fudan.edu.cnThe backward SPDEs, origin<strong>at</strong>ed from the study of optimalcontrol theory of SPDEs, can be applied to m<strong>at</strong>hem<strong>at</strong>icalfinance problems. We demonstr<strong>at</strong>e their applic<strong>at</strong>ionto stochastic Black-Scholes formula, in a generalsetting to the parameters of the model. This applic<strong>at</strong>ionis based on our recent studies of the solvability to degener<strong>at</strong>ebackward SPDEs without technical assumptions andtheir connection to forward-backward SDEs. The connectionbetween backward SPDEs and forward-backwardSDEs can also be regarded as an extension of Feynman-Kac formula to non-Markovian framework.Malliavin m<strong>at</strong>rix of degener<strong>at</strong>e PDE and gradientestim<strong>at</strong>esDong ZhaoAcademy of M<strong>at</strong>hem<strong>at</strong>ics and Systems Science, CAS,Chinadzhao@amt.ac.cnIn this talk, we present the bounded of the inverse forMalliavin M<strong>at</strong>rix of Degener<strong>at</strong>e PDE under a new condition,which is equivalent to the Hoermander condition asthe coefficients are smooth. Also, the gradient estim<strong>at</strong><strong>at</strong>sfor the semigroup is given.Special Session 2Algebraic and Complex GeometryPluricanonical maps and minimal models ofthreefoldsJunkai ChenN<strong>at</strong>ional Taiwan University, Taiwanjkchen@ntu.edu.twGiven a smooth projective variety, there are n<strong>at</strong>ural mapsinduced by the pluricanonical system. It is n<strong>at</strong>ural to askwhen the pluricanonical maps stablized bir<strong>at</strong>ionally. Onthe other hand, it is known th<strong>at</strong> there exists a minimalmodel with terminal singularities. This model play thekey ingredient in the study of geometry of threefolds. Inthis talk, we are going to demonstr<strong>at</strong>e some applic<strong>at</strong>ionof bir<strong>at</strong>ional geometry th<strong>at</strong> one can obtain by comparingabove two structures.Some bir<strong>at</strong>ionality criteria on 3-folds withp g > 1Meng ChenFudan University, Chinamchen@fudan.edu.cnWe give some bir<strong>at</strong>ionality criteria for ϕ m (m = 4, 5, 6,7) on general type 3-folds with p g ≥ 2 by means of anintensive classific<strong>at</strong>ion.Division algebras of transcendence degree twoColin IngallsUniversity of New Brunswick, Canadacingalls@unb.caWe study Artin’s conjecture th<strong>at</strong> division algebras of fractionsof domains of dimension two are either r<strong>at</strong>ional,
6 PRIMA 2013 Abstractsruled or finite over their centres. We have a proof of theconjecture th<strong>at</strong> depends adds a few other conditions. Weshow th<strong>at</strong> such domains over finite fields are finite overtheir centres. Then a deform<strong>at</strong>ion theory argument fororders over surfaces shows th<strong>at</strong> we have Artin’s conjecturedclassific<strong>at</strong>ion. This is work in progress with JasonBell.Geometry and syzygies in the first linearstrandSijong KwakKorea Advanced Institute of Science and Technology, Koreasjkwak@kaist.ac.krProperty N d,p , d ≥ 2 for algebraic sets is defined (dueto Eisenbud-Green-Hulek-Popescu) as follows: the j-thsyzygies of the homogeneous coordin<strong>at</strong>e ring are gener<strong>at</strong>edby elements of degree ≤ d−1+j for 1 ≤ j ≤ p. Whend = 2, linear syzygies of quadr<strong>at</strong>ic schemes have been focusedfor a long time. In this talk, we consider upperbounds and lower bounds of higher linear syzygies in thefirst linear strand of Betti tables for projective varietiesin arbitrary characteristic. For this purpose, we establishfundamental inequalities which govern the rel<strong>at</strong>ionsbetween the graded Betti numbers of an algebraic set Xand those of its inner projection X q in the first linearstrand. We obtain some n<strong>at</strong>ural sharp upper bounds andlower bounds for linear syzygies of any non-degener<strong>at</strong>eprojective variety using these inequalities. We also classifywh<strong>at</strong> the extremal case and next-to-extremal caseare. From the viewpoint of ’syzygies’, this is a generaliz<strong>at</strong>ionof Castelnuovo and Fano’s results on the numberof quadrics containing a given variety.C<strong>at</strong>egorific<strong>at</strong>ion of Donaldson-Thomas invariantsand Gopakumar-Vafa invariantsJun LiStanford University, USAjli@m<strong>at</strong>h.stanford.eduFor a projective Calabi-Yau threefold, we can form themoduli of stable sheaves with prescribed Chern classes.The Donaldson-Thomas invariants of this Calabi-Yauthreefolds are virtual degrees of these moduli spaces.In this talk, we will show th<strong>at</strong> each of such modulispaces admits perverse sheaves whose Euler classes arethe Donaldson-Thomas invariants associ<strong>at</strong>ed to the modulispaces. Using such sheaves, we propose a new definitionof Gopakumar-Vafa invariants of Calabi-Yau threefolds.This is a joint work with Young-Hoon Kiem.CompactsAmnon NeemanThe Australian N<strong>at</strong>ional University, AustraliaAmnon.Neeman@anu.edu.auFor a fl<strong>at</strong> map f : X −→ Y of noetherian schemes onemay define functors Lf ∗ , Rf ∗, f × and f ! on appropri<strong>at</strong>ederived c<strong>at</strong>egories of quasicoherent sheaves. In two recentpapers, one by Avramov and Iyengar and the secondby Avramov, Iyengar, Lipman and Nayak, the authorsproved some remarkable formulas rel<strong>at</strong>ing f ! , f × and certainHochschild homology objects. I will discuss a newapproach to the results in terms of a map ψ : f × −→ f ! .Smooth quartic K3 surfaces and Cremon<strong>at</strong>ransform<strong>at</strong>ionsKeiji OguisoOsaka University, Japan and Korea Institute for AdvancedStudy, Koreaoguiso@m<strong>at</strong>h.sci.osaka-u.ac.jpWe discuss about the following question of Giz<strong>at</strong>ullin:Question. Is an automorphism g of a smooth quarticK3 surface S ⊂ P 3 derived from some bir<strong>at</strong>ional automorphism,i.e., some Cremona transform<strong>at</strong>ion of the ambientspace P 3 ? More precisely, first I explain the followingneg<strong>at</strong>ive result: Theorem 1. There is a smooth K3 surfaceS of Picard number 2 such th<strong>at</strong> (i) Aut (S) ≃ Z and(ii) No element Aut (S) other than id S is derived fromBir (P 3 ) in any embedding of S into P 3 . Then, I explainthe following positive result: Theorem 2. Thereis a smooth K3 surface S of Picard number 2 such th<strong>at</strong>(i) Aut (S) ≃ Z and (ii) Aut (S) is derived from Bir (P 3 )in any embedding of S into P 3 . As I will explain inmy talk, examples in Theorem 2 are the ones found in acompletely different context. However, they turn out tobe very closely rel<strong>at</strong>ed with old works of Cayley, Snyderand Sharpe, as it is discovered by Festi, Garbagn<strong>at</strong>i, vanGeemen and vam Luijk quite recently. Being based onall of their works, I describe the automorphism group ofthese S both explicitly algebraically in terms of homogeneouscoordin<strong>at</strong>es and explicitly geometrically in terms ofSarkisov link.The Hilbert scheme of points and extensionsof local fieldsTakehiko YasudaOsaka University, Japantakehikoyasuda@m<strong>at</strong>h.sci.osaka-u.ac.jpTwo formulas very similar to each other appear in totallydifferent contexts, the Hilbert scheme of points and Bhargava’sformula for extensions of local fields. In this talk,I will explain the similarity as a special case of the wildMcKay correspondence. The talk is based on a joint workwith Melanie M<strong>at</strong>chett Wood.Positivity of log canonical divisors andMori/Brody hyperbolicityDe-Qi ZhangN<strong>at</strong>ional University of Singapore, Singaporem<strong>at</strong>zdq@nus.edu.sgLet X be a complex projective variety of dimension n andD a reduced divisor with a decomposition D = ∑ ri=1 D i,where the D i ’s are reduced Cartier but not necessarilyirreducible. The pair (X, D) is called Brody hyperbolic,respectively Mori hyperbolic, with respect to the decompositionif neither X\D nor (∩ i∈I D i )\(∪ j∈J D j ) containsa non-constant holomorphic image, respectively algebraicimage, of C for every partition of {1, . . . , r} = I ∐ J.Assuming th<strong>at</strong> the singularities of the pair (X, D) aresufficiently mild, we show th<strong>at</strong> the log canonical divisorK X +D is numerically effective in the case of Mori hyperbolicityand th<strong>at</strong> K X + D is ample provided th<strong>at</strong> eithern < 4 and D is non-empty or <strong>at</strong> least n−2 of the D i ’s areample in the case of Brody hyperbolicity. Our proof alsogives simple geometric criteria for the log canonical divisorK X + D to be numerically effective or to be ample inthe above (respective) cases and, under weaker geometricconditions, for K X + D to be pseudo-effective. This is ajoint work with Steven Lu.Special Session 3Algebraic Topology and Rel<strong>at</strong>ed TopicsHomotopy colimits and commut<strong>at</strong>ive elementsin Lie groupsAlejandro AdemUniversity of British Columbia, Canadaadem@pims.m<strong>at</strong>h.ca
7 PRIMA 2013 AbstractsIn this talk we describe homotopy invariants for a classifyingspace assembled from the commuting elements in aLie group. This involves certain homotopy colimits overa topological poset and the resulting cohomology calcul<strong>at</strong>ionsfor the unitary groups are expressed in terms ofmultisymmetric polynomials. This is joint work with JoseGomez.The topological Hochschild homology ofThom spectra as cyclotomic spectraVigleik AngeltveitAustralian N<strong>at</strong>ional University, Australiavigleik.angeltveit@anu.edu.auOne can construct a symmetric monoidal c<strong>at</strong>egory ofspectra by finding a way to internalize the external smashproduct. There is a corresponding c<strong>at</strong>egory of "spaces",Quillen equivalent to the usual c<strong>at</strong>egory of spaces butwith a more interesting symmetric monoidal structureth<strong>at</strong> mirrors the smash product of spectra. In this settingmany constructions commute with passing to spectra.For example, taking the cyclic bar construction (in spectra)of a Thom spectrum is the same as taking the Thomspectrum of the cyclic bar construction (in "spaces").Wh<strong>at</strong>’s new is th<strong>at</strong> we can exploit an equivariant versionof this to construct topological Hochschild homologyof Thom spectra as genuine equivariant spectra with certainextra structure. This is part of work in progress withBlumberg, Gerhardt, Hill and Lawson.Universal constructions on spaces of knotsRyan BudneyUniversity of Victoria, Canadarybu@uvic.caA basic unresolved question in traditional knot theory is’wh<strong>at</strong> precisely does the Vassiliev spectral sequence tell usabout the topology of the space of knots’? I will describea current approach to this question, which takes as itsinput a fairly detailed understanding of the homotopytypeof the space of knots in S 3 coming from 3-manifoldtheory and the theory of operads.Circle actions on 5-manifoldsHaibao DuanInstitute of M<strong>at</strong>hem<strong>at</strong>ics, Chinese Academy of Sciences,Chinadhb@m<strong>at</strong>h.ac.cnA circle action S 1 × M → M on a manifold M is calledregular if the quotient space N = M/S 1 is a manifoldwith dim N = dim M − 1. We classify all the 1-connected5-manifolds th<strong>at</strong> admit regular circle actions.Cohomology of moduli spaces of manifoldsSoren Gal<strong>at</strong>iusStanford University, USAgal<strong>at</strong>ius@stanford.eduI will discuss recent joint work with Oscar Randal-Williams on the cohomology of BDiff(M) when M is asmooth even-dimensional manifold.Braid groups of surfaces and their lower algebraicK-theoryDaniel Juan PinedaN<strong>at</strong>ional Autonomous University of Mexico, Mexicodaniel@m<strong>at</strong>mor.unam.mxI will review the theory of braid groups for surfaces,some of their properties and will concentr<strong>at</strong>e on the braidgroups for the sphere and the proyective plane. I will alsoexplain how the geometry of the braid groups determinethe lower algebraic K theory of their integral group rings.Equivariant Chern numbers and the numberof fixed points for unitary torus manifoldsZhi LüFudan University, Chinazlu@fudan.edu.cnLet M 2n be a unitary torus (2n)-manifold, i.e., a (2n)-dimensional oriented stable complex connected closedT n -manifold having a nonempty fixed set. We showth<strong>at</strong> M bounds equivariantly if and only if the equivariantChern numbers 〈(c T n1 )i (c T n2 )j , [M]〉 = 0 for all i, j ∈ N,where c T nl denotes the lth equivariant Chern class of M.As a consequence, we also show th<strong>at</strong> if M does notbound equivariantly then the number of fixed points is<strong>at</strong> least ⌈ n 2 ⌉ + 1, where ⌈ n ⌉ denotes the minimal integer2no less than n 2 .Virtual orbifold cohomologyErnesto LupercioCenter for Research and Advanced Studies of the N<strong>at</strong>ionalPolytechnic Institute, Mexicolupercio@m<strong>at</strong>h.cinvestav.mxIn this talk I will introduce Virtual Orbifold Cohomologyas an open-closed nearly orbifold TQFT and explain itsrel<strong>at</strong>ion to Chen-Ruan cohomology and to String Topology.This is joint work with Ana Gonzalez, BernardoUribe and Carlos Segovia.Cohomology fo symmetric and altern<strong>at</strong>inggroupsDev P. SinhaUniversity of Oregon, USAdps@uoregon.eduThe homology and cohomology of symmetric groups hasa long history. Recently we have found th<strong>at</strong> a Hopf ringstructure first discovered by Strickland and Turner helpsto give a description of the mod-two ring structure whichgives rise to a new additive basis with explicit multiplic<strong>at</strong>ionrules, as well as clarifies and illumin<strong>at</strong>es previousapproaches. I will describe this structure, and then addressother coefficients for symmetric groups as well asthe mod-two cohomology of altern<strong>at</strong>ing groups.Classific<strong>at</strong>ion of complex projective towers upto dimension 8 and cohomological rigidityDong Youp SuhKorea Advanced Institute of Science and Technology, Koreadysuh@kaist.ac.krA complex projective tower or simply a CP -tower is an iter<strong>at</strong>edcomplex projective fibr<strong>at</strong>ions starting from a point.In this paper we classify all 6-dimensional CP -towers upto diffeomorphism, and as a consequence, we show th<strong>at</strong>all such manifolds are cohomologically rigid, i.e., they arecompletely determined up to diffeomorphism by their cohomologyrings. We also show th<strong>at</strong> cohomological rigidityis not valid for 8-dimensional CP -towers by classifyingsome CP 1 -fibr<strong>at</strong>ions over CP 3 up to diffeomorphism. As
8 PRIMA 2013 Abstractsa corollary we show th<strong>at</strong> such CP -towers are diffeomorphicif they are homotopy equivalent.Homology of Hurwitz spaces and the Cohen-Lenstra heuristicsCraig WesterlandUniversity of Melbourne, AustraliaC.Westerland@ms.unimelb.edu.auWe will examine Hurwitz moduli spaces of branched coversof Riemann surfaces, and study their stable homology(as the number of branch points tends to infinity). Theresults may be used to prove a function field analogue ofthe Cohen-Lenstra heuristics on the distribution of classgroups of imaginary quadr<strong>at</strong>ic number fields. The maintools are a homological stability theorem for these spaces,as well as an identific<strong>at</strong>ion of their limit as a space of functionsinto a target which supports a certain “universal”branched cover.On simplicial resolutions of framed linksJie WuN<strong>at</strong>ional University of Singapore, Singaporem<strong>at</strong>wujnus.edu.sgIn this paper, we investig<strong>at</strong>e the simplicial groups obtainedfrom the link groups of naive cablings on anygiven framed link. Our main result st<strong>at</strong>es th<strong>at</strong> the resultingsimplicial groups have the homotopy type of theloop space of a wedge of 3-spheres. This gives simplicialgroup models for some loop spaces using link groups.Joint with Fengchun Lei and Fengling LiRigidity of m<strong>at</strong>rix groupsShengkui YeUniversity of Oxford, UKShengkui.Ye@m<strong>at</strong>hs.ox.ac.ukLet R be a general ring and E n(R) the subgroup ofgeneral linear group gener<strong>at</strong>ed by elementary m<strong>at</strong>rices.Is there a nontrivial group homomorphism E n+1 (R) →E n(R)? I will talk about how to consider such a problemby group actions on CAT(0) spaces, spheres and acyclicmanifolds.Special Session 4Applic<strong>at</strong>ions of Harmonic Maps and SubmanifoldTheoryThe Liouville property for pseudoharmonicmaps with finite Dirichlet energyTing-Hui ChangAcademia Sinica, Taiwan, R.O.C.thc@m<strong>at</strong>h.sinica.edu.twIn this talk, we first derive the CR Bochner formula andthe CR K<strong>at</strong>o’s inequality for pseudoharmonic maps. Secondly,by applying the CR Bochner formula and the CRK<strong>at</strong>o’s inequality we are able to prove the Liouville propertyfor pseudoharmonic maps with finite Dirichlet energyin a complete (2n + 1)-pseudohermitian manifold. Thisis served as an analogue to the Liouville theorem for harmonicmaps in Riemannian Geometry.On the Toda systems of VHS typeChen-Yu ChiN<strong>at</strong>ional Taiwan University, Taiwancychi@m<strong>at</strong>h.ntu.edu.twWe consider the Toda systems of VHS type with singularsources and provide a criterion for the existence ofsolutions with prescribed asymptotic behaviour near singularities.We also prove the uniqueness of solution. Ourapproach uses Simpson’s theory of constructing Higgs-Hermitian-Yang-Mills metrics from stability.A rigidity theorem for self-shrinkers of themean curv<strong>at</strong>ure flowHezi LinFujian Normal University, Chinalhz1@fjnu.edu.cnIn this talk, by using a Simons’ type inequality and an improvedSobolev inequality of submanifolds, we can provea global rigidity theorem for self-shrinkers as hypersurfaceswhose mean curv<strong>at</strong>ure and total curv<strong>at</strong>ure s<strong>at</strong>isfysome appropri<strong>at</strong>e conditions.Geometry of Lagrangian submanifolds rel<strong>at</strong>edto isoparametric hypersurfacesYoshihiro OhnitaOsaka City University & OCAMI, Japanohnita@sci.osaka-cu.ac.jpIn this talk I shall provide a survey of my recent works andtheir environs on differential geometry of Lagrangian submanifoldsin specific Kähler manifolds, such as complexprojective spaces, complex space forms, Hermitian symmetricspaces and so on. I shall emphasis on the rel<strong>at</strong>ionshipbetween certain minimal Lagrangian submanifold incomplex hyperquadrics and isoparametric hypersurfacesin spheres. This talk is mainly based on my joint workwith Associ<strong>at</strong>e Professor Hui Ma (Tsinghua University,Beijing).Definite affine spheres by the DPW methodErxiao WangHong Kong University of Science and Technology, HongKong, Chinamaexwang@ust.hkWe will first clarify the loop group formul<strong>at</strong>ions for bothhyperbolic and elliptic proper definite affine spheres inR 3 , rel<strong>at</strong>ing them to primitive harmonic maps from aRiemann surface to 6-symmetric spaces SL 3 (R)/SO 2 (R).Then we will apply Dorfmeister-Pedit-Wu’s method togive Weierstrass type represent<strong>at</strong>ion of such surfaces usingholomorphic/meromorphic potentials. New examplesand pictures constructed from special type of potentialswill be presented in the end, including equivariant ones.This is a joint work with Professor Josef Dorfmeister.Willmore surfaces by using geometric methodsand loop group theoryPeng WangTongji University, Chinanetwangpeng@tongji.edu.cnIn this talk we will first introduce the notion of adjointtransforms of Willmore surfaces in S n . The rel<strong>at</strong>ions betweenadjoint transforms of Willmore surfaces and theother harmonic maps associ<strong>at</strong>ed with Willmore surfaced
9 PRIMA 2013 Abstractsindependently by Hélein and Xiang Ma, are also discussedbriefly. Applying the DPW methods and the theoryof Burstall-Guest for harmonic maps of finite uniton,we obtained some descriptions of adjoint transforms andHélein-Ma’s harmonic maps as well as some interestingexamples of Willmore surfaces together with their adjointsurfaces. Some of these results is an adjoint work withProf. Josef Dorfmeister.Special Session 5Combin<strong>at</strong>orics and Discrete M<strong>at</strong>hem<strong>at</strong>icsOn tight rel<strong>at</strong>ive t-designsEiichi BannaiShanghai Jiao Tong University, Chinabannai@sjtu.edu.cnThe purpose of design theory is to study good subsetswhich approxim<strong>at</strong>e the whole space. This is the case forspherical t-designs (i.e. finite subsets of spheres) or forcombin<strong>at</strong>orial t-designs, here a combin<strong>at</strong>orial t-(v, k, λ)design means a good subset which approxim<strong>at</strong>es the spaceof all k element subsets of a v set. Euclidean t-designsare certain generaliz<strong>at</strong>ions of spherical designs. Rel<strong>at</strong>ivet-designs (defined by Delsarte) are certain generaliz<strong>at</strong>ionsof combin<strong>at</strong>orial t-designs. Note th<strong>at</strong> t-designsand rel<strong>at</strong>ive t-designs are defined for any Q-polynomialassoci<strong>at</strong>ion schemes. In particular, for the binary Hammingassoci<strong>at</strong>ion scheme H(n, 2) (i.e. the n-dimensionalvector space over the binary field) the concept of rel<strong>at</strong>ivet-design is equivalent to the concept called regular t-wise balanced design in combin<strong>at</strong>orial design theory. Ourmain purpose is to study (and classify if possible) theobjects called tight design, i.e. those t-designs or rel<strong>at</strong>ivet-designs whose cardinalities <strong>at</strong>tain the n<strong>at</strong>ural lowerbounds called Fisher type lower bounds, in various situ<strong>at</strong>ions.Usually, these tight designs are expected to havegood algebraic structures, such as associ<strong>at</strong>ion schemes, orcoherent configur<strong>at</strong>ions.It is known th<strong>at</strong> there are close similarities between "theoryof spherical t-designs vs. theory of Euclidean t-designs" and "theory of combin<strong>at</strong>orial t-designs vs. theoryof rel<strong>at</strong>ive t-designs in binary Hamming schemes."The former theories have been studied more extensivelythan the l<strong>at</strong>ter ones, since spherical harmonics is moretransparent than the theory of harmonic analysis on finitehomogeneous spaces, i.e. on certain associ<strong>at</strong>ion schemes.We will discuss how much we can imit<strong>at</strong>e the former theoriesto get similar results in the l<strong>at</strong>ter case. For example,we obtain the following explicit results on tight rel<strong>at</strong>ivet-designs in binary Hamming associ<strong>at</strong>ion schemes.(i) For tight rel<strong>at</strong>ive 2e-designs in binary Hamming associ<strong>at</strong>ionschemes, the weight function must be constant oneach shell.(ii) For tight rel<strong>at</strong>ive 2-designs on two shells in binaryHamming associ<strong>at</strong>ion schemes H(n, 2), we can have thestructure of coherent configur<strong>at</strong>ions.(iii) We can classify tight rel<strong>at</strong>ive 2-designs on two shellsin binary Hamming associ<strong>at</strong>ion schemes H(n, 2) for smalln, say n ≤ 30.We will also study more general results for more generalassoci<strong>at</strong>ion schemes. The contents of this talk are basedon the following two joint papers with other authors.(1) Eiichi Bannai, Etsuko Bannai, Sho Suda and HajimeTanaka: On rel<strong>at</strong>ive t-designs in polynomial associ<strong>at</strong>ionschemes, arXiv:1303.7163(2) Eiichi Bannai, Etsuko Bannai and Hideo Bannai: Onthe existence of tight rel<strong>at</strong>ive 2-designs on binary Hammingassoci<strong>at</strong>ion schemes, arXiv:1304.5760On the efficient solution of some packing andcovering problems in graphsAndreas BrandstädtUniversity of Rostock, Germanyab@inform<strong>at</strong>ik.uni-rostock.deLet G be a finite undirected and simple graph whose set ofedges represents the “conflicts” of some objects. A packingproblem asks for a largest set of vertices which arepairwise conflict-free, and a covering problem asks for asmallest set of vertices which “cover” some objects. Typicalexamples are Maximum Independent Set as packingproblem and Minimum Vertex Cover as covering problem,however, there are many other variants such as domin<strong>at</strong>ionproblems. In many cases, the problems are alsoweighted, and sometimes covering and packing conditionsare combined. It is well known th<strong>at</strong> such problems aretypically NP-complete, and most of them are hard to approxim<strong>at</strong>e.We look <strong>at</strong> some examples such as Efficient Domin<strong>at</strong>ion,Efficient Edge Domin<strong>at</strong>ion (which is sometimes calledDomin<strong>at</strong>ing Induced M<strong>at</strong>ching), and Maximum InducedM<strong>at</strong>ching and restrict them to inputs from structuredgraph classes. If the graph class has certain kinds oftree structure, most of the problems become efficientlysolvable. This holds for tree decomposition by clique separ<strong>at</strong>orsand modular decomposition into “simple” partsas well as width restrictions such as treewidth and cliquewidth.Moreover, there are some useful closure propertiesof squares of graphs and line graphs.From metrics to diversitiesDavid Bryant & Paul TupperUniversity of Otago, New Zealand and Simon Fraser University,Canadadavid.bryant@otago.ac.nzA diversity is a generalis<strong>at</strong>ion of metric spaces to beyondpairwise comparisons. Formally, it is a pair (X, δ) whereX is a set and δ is a non-neg<strong>at</strong>ive function defined onfinite subsets of X s<strong>at</strong>isfying the two axioms1. δ(A) = 0 if and only if |A| ≤ 1;2. δ(A ∪ C) ≤ δ(A ∪ B) + δ(B ∪ C) whenever B ≠ ∅.Note th<strong>at</strong> δ restricted to pairs gives a metric. Examplesof diversities include the diameter, the mean width, thelength of the minimum tour, and the length of an optimalSteiner tree. Diversities were introduced in a recent paperof Bryant and Tupper, and gener<strong>at</strong>e a rich theory whichwe are only just beginning to explore. We survey some ofthe main results and then specul<strong>at</strong>e wildly on applic<strong>at</strong>ionsand future developments.Boxicity and cubicity of graphsLeela Sunil ChandranIndian Institute of Science, Indiasunil.cl@gmail.comA graph is said to have a d-dimensional box represent<strong>at</strong>ion(respectively cube represent<strong>at</strong>ion-we consider d-dimensional cubes of unit volume) if the vertices of Gcan be assigned axis parallel d-dimensional boxes (resp.cubes) in such a way th<strong>at</strong> two vertices are adjacent if andonly i the corresponding boxes (resp. cubes) intersect.The smallest non-neg<strong>at</strong>ive integer d for which this is possible,is the boxicity (resp. cubicity) of the graph G. Inthis talk we will present an overview of the results weobtained on boxicity and cubicity of graphs over the lastfew years. For example, we will discuss the rel<strong>at</strong>ion ofboxicity and cubicity with the width parameters such astreewidth and bandwidth, the connection between boxicityand the partial order dimension and upper boundsfor cubicity in terms of boxicity, and some interesting resultsregarding the boxicity and cubicity of certain specialclasses of graphs.Parallelohedra: from Minkowski and Voronoito the present day
10 PRIMA 2013 AbstractsNikolai DolbilinSteklov Institute of M<strong>at</strong>hem<strong>at</strong>ics, Russiadolbilin@mi.ras.ruA parallelohedron is a convex polyhedron which tiles theEuclidean space by parallel copies in face-to face way. Theconcept of parallelohedron was introduced by E. Fedorov,the Russian crystallographer. He found all the five combin<strong>at</strong>orialtypes of 3-dimensional parallelohedra which areof gre<strong>at</strong> importance in crystallography. High-dimensionalparallelohedra have many applic<strong>at</strong>ions in geometry ofnumbers and some other other fields of m<strong>at</strong>hem<strong>at</strong>ics. Inaddition, high-dimensional parallelohedra present an extremelyinteresting class of polyhedra in itself. An obviousexample of a parallelohedron of any dimension isthe parallelepiped. Much more interesting type of a parallelohedronis presented by the permutahedron of anydimension.First fundamental theorems on parallelohedra were beenfound by H. Minkowski. G. Voronoi developed the theoryof a special type of a parallelohedra th<strong>at</strong> are Voronoiregions for l<strong>at</strong>tices and now called the Voronoi parallelohedra.Voronoi showed their importance for the studyof arbitrary parallelohedra. Further important steps inthe field have been done by B. Delone, A. Alexandrov,O. Zhitomirski, B. Venkov, S.Ryshkov, P. McMullen, R.Erdahl, and others.At the same time, despite the considerable efforts, thecentral problem - a proof of the Voronoi conjecture onthe affine equivalence of an arbitrary parallelohedron tosome Voronoi parallelohedron - remains unresolved. Inthe talk we are going to present an overview of classicalresults of the theory of parallelohedra as well as some recentresults obtained by the author and his students A.Garber, A. Magazinov, and A.Gavrilyuk.Wh<strong>at</strong> is and to which end does one study phylogeneticcombin<strong>at</strong>orics?Andreas DressCAS-MPG Partner Institute for Comput<strong>at</strong>ional Biology,Chinaandreas@picb.ac.cnWhen Friedrich Schiller gave his inaugural lecture as aProfessor of History in Jena on May 26, 1789, he entitledit "Was heißt und zu welchem Ende studiert man Universalgeschichte?",th<strong>at</strong> is, "Wh<strong>at</strong> is and to which enddoes one study world history?". In this lecture, he distinguishedtwo kinds of scholars, the bread scholar whojust works for the money and with neither interest norability to recognize the "big picture" (Gesamtzusammenhänge)and who is frightened of any innov<strong>at</strong>ion because itsh<strong>at</strong>ters the old traditional system th<strong>at</strong> he so laboriouslyadopted, and the philosophical mind whose efforts aredirected toward the perfection of his knowledge, who is delightedby new discoveries in the sphere of his activities,who has always loved the truth more than his system, andwho will gladly be the first to abandon to re-establish amore perfect view.Similarly, one studies phylogenetic combin<strong>at</strong>orics to elucid<strong>at</strong>ethe rules and p<strong>at</strong>terns of species evolution andpopul<strong>at</strong>ion genetics under the influence of the four mainevolutionary processes: n<strong>at</strong>ural selection, genetic drift,mut<strong>at</strong>ion and gene flow (Wikipedia) and needs to combinemodern biological knowledge and insight with innov<strong>at</strong>ivem<strong>at</strong>hem<strong>at</strong>ical conceptualiz<strong>at</strong>ion, modelling andalgorithm design supported by computer-science based ITarchitectures and str<strong>at</strong>egies.In the lecture, I will particularly stress the importanceof phylogenetic networks and the m<strong>at</strong>hem<strong>at</strong>icalconcepts th<strong>at</strong> support phylogenetic-network construction,the tight-span concept, the method of splitdecomposition,and the quartet-analysis based approach.Slim systems of binary phylogenetic treesStefan GrünewaldCAS-MPG Partner Institute for Comput<strong>at</strong>ional Biology,Chinastefan@picb.ac.cnA phylogenetic tree is a tree where the leaves are labeledby taxonomic units, e.g. species. Such trees are used insystem<strong>at</strong>ic biology to visualize the evolutionary history ofthose taxa. A common problem in phylogenetics is th<strong>at</strong>we observe several small trees with overlapping but nonidenticaltaxa sets and we would like to construct a treeon the union of the taxa th<strong>at</strong> displays all the inform<strong>at</strong>ionof the input trees. In general, it is NP-complete to decidewhether such a "supertree" exists and whether it isunique. On the other hand, there is a lower bound on thetotal number of interior edges in order to have a uniquesupertree. If this bound is exactly <strong>at</strong>tained, then theuniqueness question can be decided in polynomial timeand the supertree can be constructed by gluing them togetherin a pairwise fashion. This surprising result wasfirst established in the PhD thesis by Sebastian Böcker in1999 and was referred to as “one of the most mysteriousand apparently difficult results in phylogeny". In my talkI will sketch a simplified proof th<strong>at</strong> I published in 2012and some further improvement made by Andreas Dress.New trends for graph searchesMichel HabibUniversity Paris Diderot - Paris VII, Francehabib@liafa.jussieu.frSince the 1950s, search, a mechanism for visiting the verticesand edges of a graph, has been a fundamental techniquein the design of graph algorithms. In this talk Iwill survey some new results of comput<strong>at</strong>ion of graph parametersusing graph searches, but also how to discovergraph structure using a series of graph searches. In factusing the seminal work [2], many graph searches can becharacterized by conditions on the visiting order of thevertices. These conditions are very useful for algorithmdesign.First I will describe how to evalu<strong>at</strong>e the diameter ofa graph using only 4 successive BFS (Breadth Firstsearches). This heuristic is very acur<strong>at</strong>e and can be appliedon huge graphs. Furthermore it can be completedby an exact algorithm which seems to be very efficient(much more th<strong>at</strong> its worst case complexity indic<strong>at</strong>es).Then I will focuse on cocomparability graphs showingth<strong>at</strong> first LDFS (Lexicographic Depth First Search) canbe used to compute a minimum p<strong>at</strong>h cover. A comparabilitygraph is a graph th<strong>at</strong> admits a transitive orient<strong>at</strong>ion,and a cocomparability graph is simply the complementof a comparability graph. Both classes comparabilityand cocomparability graphs are well studied subclassesof perfect graphs [3]. Cocomparability graphs generalizeinterval graphs, and we generalize for cocomparabilitygraphs some algorithmic results already obtainedfor interval graphs [1].I will finish by describing some fixed point properties ofgraph search acting on a cocomparability graph, describingmany open problems.[1] Corneil D.G., Dalton B., Habib M.: LDFS-based certifyingalgorithm for the Minimum P<strong>at</strong>h Cover problemon cocomparability graphs, to appear SIAM J. Comput.[2] Corneil D.G., Krueger R.: A Unified View of GraphSearching, SIAM J. Discrete M<strong>at</strong>h. 22(4): 1259-1276(2008).[3] M. C. Golumbic Algorithmic Graph Theory and PerfectGraphs, Volume 57, Second Edition, Annals of DiscreteM<strong>at</strong>hem<strong>at</strong>ics, 2004.Enumer<strong>at</strong>ion in graph classesPinar HeggernesUniversity of Bergen, Norwaypinar.heggernes@ii.uib.no
11 PRIMA 2013 AbstractsEnumer<strong>at</strong>ing, counting, and determining the maximumnumber of various objects in graphs have long been establishedas important areas within graph theory and graphalgorithms. As the number of enumer<strong>at</strong>ed objects is veryoften exponential in the size of the input graph, enumer<strong>at</strong>ionalgorithms fall into two c<strong>at</strong>egories depending on theirrunning time: those whose running time is measured inthe size of the input, and those whose running time ismeasured in the size of the output. Based on this, weconcentr<strong>at</strong>e on the following two types of algorithms.1. Exact exponential time algorithms. The design ofthese algorithms is mainly based on recursive branching.The running time is a function of the size of the inputgraph, and very often it also gives an upper bound on thenumber of enumer<strong>at</strong>ed objects any graph can have.2. Output polynomial algorithms. The running time ofthese algorithms is polynomial in the number of the enumer<strong>at</strong>edobjects th<strong>at</strong> the input graph actually contains.Some of these algorithms have even better running timesin form of incremental polynomial or polynomial delay,depending on the time the algorithm spends between eachconsecutive object th<strong>at</strong> is output.The methods for designing the two types of algorithmsare usually quite different. Common to both approachesis th<strong>at</strong> efforts have traditionally mainly been concentr<strong>at</strong>edon arbitray graphs, whereas graphs with particular structurehave largely been left un<strong>at</strong>tended. In this talk welook <strong>at</strong> enumer<strong>at</strong>ion of objects in graphs with specialstructure. In particular, we focus on enumer<strong>at</strong>ing minimaldomin<strong>at</strong>ing sets in various graph classes.Algorithms of type 1: The number of minimal domin<strong>at</strong>ingsets th<strong>at</strong> any graph on n vertices can have is knownto be <strong>at</strong> most 1.7159 n . This upper bound might not betight, since no examples of graphs with 1.5705 n or moreminimal domin<strong>at</strong>ing sets are known. For several classesof graphs, like chordal, split, and proper interval graphs,we substantially improve the upper bound on the numberof minimal domin<strong>at</strong>ing sets. At the same time, wegive algorithms for enumer<strong>at</strong>ing all minimal domin<strong>at</strong>ingsets, where the running time of each algorithm is withina polynomial factor of the proved upper bound for thegraph class in question. In some cases, we provide examplesof graphs containing the maximum possible numberof minimal domin<strong>at</strong>ing sets for graphs in th<strong>at</strong> class,thereby showing the corresponding upper bounds to betight.Algorithms of type 2: Enumer<strong>at</strong>ion of minimal domin<strong>at</strong>ingsets in graphs has very recently been shown to beequivalent to enumer<strong>at</strong>ion of minimal transversals in hypergraphs.The question whether the minimal transversalsof a hypergraph can be enumer<strong>at</strong>ed in output polynomialtime is a fundamental and challenging question;it has been open for several decades and has triggeredextensive research. We show th<strong>at</strong> all minimal domin<strong>at</strong>ingsets of a line graph can be gener<strong>at</strong>ed in incrementalpolynomial, and consequently output polynomial, time.We are able to improve the delay further on line graphsof bipartite graphs. Finally we show th<strong>at</strong> our methodis also efficient on graphs of large girth, resulting in anincremental polynomial time algorithm to enumer<strong>at</strong>e theminimal domin<strong>at</strong>ing sets of graphs of girth <strong>at</strong> least 7.The present<strong>at</strong>ion is based on joint works with followingco-authors: Jean-Francois Couturier, Petr Golovach, Pimvan ’t Hof, Dieter Kr<strong>at</strong>sch, and Yngve Villanger.M<strong>at</strong>rix partitionsPavol HellSimon Fraser University, Canadapavol@sfu.caI will survey recent work on vertex partitions of graphswith certain internal and certain external constraints.(These constraints are conveniently encoded in a m<strong>at</strong>rix.)Many well studied examples, especially from the study ofperfect graphs, fit into this model. The results discussedwill include both algorithms and characteriz<strong>at</strong>ions. Manyopen problem will be posed.The lexicographic methodJing HuangUniversity of Victoria, Canadajing@m<strong>at</strong>h.uvic.caLexicographic techniques have been identified as an importanttool in the design of graph algorithms. In thistalk I will give a short survey of how the techniques areused for solving graph problems such as recognitions, orient<strong>at</strong>ions,represent<strong>at</strong>ions, and homomorphisms.On m-walk-regular graphs, a generaliz<strong>at</strong>ion ofdistance-regular graphsJack KoolenUniversity of Science and Technology of China, China andPohang University of Science and Technology, Koreakoolen@postech.ac.krIn this talk I will discuss m-walk-regular graphs. Thesegraphs were introduced by Fiol and Garriga in 1999 as ageneraliz<strong>at</strong>ion of distance-regular graphs. 0-Walk-regulargraphs were earlier introduced by Godsil and McKay aswalk-regular graphs. They showed th<strong>at</strong> a graph G is walkregularif and only if the spectrum of G where I delete avertex x does not depend on the vertex x.Our main motiv<strong>at</strong>ion to study m-walk-regular graphs is tounderstand the difference between m-walk-regular graphsand distance-regular graphs. We will show th<strong>at</strong> manyresults on distance-regular graphs can be generalized to2-walk-regular graphs. We also give many examples of m-walk-regular graphs which are not distance-regular. Butwe also show th<strong>at</strong> some results on distance-regular graphsare not true for 2-walk-regular graphs.Geometric represent<strong>at</strong>ions of graphsJan Kr<strong>at</strong>ochvilCharles University in Prague, Czech Republichonza@kam.mff.cuni.czGeometric represent<strong>at</strong>ions of graphs are intensively studiedboth for their practical motiv<strong>at</strong>ion and interestingcombin<strong>at</strong>orial properties. We will survey recent developmentin this area, including recent results on coloring geometricintersection graphs and comput<strong>at</strong>ional complexityof extending partial geometric represent<strong>at</strong>ions.The practice of graph isomorphismBrendan D. McKayAustralian N<strong>at</strong>ional University, Australiabdm@cs.anu.edu.auWe are concerned with the practical aspects of computingthe automorphism groups of graphs, and determiningcanonical labellings of graphs. The speaker’s programnauty has been around since 1976, though it wasn’t calledth<strong>at</strong> until about 1983. Until a few years ago, there wasn’tvery much competition, but then came saucy, Bliss,conauto, and some other programs th<strong>at</strong> could outperformnauty in many cases.Our aim in the talk is to describe our response to thechallenge. In particular, nauty is now bundled with ahighly innov<strong>at</strong>ive program called Traces. We contendth<strong>at</strong> the present edition of Traces is now the performancechampion. The talk will describe how these programswork and give a comparison between them.This is joint work with Adolfo Piperno (University ofRome).
12 PRIMA 2013 AbstractsStructural limits in logical and analytic contextJaroslav NešetřilCharles University in Prague, Czech Republicnesetril@iuuk.mff.cuni.czWe survey recent development of limits of graphs (andother structures) in the unifying context of model theory.Particularly, this leads to the analysis of limits of sparsegraphs (with unbounded degrees). This is joint work withP<strong>at</strong>rice Ossona de Mendez (EHESS, Paris).Unavoidable vertex-minors in large primegraphsSang-il OumKorea Advanced Institute of Science and Technology, Koreasangil@kaist.eduA graph is prime (with respect to the split decomposition)if its vertex set does not admit a partition (A, B)(called a split) with |A|, |B| ≥ 2 such th<strong>at</strong> if a pair of verticesin A have neighbors in B, then they have the sameset of neighbors in B. We prove th<strong>at</strong> for each t, every sufficientlylarge prime graph must contain a vertex-minorisomorphic to either a cycle of length t or a graph consistingof two vertices joined by t 3-edge p<strong>at</strong>hs and no otheredges. This is a joint work with O-joung Kwon (KAIST).The structure of a typical H-free graphBruce ReedMcGill University, Canadabreed@cs.mcgill.caWe discuss the structure of a typical graph which does notcontain H as an induced subgraph and prove a weakeningof the Erdos-Hajnal conjecture. The talk presents jointwork with F. Havet, R. Kang, P. Keevash, M. Loebl, C.McDiarmid, J. Noel, A. Scott, and A. Thomason.Hamiltonian cycles in prismsMoshe RosenfeldUniversity of Washington, Tacoma, USAmoishe@uw.eduThe prism over a graph G is the Cartesian product ofG with K 2 . My interest in prisms began in 1973 whenI tried to tackle Dave Barnette’s conjecture (1970) th<strong>at</strong>all simple 4-polytopes are Hamiltonian (still open). Subsequently,we merged the study of Hamiltonian cycles inprisms with other refinements of Hamiltonian cycles. Weobserved th<strong>at</strong> if G has a Hamiltonian prism then G hasa spanning closed 2-walk but the opposite is not true,th<strong>at</strong> is having a Hamiltonian prism is "closer" to beingHamiltonian than having a spanning, closed 2-walk. Thisobserv<strong>at</strong>ion cre<strong>at</strong>ed many opportunities to study variousclassical problems on Hamiltonicity of graphs.In this talk I will discuss some results on prism Hamiltonicity,further refinements of Hamiltonicity and rel<strong>at</strong>edopen problems.On the comput<strong>at</strong>ion of the Radon number insome graph convexitiesJayme L SzwarcfiterFederal University of Rio de Janeiro, Braziljayme@nce.ufrj.brA graph convexity is a pair (G, C), where G is a finitegraph with vertex V (G) and C a family of subsets ofV (G) s<strong>at</strong>isfying ∅, V (G) ∈ C and being closed under intersections.The sets C ∈ C are called convex sets. Themost common graph convexities are those whose convexsets are defined through special p<strong>at</strong>hs of the graph.Among them the most prominent are the geodesic convexity,where C is closed under taking shortest p<strong>at</strong>hs, themonophonic convexity, where C is closed under inducedsubgraphs and the P 3 convexity, whose convex sets areclosed under pairs of common neighbors. In special, thel<strong>at</strong>ter is closely rel<strong>at</strong>ed to some well studied graph processes,as percol<strong>at</strong>ion and conversion processes. We examinesome common parameters of graph convexities, as thegeodetic number, convexity number, hull number, Hellynumber, Car<strong>at</strong>héodory number and Radon number. Inparticular, we describe complexity results rel<strong>at</strong>ed to thecomput<strong>at</strong>ion of the Radon number. These include hardnessresults, polynomial-time algorithms and bounds.A class of periodic continued fractions andfactoriz<strong>at</strong>ion in modular groupMikhail TyaglovShanghai Jiao Tong University, Chin<strong>at</strong>yaglov@sjtu.edu.cnIn this talk we introduce some properties of periodiccontinued fractions of the form−1 −1 −1b 1 + b 2 +···+ b} {{ n}n+−1 −1 −1b 1 + b 2 +···+ b · · · , (1)} {{ n +}nwhere b k are (positive) integers. Such continued fractionsare called periodic neg<strong>at</strong>ive-regular continuedfraction. By Tietze’s theorem [1], the fraction (1)converges to an irr<strong>at</strong>ional number if |b k | 2 (exceptfor the case |b k | = 2 for all k).We have proved th<strong>at</strong> without the requirement |b k | 2 the fraction (1) may converge to r<strong>at</strong>ional numbersor diverge. This is the difference between neg<strong>at</strong>iveregularcontinued fractions and classical regular continuedfractions. The last one always converge toirr<strong>at</strong>ional numbers.Several algorithms for construction of periods{b 1, . . . , b n} of periodic neg<strong>at</strong>ive-regular continuedfractions converging to r<strong>at</strong>ional numbers are given.The periods of a given length can be obtained by Ferm<strong>at</strong>’sinfinite descent method applied to some Diophantineequ<strong>at</strong>ions. An explicit simple formula forthe minimal period for x is presented. A constructionusing the Calkin-Wilf tree and Stern’s di<strong>at</strong>omic seriesis described. Arbitrary primitive periods are in oneto-onecorrespondence with elements of the modulargroup Γ. Explicit formulas converting products ofthe standard gener<strong>at</strong>ors S and ST in Γ into primitiveperiods are obtained. The periods of elliptic elementsof Γ are completely described. This description resultsin a parametric formula for primitive periods ofr<strong>at</strong>ional numbers. A periodic neg<strong>at</strong>ive-regular continuedfraction diverges if and only if either its periodor its double or its triple represents the identity inΓ.[1] H. Tietze, "Uber Kriterien für Konvergenz undIrr<strong>at</strong>ionalität unendlicher Ketenbrüche”, M<strong>at</strong>h. Ann.70 (1911).The graph isomorphism problem on geometricgraphs
13 PRIMA 2013 AbstractsRyuhei UeharaJapan Advanced Institute of Science and Technology,Japanuehara@jaist.ac.jpThe graph isomorphism (GI) problem asks whether twogiven graphs are isomorphic or not. Th<strong>at</strong> is, it askswhether there exists a one-to-one mapping between twogiven graphs. The GI problem is quite basic and simple,however, it’s time complexity is a long standing openproblem. The problem is clearly in NP, but it is notknown to be NP-complete or not. The GI problem is oneof candid<strong>at</strong>es between the classes NP and P. The problemhas four aspects from the viewpoints of theoretical computerscience. (1) Wh<strong>at</strong> the comput<strong>at</strong>ional complexityclass th<strong>at</strong> captures the GI problem? (2) How fast can wesolve the problem (in exponential time)? (3) Wh<strong>at</strong> thegraph classes such th<strong>at</strong> the GI problem is still as hardas general graphs? (4) Wh<strong>at</strong> the graph classes such th<strong>at</strong>the GI problem can be solved in polynomial time. In thistalk, I focus on (3) and (4). If we can clarify this gap, itindic<strong>at</strong>es the essential difficulty of the GI problem. Lastfew decades, many graph classes are proposed and investig<strong>at</strong>ed.Among them, we focus on some graph classesth<strong>at</strong> have geometric characteriz<strong>at</strong>ion. Typical examplesare interval graphs, th<strong>at</strong> are intersection graphs of intervals,and chordal graphs, th<strong>at</strong> are intersection graphs ofsubtrees of a tree. The GI problem can be solved in lineartime for interval graphs, while the GI problem forchordal graphs is as hard as general graphs. Some basictechniques to show these results are presented, and Ipresent some graph classes such th<strong>at</strong> the complexity ofthe GI problem are not known.On-line list colouring of graphsXuding ZhuZhejiang Normal University, Chinaxudingzhu@gmail.comThe on-line choice number of a graph is a vari<strong>at</strong>ion of thechoice number defined through a two person game. Givena finite graph G and a mapping f : V (G) → N, two players,the Lister and the Painter, play the on-line (G, f)-listcolouring game defined as follows: In the i-th step, theLister presents a non-empty subset V i of V (G) \ ∪ i−1j=1 X j,and the Painter chooses an independent set X i containedin V i . If v ∈ V i , then we say colour i is a permissiblecolour of vertex v. If v ∈ X i , then we say v is colouredby colour i. If <strong>at</strong> the end of a certain step, a vertex vis given f(v) permissible colours but remains uncoloured,then the game ends and the Lister wins the game. Otherwise,<strong>at</strong> some step, all vertices are coloured, the gameends and the Painter wins the game. We say G is on-linef-choosable if the Painter has a winning str<strong>at</strong>egy in theon-line (G, f)-list colouring game, and we say G is on-linek-choosable if G is on-line f-choosable for the constantfunction f ≡ k. The on-line choice number of G, denotedby χ P (G), is the minimum k for which G is on-linek-choosable. It follows from the definition th<strong>at</strong> for anygraph χ P (G) ≥ ch(G), where ch(G) is the choice numberof G. There are graphs G for which χ P (G) is strictlylarger than ch(G). In particular, there are graphs G with|V (G)| = 2χ(G) + 1 with χ P (G) > χ(G), in contrast toa recently confirmed conjecture of Ohba th<strong>at</strong> every suchgraph has χ(G) = ch(G). It was conjectured by Huang,Wong and Zhu th<strong>at</strong> every graph G with |V (G)| ≤ 2χ(G)has χ P (G) = χ(G). This talk presents some progresson the study of the conjecture, and some results on theupper bounds for the on-line choice number of classes ofgraphs.Special Session 6Geometric AnalysisConvergence of scalar-fl<strong>at</strong> metrics on manifoldswith boundary under the Yamabe flowSérgio AlmarazUniversidade Federal Fluminense, Brazilalmaraz@vm.uff.brIn this talk I will discuss a convergence theorem for aYamabe-type flow on manifolds with boundary. This isa flow th<strong>at</strong> evolves conformal scalar-fl<strong>at</strong> metrics accordingto equ<strong>at</strong>ions envolving the boundary mean curv<strong>at</strong>ure.Convergence to a scalar-fl<strong>at</strong> metric with constant boundarymean curv<strong>at</strong>ure is established assuming either a positivemass theorem or a genetric condition.Curv<strong>at</strong>ure behavior <strong>at</strong> singularity time ofRicci flowXiaodong CaoCornell University, USAcao@m<strong>at</strong>h.cornell.eduIn this talk, we will first survey some known result aboutcurv<strong>at</strong>ure behavior <strong>at</strong> the first finite-singularity time underthe Ricci flow. Then we will discuss some recent developmentin this direction and their applic<strong>at</strong>ions.Complete pseudohermitian manifolds withpositive spectrumShu-Cheng Chang 1 , Jui-Tang Chen 2 & Ting-Jung Kuo 31 N<strong>at</strong>ional Taiwan University, Taiwan, R.O.C.scchang@m<strong>at</strong>h.ntu.edu.tw2 N<strong>at</strong>ional Taiwan Normal University, Taiwan, R.O.C.jtchen@ntnu.edu.tw3 N<strong>at</strong>ional Taiwan University, Taiwantjkuo@ntu.edu.twIn this paper, we study complete noncompact pseudohermitianmanifolds with positive spectrum of the sub-Laplacian. We proved splitting- type theorems for a classof complete noncompact pseudohermitian manifolds withvanishing torsion whose spectrum of the sub-Laplacianhas an optimal positive lower bound. These can be viewedas the CR analogue of theorems of Li-Wang and the equalitycase of a theorem of Cheng.Affine cones over smooth del Pezzo surfacesIvan CheltsovThe University of Edinburgh, UKcheltsov@yahoo.comWe answer neg<strong>at</strong>ively the old question of Misha Zaidenbergand Hubert Flenner by proving th<strong>at</strong> affine cones oversmooth cubic surfaces do not admit non-trivial actions ofthe additive group. Our proof uses the alpha-functionsof smooth del Pezzo surfaces and classical bir<strong>at</strong>ional constructionsth<strong>at</strong> go back to Manin and Serge.Symplectic mean curv<strong>at</strong>ure flow in CP 2Xiaoli HanTsinghua University, Chinahanxiaoli@m<strong>at</strong>h.tsinghua.edu.cnI will give a talk about the symplectic mean curv<strong>at</strong>ureflow in CP 2 . Under some pinching conditions, the symplecticmean curv<strong>at</strong>ure flow exists for long time and convergesto a holomorphic curve.
14 PRIMA 2013 AbstractsRicci flow and 4-manifolds with positiveisotropic curv<strong>at</strong>ureHong HuangBeijing Normal University, Chinahhuang@bnu.edu.cnWe’ll survey the work by Hamilton, Chen, Tang, Zhu andthe speaker on the classific<strong>at</strong>ion of complete 4-manifolds(or orbifolds) with positive isotropic curv<strong>at</strong>ure. The maintool used here is the Hamilton-Perelman theory on Ricciflow with surgery. When we consider noncompact manifoldsor orbifolds we need to adapt the original Hamilton-Perelman theory. We’ll indic<strong>at</strong>e the necessary modific<strong>at</strong>ionsin these cases.Convergence of Calabi flow with small initiald<strong>at</strong>aHaozhao LiUniversity of Science and Technology of China, Chinahzli@ustc.edu.cnWe will discuss the long time existence and convergence ofthe Calabi flow under some small initial conditions withoutassuming the existence of constant scalar curv<strong>at</strong>ureKähler metrics. This is joint work with Kai Zheng.K-stability of Fano varieties and Alpha invariantYuji OdakaKyoto university, Japanyodaka@m<strong>at</strong>h.kyoto-u.ac.jpThe K-stability is first defined by Tian and l<strong>at</strong>er generalizedby Donaldson formally as a positivity of generalizedFutaki invariants. This talk will focus on the case of Fanovarieties.Thanks to the recent celebr<strong>at</strong>ed works of the proofof existence of Kähler-Einstein metrics on K-stable Fanomanifolds due to Chen-Donaldson-Sun and Tian, the K-stability has been finally proved to be equivalent to theexistence of Kähler-Einstein metrics i.e. we can in principlestudy the existence problem algebro-geometrically.However it is in general hard, <strong>at</strong> the moment, to testK-stability.The speaker will review the basic structure of the generalizedFutaki invariants from algebro-geometric viewpointand gives rel<strong>at</strong>ion with (the Minimal modelprogram-based) bir<strong>at</strong>ional geometry, in particular introducingthe notion of “destabilizing subschemes" afterthe wake of Ross-Thomas. This analysis in particularwill give a proof of K-stability of Fano n-fold X withα(X) >n which corresponds to the theorem of Tiann+1in 80s where the alpha invariant α(X) was introduced.This talk will be based on a joint work with Yuji Sano.α-functions of smooth del Pezzo surfacesJihun ParkInstitute for Basic Science & Pohang University of Scienceand Technology, Koreawlog@postech.ac.krWe define α-functions of Fano varieties by considering theα-invariants of G. Tian locally. We demonstr<strong>at</strong>e how toobtain the α-functions of smooth del Pezzo surfaces. Inaddition, their applic<strong>at</strong>ions are briefly introduced.Bergman kernel of a polarized Kähler ALEmanifoldYalong ShiNanjing University, Chinashiyl@nju.edu.cnI shall report some recent joint work with Claudio Arezzoand Alberto Della Vedova on the Bergman kernel of KählerALE manifolds.The first eigenvalue of minimal submanifoldsin an unit sphereZizhou TangBeijing Normal University, ChinaWe will talk about the first eigenvalue of a minimalisoparametric hypersurface in a unit spheres, as well asth<strong>at</strong> of their focal submanifolds. For the special case, weverify Yau’s conjecture.The regularity of limit spaceBing WangUniversity of Wisconsin-Madison, USAbwang@m<strong>at</strong>h.wisc.eduThis is a joint work with Tian. We study the structure ofthe limit space of a sequence of almost Einstein manifolds,which are generaliz<strong>at</strong>ions of Einstein manifolds.Roughlyspeaking, such manifolds are the initial manifolds of somenormalized Ricci flows whose scalar curv<strong>at</strong>ures are almostconstants over space-time in the L 1 -sense, Ricci curv<strong>at</strong>uresare bounded from below <strong>at</strong> the initial time. Underthe non-collapsed condition, we show th<strong>at</strong> the limitspace of a sequence of almost Einstein manifolds has mostproperties which is known for the limit space of Einsteinmanifolds. As applic<strong>at</strong>ions, we can apply our structureresults to study the properties of Kähler manifolds.The limit of the Yang-Mills-Higgs flow onsemi-stable Higgs bundlesJiayu Li & Xi ZhangUniversity of Science and Technology of China, Chinam<strong>at</strong>hzx@ustc.edu.cnIn this talk, we consider the gradient flow of the Yang-Mills-Higgs functional for Higgs pairs on a Hermitianvector bundle (E, H 0 ) over a compact Kähler manifold(M, ω). We study the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs <strong>at</strong> infinity, and show th<strong>at</strong>the limiting Higgs sheaf is isomorphic to the double dualof the graded Higgs sheaves associ<strong>at</strong>ed to the Harder-Narasimhan-Seshadri filtr<strong>at</strong>ion of the initial Higgs bundle.Ricci curv<strong>at</strong>ure in Kahler-Ricci flowZhou ZhangUniversity of Sydney, Australiazhangou@m<strong>at</strong>hs.usyd.edu.auRicci curv<strong>at</strong>ure is a geometric quantity n<strong>at</strong>urally rel<strong>at</strong>edto the behaviour of Ricci flow. In this talk, we discusssome recent results on the rel<strong>at</strong>ions between the variousbounds of Ricci curv<strong>at</strong>ure and the Kähler-Ricci flow existingfor either finite or infinite time.A class of Weingarten curv<strong>at</strong>ure measuresBin ZhouPeking University, Chinabzhou@pku.edu.cn
15 PRIMA 2013 AbstractsIn this talk, we study the weak continuity of k-curv<strong>at</strong>uremeasures of locally bounded, upper semicontinous functionswhich are subharmonic with respect to k-curv<strong>at</strong>ureoper<strong>at</strong>ors. The the proof uses the monotonicity integralinequality. This is a joint work with Qiuyi Dai and Xu-jiaWang.Special Session 7Geometric Aspects of Semilinear EllipticEqu<strong>at</strong>ions: Recent Advances & Future PerspectivesRegulariz<strong>at</strong>ion of point vortex solution forEuler equ<strong>at</strong>ionDaomin CaoChinese Academy of Sciences, Chinadmcao@amt.ac.cnIn this talk the speaker will talk about the regulariz<strong>at</strong>ionof point vortex solution for Euler equ<strong>at</strong>ion of 2 dimension.The existence of point vortex solutions is closelyrel<strong>at</strong>ed to the so called Kirchhoff Routh function. Thecritical points of Kirchhoff Routh function can deduce asteady point vortex solution. For a given critical point ofKirchhoff Routh function, can one establish the existenceof smooth steady solutions approxim<strong>at</strong>ing the point vortexsolution deduced by the point? He will talk about theprevious study concerning this respect. A newly obtainedresults by the speaker and his collabor<strong>at</strong>ors, Liu ZhongYuan and Wei Juncheng, will be introduced.Nonlocal minimal surfacesJuan DávilaUniversidad de Chile, Chilejdavila@dim.uchile.clCaffarelli, Roquejoffre and Savin (2010) introduced a notionof nonlocal minimal surface, which is a boundary ofa set th<strong>at</strong> is minimal with respect to an s-perimeter functional,where 0 < s < 1. It is n<strong>at</strong>ural to consider criticalpoints of the s-perimeter, which we call s-minimal surfaces.Up to now there are very few examples of such sets.Starting from the property th<strong>at</strong> as s → 1, the s-minimalequ<strong>at</strong>ion approaches the classical minimal surface equ<strong>at</strong>ion,we construct new examples of s-minimal surfaces fors close to 1.This is joint work with Manuel del Pino (Universidad deChile) and Juncheng Wei (Chinese University Of HongKong and University of British Columbia).Solutions for a semilinear elliptic equ<strong>at</strong>ion indimension two with supercritical growthIgnacio GuerraUniversidad de Santiago de Chile, Chileignacio.guerra@usach.clWe consider the problem−∆u = λue up , u > 0, in Ω,u = 0 on ∂Ω,where Ω ⊂ R 2 and p > 2. Let λ 1 be the first eigenvalueof the Laplacian. For each λ ∈ (0, λ 1 ), we prove the existenceof solutions for p sufficiently close to 2. In the caseof Ω a ball, we also describe numerically the bifurc<strong>at</strong>iondiagram (λ, u) for p > 2.On the entire radial solutions arising inChern-Simons equ<strong>at</strong>ionsHsin-Yuan HuangN<strong>at</strong>ional Sun Y<strong>at</strong>-sen University, Taiwan, R.O.Chyhuang@m<strong>at</strong>h.nsysu.edu.twIn this paper, we study the the entire radial solutions of(∗):∆u = − (1 + a)(e u − (1 + a)e 2u + ae u+v )+ a(e v − (1 + b)e 2v + be u+v )+ 4πN 1 δ 0∆v = − (1 + b)(e v − (1 + b)e 2v + be u+v )+ b(e u − (1 + a)e 2u + ae u+v )+ 4πN 2 δ 0 .Here, a > 0, b > 0, N 1 ≥ 0, and N 2 ≥ 0. This systemis motiv<strong>at</strong>ed by studying the equ<strong>at</strong>ions of rel<strong>at</strong>ivisticnon-Abelian Chern-Simons model proposed by by Kao-Lee and Dunne and Gudnason model of N =2 supersymmetricYang-Mills-Cherns-Simons-Higgs theory. Understandingthe structure of entire radial solutions is oneof fundamental issues for the system of nonlinear equ<strong>at</strong>ions.Under certain technical conditions for a and b,we prove th<strong>at</strong> any entire radial solutions of (∗) must beone of topological, non-topological and mixed type solutions,and completely classify the asymptotic behaviors<strong>at</strong> infinity of these solutions. As an applic<strong>at</strong>ion of thisclassific<strong>at</strong>ion, we prove th<strong>at</strong> the two components u and vhave intersection <strong>at</strong> most finite times.Existence and non-existence of positive solutionson the Hardy-Littlewood-Sobolev typesystemsCongming LiShanghai Jiao Tong University, China and University ofColorado <strong>at</strong> Boulder, USAcli@colorado.eduIn this present<strong>at</strong>ion, we provide some existence, nonexistence,and classific<strong>at</strong>ion of positive solutions for Hardy-Littlewood-Sobolev type systems. In deriving these results,some useful methods are cre<strong>at</strong>ed. We will brieflyintroduce some of the involved methods.Singly periodic solutions of the Allen-Cahnequ<strong>at</strong>ion and the Toda l<strong>at</strong>ticeYong LiuNorth China Electric Power University, Chinaliuyong@ncepu.edu.cnWe study the Allen-Cahn equ<strong>at</strong>ion in the plane:−∆u = u − u 3 , in R 2 .Of interest are bounded entire solutions whose behavior<strong>at</strong> infinity is in some sense simple. Examples arethose with finite Morse index, which have been extensivelystudied in the past. Here we will construct solutionswhich are periodic in one direction in the plane, butare not doubly periodic. The core of the construction isthe one-soliton solution of the Toda l<strong>at</strong>tice, which is aclassical integrable system. This is joint work with M.Kowalczyk, F. Pacard and J. Wei.Critical Trudinger Moser equ<strong>at</strong>ion in R 2Monica MussoUniversidad C<strong>at</strong>ólica de Chile, Chilemmusso@m<strong>at</strong>.puc.cl
16 PRIMA 2013 AbstractsWe review some new results on construction of singleand multiple bubbling solutions for vari<strong>at</strong>ional problemsleading to semlinear equ<strong>at</strong>ions with nonlinearitiesof Trudinger Moser type.Multi-dimensional traveling fronts in bistablereaction-diffusion equ<strong>at</strong>ionsMasaharu TaniguchiOkayama University, Japantaniguchi-m@okayama-u.ac.jpMulti-dimensional traveling fronts have been studied bym<strong>at</strong>hem<strong>at</strong>icians for bistable reaction-diffusion equ<strong>at</strong>ionsin the whole space. Especially, cylindrically symmetrictraveling fronts have been studied by Hamel, Monneauand Roquejoffre (2005). We study traveling fronts ofcylindrically non-symmetric shapes in bistable reactiondiffusionequ<strong>at</strong>ions.Existence and regularity of mean curv<strong>at</strong>ureflow with transport termYoshihiro TonegawaHokkaido University, Japantonegawa@m<strong>at</strong>h.sci.hokudai.ac.jpGiven a compact C 1 hypersurface in R n (n ≥ 2) anda vector field u : R n × [0, ∞) → R n which belongs toL q 1,ploc ([0, ∞); Wloc (Rn )), p > n 2 · q, p ≥ 2, q > 2,q−1we prove some existence result for evolving hypersurfaceswhose velocity is given by its mean curv<strong>at</strong>ure plus u. Forthe existence, we take the singular perturb<strong>at</strong>ion limit ofthe Allen-Cahn equ<strong>at</strong>ion with additional transport term.The regularity issue is also discussed. This is a joint workwith K. Takasao.Monotonicity formula and Liouville theoremsfor stable solutions of some elliptic problemsKelei WangWuhan Institute of Physics and M<strong>at</strong>hem<strong>at</strong>ics, CAS,Chinawangkelei@wipm.ac.cnI will report some recent progress on the understandingof stable solutions to a class of second and fourth ordernonlinear elliptic equ<strong>at</strong>ions, such as the Liouvile theoremsfor stable and finite Morse index solutions and the partialregularity problems. In particular, I will discuss theapplic<strong>at</strong>ion of monotonocity formula and the method oftangent cone analysis in these problems, which goes backto W. H. Fleiming. The talk is based on joint work withJuan Davila, Louis Dupaigne and Juncheng Wei.Global bifurc<strong>at</strong>ion diagrams and exact multiplicityof positive solutions for a onedimensionalprescribed mean curv<strong>at</strong>ure problemarising in MEMSShin-Hwa WangN<strong>at</strong>ional Tsing Hua University Hsinchu, Taiwanshwang@m<strong>at</strong>h.nthu.edu.twWe study global bifurc<strong>at</strong>ion diagrams and exact multiplicityof positive solutions for the one-dimensional prescribedmean curv<strong>at</strong>ure problem arising in MEMS⎧⎪⎨⎪⎩⎛⎞′⎜ u ′ (x) ⎟ λ−⎝√⎠ =1 + (u ′ (x)) 2 (1 − u) p , u 0.Concerning this open question, we find and prove th<strong>at</strong>global bifurc<strong>at</strong>ion diagrams for 0 < p < 1 are different toand more complic<strong>at</strong>ed than those for p ≥ 1. This is jointwork with Yan-Hsiou Cheng and Kuo-Chih Hung.Synchronized and segreg<strong>at</strong>ed solutions forcoupled nonlinear Schrödinger equ<strong>at</strong>ionsZhi-Qiang WangNankai University, China and Utah St<strong>at</strong>e University, USAzhi-qiang.wang@usu.edulIn this talk we report recent work on new type of solutionsfor the coupled nonlinear Schrodinger equ<strong>at</strong>ions.Depending upon the system being <strong>at</strong>tractive or repulsivemultiple (infinitely many) synchronized or segreg<strong>at</strong>edtype solutions can be constructed, further making correl<strong>at</strong>ionbetween the coupling constants and the existenceof different type of solutions.Bubbling solutions for the Chern-SimonsmodelShusen YanThe University of New Englandsyan@turing.une.edu.auWe study the following Chern-Simons-Higgs equ<strong>at</strong>ion:{∆u +1ε 2 e u (1 − e u ) = 8πδ p, in Ω,u is doubly periodic in ∂Ω,where Ω is a rectangle. We show th<strong>at</strong> the above problemhas exactly two solutions if ε > 0 is small. This is a jointwork with Chang-Shou Lin.Gamma convergence for Maxwell-Chern-Simons-Higgs energyYong YuThe Chinese University of Hong Kong, Hong Kong, Chinayongyu@m<strong>at</strong>h.cuhk.edu.hkA gamma convergence result associ<strong>at</strong>ed with theMaxwell-Chern-Simons-Higgs energy will be presented.As a consequence, we obtain a non-local free boundaryproblem, which describes the condens<strong>at</strong>ion of vortices inthe MCSH theory. This result generalize the classicalresult on the mean field limit of the magnetic Ginzburg-Landau theory.
17 PRIMA 2013 AbstractsSpecial Session 8Hyperbolic Conserv<strong>at</strong>ion Laws and Rel<strong>at</strong>edApplic<strong>at</strong>ionsSome counterexamples in the theory of conserv<strong>at</strong>ionlawsAlberto BressanPennsylvania St<strong>at</strong>e University, USAbressan@m<strong>at</strong>h.psu.eduThe first part of the talk is concerned with sticky particlemodels in two space dimensions. Examples of Cauchyproblems can be constructed with two and with zero solutions,respectively. Similar ideas apply to the equ<strong>at</strong>ionsof pressureless gases in two space dimensions, with L ∞initial d<strong>at</strong>a.The second set of examples concern the p-system of isentropicgas dynamics. For initial d<strong>at</strong>a with large totalvari<strong>at</strong>ion, one can arrange repe<strong>at</strong>ed wave-front interactionsin such a way th<strong>at</strong> the total strength of all wavefronts becomes arbitrarily large.Nonlinear mixed type equ<strong>at</strong>ions arisen inMach reflectionShuxing ChenFudan University, Chinasxchen@fudan.edu.cnIn the study of Mach reflection we find a kind of nonlinearmixed type equ<strong>at</strong>ions. The solvability of the generalizedTricomi problem of the mixed type equ<strong>at</strong>ion leads thestability of corresponding Mach configur<strong>at</strong>ion.Self-similar vortex spiral solutions of the 2dincompressible Euler Equ<strong>at</strong>ionsVolker EllingUniversity of Michigan, Ann Arbor, USAvelling@umich.eduVortex spirals are ubiquitous in fluid flow, for example asturbulent eddies or as trailing vortices <strong>at</strong> aircraft wings.However, there are few proofs of existence for any of thecommon fluid models. We consider solutions of the incompressibleEuler equ<strong>at</strong>ions th<strong>at</strong> have vorticity str<strong>at</strong>ifyinginto algebraic spirals. The solutions are selfsimilar:velocity v(t, x) = t m−1 v(t −m x), for similarity exponent1< m < ∞. Selfsimilar flows are special solutions of the2full initial-value problem, but obtained by solving moretractable boundary value problems. The key to the existenceproof is an coordin<strong>at</strong>e change which is implicit,depending on the a priori unknown solution. We willalso discuss the importance of the program for showingnon-uniqueness in the initial-value problem for the 2d incompressibleEuler solutions.Some results about compressible Oldroyd-BDaoyuan FangZhejiang University, Chinadyf@zju.edu.cnIn this talk, I will show some results about the compressibleOldroyd-B model, which is the joint work withRuizhao Zi. For such medel, we proved th<strong>at</strong> the systemadmits a unique local strong solution with initial densityvanishes from below, and give a blow-up criterion; Inthe framework of critical spaces, we establish the globalsolutions if the initial d<strong>at</strong>a and coupling constant are sufficientlysmall. We also proved th<strong>at</strong> as the Mach numbertends to zero, the global solution converges to the solutionto the corresponding incompressible model in somefunction spaces,and obtained a kind of the converge r<strong>at</strong>es.Shock reflection and von Neumann conjecturesMikhail FeldmanUniversity of Wisconsin-Madison, USAfeldman@m<strong>at</strong>h.wisc.eduWe discuss shock reflection problem for compressible gasdynamics, and von Neumann conjectures on transitionbetween regular and Mach reflections. Then we describerecent results on existence of regular reflection solutionsfor potential flow equ<strong>at</strong>ion up to the detachment angle,and discuss some techniques. The approach is to reducethe shock reflection problem to a free boundary problemfor a nonlinear equ<strong>at</strong>ion of mixed elliptic-hyperbolic type.Open problems will also be discussed. The talk will bebased on the joint work with Gui-Qiang Chen.Normal forms and a Burgers-Hilbert equ<strong>at</strong>ionJohn K. HunterUniversity of California, Davis, USAjkhunter@ucdavis.eduThe Burgers-Hilbert equ<strong>at</strong>ion arises as a model equ<strong>at</strong>ionfor the motion of a vortex p<strong>at</strong>ch or vorticity discontinuityin a two-dimensional, inviscid, incompressible fluid flow,and describes the effect of nonlinear steepening on an interfaceor wave th<strong>at</strong> oscill<strong>at</strong>es <strong>at</strong> a constant backgroundfrequency. For small amplitudes, these oscill<strong>at</strong>ions delaywave breaking. We will explain how non-standardnormal form methods can be used to prove an enhancedlife-span of small smooth solutions of the Burgers-Hilbertequ<strong>at</strong>ion in comparison with the inviscid Burgers equ<strong>at</strong>ion.These normal form methods can be applied to otherquasilinear wave equ<strong>at</strong>ions, for which the Burgers-Hilbertequ<strong>at</strong>ion provides a useful test case. This is joint workwith M. Ifrim, D. T<strong>at</strong>aru, and D. Wong.Incompressible limit of the non-isentropicideal magnetohydrodynamic equ<strong>at</strong>ionsSong JiangInstitute of Applied Physics and Comput<strong>at</strong>ional M<strong>at</strong>hem<strong>at</strong>ics,Chinajiang@iapcm.ac.cnWe first give a short review of results on the low Machnumber limit for the compressible magnetohydrodynamicequ<strong>at</strong>ions. Then, we study the incompressible limit of thecompressible non-isentropic ideal magnetohydrodynamicequ<strong>at</strong>ions with general initial d<strong>at</strong>a in the whole space IR d(d = 2, 3), and establish the existence of classic solutionson a time interval independent of the Mach number. Finally,by deriving uniform a priori estim<strong>at</strong>es, we obtainthe convergence of the solution to th<strong>at</strong> of the incompressiblemagnetohydrodynamic equ<strong>at</strong>ions as the Mach numbertends to zero.(joint-work with Q.C. Ju and F.C. Li)The Cauchy problem to the Kazhikhov-Vaigant model in compressible flowQuansen JiuCapital Normal University, Chinajiuqs@mail.cnu.edu.cnIn this talk, we will present some recent progresses ofthe global well-posedness of the Cauchy problem to the
18 PRIMA 2013 AbstractsKazhikhov-Vaigant model which is a kind of compressibleNavier-Stokes equ<strong>at</strong>ions with the shear viscosity µ a positiveconstant and the bulk viscosity λ is a power functionof the density.The initial d<strong>at</strong>a can be arbitrarily large tocontain vacuum st<strong>at</strong>es. This is joint with Yi Wang andZhouping Xin.Global solutions for transonic self-similar twodimensionalRiemann problemsEun Heui KimCalifornia St<strong>at</strong>e University, Long Beach, USAEunHeui.Kim@csulb.eduWe discuss the recent development of multi-dimensionaltransonic Riemann problems. More precisely we discussanalytical results and numerical results on a simplifiedmodel system – the nonlinear wave system.Long Time behaviors of the Vlasov-Poisson-Boltzmann Equ<strong>at</strong>ionsHai-Liang LiCapital Normal University, Chinahailiang.li.m<strong>at</strong>h@gmail.comThis talk is concerned with the long time behaviors ofglobal solution to the Vlasov-Poisson-Boltzmann (VPB)equ<strong>at</strong>ions with binary elastic collision of hard sphere asthe initial d<strong>at</strong>a is a small perturb<strong>at</strong>ion of the globalMaxwellian. In terms of the spectrum analysis of linearizedsystem and energy estim<strong>at</strong>es, the optimal timedecay r<strong>at</strong>es of global solution is established, and the influenceof electric filed governed by the self-consistent Poissonequ<strong>at</strong>ion on the distribution of the spectra and thetime-asymptotical behaviors are justified.Traveling waves of chemotaxis modelsTong LiUniversity of Iowa, USAtong-li@uiowa.eduWe study global existence and long time behavior of classicalsolutions for a hyperbolic-parabolic system derivedfrom the Keller-Segel model describing chemotaxis. Weestablish the existence and the nonlinear stability of largeamplitudetraveling wave solutions to the system of nonlinearconserv<strong>at</strong>ion laws derived from Keller-Segel model.Asymptotic behavior of solutions to Euler-Poisson equ<strong>at</strong>ions for bipolar hydrodynamicmodel of semiconductorsMing MeiChamplain College Saint-Lambert and McGill University,Canadammei@champlaincollege.qc.ca, ming.mei@mcgill.caIn this talk, we study the Cauchy problem for 1-D Euler-Poisson system, which represents a physically relevanthydrodynamic model but also a challenging case for abipolar semiconductor device by considering two differentpressure functions and a non-fl<strong>at</strong> doping profile. Differentfrom the previous studies for the case with two identicalpressure functions and zero doping profile, we realize th<strong>at</strong>the asymptotic profiles of this more physical model aretheir corresponding st<strong>at</strong>ionary waves (steady-st<strong>at</strong>e solutions)r<strong>at</strong>her than the diffusion waves. Furthermore, weprove th<strong>at</strong>, when the flow is fully subsonic, by means ofa technical energy method with some new development,the smooth solutions of the system are unique, exist globallyand time-algebraically converge to the correspondingst<strong>at</strong>ionary solutions. The optimal algebraic convergencer<strong>at</strong>es are obtained.This is a joint work with D. Don<strong>at</strong>elli, B. Rubino and R.SampalmieriCompressible Navier-Stokes equ<strong>at</strong>ions withChapman dissip<strong>at</strong>ionRonghua PanGeorgia Institute of Technology, USApanrh@m<strong>at</strong>h.g<strong>at</strong>ech.eduFrom its physical origin, the viscosity and he<strong>at</strong> conductivityin compressible fluids depend on absolute temper<strong>at</strong>urethrough power laws. The m<strong>at</strong>hem<strong>at</strong>ical theory onthe well-posedness and regularity on this setting is widelyopen. I will report some recent progress made on thisdirection, with emphasis on the lower bound of temper<strong>at</strong>ure,and global existence of solutions in one or multipledimensions. The rel<strong>at</strong>ion between thermodynamics lawsand Navier-Stokes equ<strong>at</strong>ions will also be discussed. Thistalk is based on joint works with Weizhe Zhang.Stability of steady st<strong>at</strong>e solutions for Euler-Maxwell equ<strong>at</strong>ionsYue-Jun PengBlaise Pascal University, Francepeng@m<strong>at</strong>h.univ-bpclermont.frWe consider Euler-Maxwell equ<strong>at</strong>ions arising in the modelingof magnetized plasmas. For such equ<strong>at</strong>ions steadyequilibrium st<strong>at</strong>es with zero velocity exist. For small initiald<strong>at</strong>a, we show global existence of smooth solutionswith convergence toward the steady st<strong>at</strong>es as the timegoes to infinity. In this problem, the main ingredient isan induction argument on the order of the deriv<strong>at</strong>ives ofsolutions in energy estim<strong>at</strong>es. It is also efficient to obtainthe global stability of solutions with exponential decaynear steady st<strong>at</strong>es for Euler-Poisson equ<strong>at</strong>ions.Traveling waves for slow erosionWen ShenPennsylvania St<strong>at</strong>e University, USAshen_w@m<strong>at</strong>h.psu.eduWe consider an integro-differential equ<strong>at</strong>ion th<strong>at</strong> describesthe slow erosion of granular flow in one space dimension,{(u t+exp ∫ +∞xu(x, 0) = ū(x).)f(u x(t, y)) dy =0, xHere u(x, t) denotes the height of the standing profile<strong>at</strong> the point (x, t), and the time variable t denotes theamount of mass th<strong>at</strong> passes through. The function f(u x)is the erosion function, which denotes the r<strong>at</strong>e of erosion(or deposition if neg<strong>at</strong>ive) per unit mass per distancetravelled. In a normalized model, f(1) = 0, indic<strong>at</strong>ing acritical slope u x = 1 where no erosions or depositionsoccur.Due to the nonlinearity of the function f, various typesof singularities will form in the solution u(x, t), includingkinks (jumps in u x) and shocks (jumps in u). Existenceof BV solutions is proved in [4], and semi-group solutionsare established in [2], using a modified form of wave fronttracking approxim<strong>at</strong>ion. In the simpler case where u xdoes not blow up, uniqueness of solutions is also achieved[1].In this talk we construct particular forms of travelingwave solutions for (1), which connect to x = ±∞ with(1)
19 PRIMA 2013 Abstractscritical slope u x = 1. We show th<strong>at</strong>, for a fixed rel<strong>at</strong>ionof the asymptote <strong>at</strong> x = ±∞, there exists a unique travelingwave solution. Furthermore, such traveling wavesolutions are local <strong>at</strong>tractors. Nearby solutions approachthe traveling wave asymptotically as t → ∞. This is ajoint work with Graziano Guerra, see [3].[1] D. Amadori and W. Shen, Front tracking approxim<strong>at</strong>ionsfor slow erosion, Discrete Contin. Dyn. Syst., 32(2012), no. 5, 1481–1502.[2] R. M. Colombo, G. Guerra, and W. Shen, Lipschitzsemigroup for an integro–differential equ<strong>at</strong>ion for slowerosion, Quart. Appl. M<strong>at</strong>h., 70 (2012), 539–578.[3] G. Guerra, and W. Shen, Existence and Stability ofTraveling Waves for an Integro-differential Equ<strong>at</strong>ion forSlow Erosion Preprint, 2013.[4] W. Shen and T.Y. Zhang, Erosion profile by a globalmodel for granular flow, Arch. R<strong>at</strong>ion. Mech. Anal., 204(2012), no. 3, 837–879.On the existence of Meyer type transonicflows and a degener<strong>at</strong>e change type equ<strong>at</strong>ionZhouping XinThe Chinese University of Hong Kong, Hong Kong, Chinazpxin@ims.cuhk.edu.hkHistorically, two types of smooth steady compressibleirrot<strong>at</strong>ional transonic flows were conjectured for 2-dimensional de Laval nozzles: Taylor type and Meyertype. However, it has known since Lipman Bers th<strong>at</strong> Taylortype transonic flows may not exist in general, whilethe existence of Meyer type transonic flows with suitablephysical boundary condition has been a long standingopen problem. Such a flow is governed by a quasilinearequ<strong>at</strong>ion which changes type and becomes degener<strong>at</strong>eupon crossing sonic st<strong>at</strong>e where the flow may havesingularities. In this talk, I will report some progress onstudies of such problems. First, by investig<strong>at</strong>ing the propertiesstructure of the sonic curve, in particular its exceptionalpoints, for C 2 -smooth transonic flows in a generalnozzle, we show the instability of Taylor type flowsand Meyer type flows with non-empty exceptional points.Then we identify a class of de Laval nozzles and suitablephysical boundary conditions such th<strong>at</strong> Meyer type transonicflow exists with sonic curve everywhere exceptional.Some global properties of such a solution and rel<strong>at</strong>ed openproblems will be discussed.Weakly nonlinear geometric optics for hyperbolicsystems of conserv<strong>at</strong>ion lawsYongqian ZhangFudan University, Chinayongqianz@fudan.edu.cnIn this talk I will present a new approach to analyze thevalid<strong>at</strong>ion of weakly nonlinear geometric optics for entropysolutions of nonlinear hyperbolic systems of conserv<strong>at</strong>ionlaws whose eigenvalues are allowed to have constantmultiplicity and corresponding characteristic fieldsto be linearly degener<strong>at</strong>e. The approach is based on ourcareful construction of more accur<strong>at</strong>e auxiliary approxim<strong>at</strong>ionto weakly nonlinear geometric optics, the propertiesof wave front-tracking approxim<strong>at</strong>e solutions, the behaviorof solutions to the approxim<strong>at</strong>e asymptotic equ<strong>at</strong>ions,and the standard semigroup estim<strong>at</strong>es. This is ajoint work with Guiqiang Chen and Wei Xiang of Universityof Oxford.Special Session 9Inverse ProblemsInverse sc<strong>at</strong>tering problems in wave propag<strong>at</strong>ionGang BaoZhejiang University, China and Michigan St<strong>at</strong>e University,USAdrbaogang@gmail.comRecent progress of our research group on inverse sc<strong>at</strong>teringproblems in wave propag<strong>at</strong>ion will be reported. Issueson uniqueness/stability and numerical solution for the inverseproblems will be discussed.Multi-scale full waveform inversion for seismicimagingMichael P. LamoureuxUniversity of Calgary, Canadamikel@ucalgary.caThe seismic imaging problem entails recovering an imageof the earth’s subsurface from d<strong>at</strong>a th<strong>at</strong> is recorded onthe surface of the earth, determined by the propag<strong>at</strong>ion ofseismic (vibr<strong>at</strong>ional) waves through the body of the earth.The 2D or 3D acoustic wave equ<strong>at</strong>ion is commonly usedas a simplified m<strong>at</strong>hem<strong>at</strong>ical model for this seismic wavepropag<strong>at</strong>ion. The full waveform inverse problem aims todeduce the physical parameters of the (acoustic) mediumof propag<strong>at</strong>ion from recorded d<strong>at</strong>a of impulsive waves th<strong>at</strong>are transmitted or reflected through the medium, andthus form an image of the subsurface.In this study, we demonstr<strong>at</strong>e a numerical algorithmth<strong>at</strong> uses factoriz<strong>at</strong>ion in the PDE solver of the 2D acousticwave model, a multi-scale approach to the inverse solution,and a projection-based lineariz<strong>at</strong>ion search for thesolution to the inverse problem. The multi-scale approachis used to decrease the rank of the inverse problem, thusdecreasing the ill-posedness and under-determinedness ofthe solution. With a few examples, we show the robustproperties of the inversion algorithm, a fast numericalconvergence r<strong>at</strong>e, and the advantages of multi-scaling.Joint with Gary F. Margrave, Vladimir ZubovOn the inverse problems for the coupled continuumpipe flow model for flows in karstaquifersShuai LuFudan University, Chinaslu@fudan.edu.cnIn this talk, we investig<strong>at</strong>e a coupled continuum pipe flow(CCPF) model which describes the fluid flows in karstaquifers. After generalizing the well-posedness of the forwardproblem to the anisotropic exchange r<strong>at</strong>e case whichis a space-dependent variable, we present the uniquenessof this parameter by measuring the Cauchy d<strong>at</strong>a. Finally,some regulariz<strong>at</strong>ion schemes are provided to solveone proposed inverse problem.A he<strong>at</strong> source reconstruction formula fromsingle internal measurements using a familyof null controlsAxel OssesUniversidad de Chile, Chileaxosses@dim.uchile.clWe consider the inverse problem of determining the sp<strong>at</strong>ialdependence f(x) of the source term in a he<strong>at</strong> equ<strong>at</strong>ionu t − γ∆u = f(x)σ(t) in Ω × (0, T ) assuming σ(t) known,
20 PRIMA 2013 Abstractsfrom a single partial internal measurement of the solutionin O × (0, T ), O ⊂ Ω. The purpose of this paper isto establish a reconstruction formula for f(x) using exactcontrols, and th<strong>at</strong> could be generalized for generalparabolic equ<strong>at</strong>ions. The reconstruction formula is associ<strong>at</strong>edto a family of exact controls v(τ) indexed byτ ∈ (0, T ). We perform numerical simul<strong>at</strong>ions in orderto illustr<strong>at</strong>e the feasibility, accuracy and stability of theproposed reconstruction formula.Inverse boundary value problems for timeharmonicacoustic waves: conditional stabilityand iter<strong>at</strong>ive reconstructionLingyun QiuPurdue University, USAqiu@purdue.eduThe inverse boundary value problem for time-harmonicacoustic waves is to determine the property of the mediuminside a domain from the measurements of the displacementand normal stress on its boundary. The governingequ<strong>at</strong>ion is the Helmholtz equ<strong>at</strong>ion. In the partial d<strong>at</strong>acase, the measurements are g<strong>at</strong>hered over a subset of theboundary.In this work, we first prove a Lipschitz type stabilityestim<strong>at</strong>e for the inverse problem assuming th<strong>at</strong> thewavespeed is piecewise constant with discontinuities ona finite number of known interfaces. Then, a hierarchyalgorithm is proposed and analysed for the iter<strong>at</strong>ive reconstructionwith multi-frequency d<strong>at</strong>a. The algorithm isbased on a projected steepest descent iter<strong>at</strong>ion with stabilityconstraints. The numerical results demonstr<strong>at</strong>e theproposed methodology has good performance in stabilityand accuracy.Inverse problems to elliptic systems in quantit<strong>at</strong>ive(fluorescence) photoacoustic tomographyKui RenUniversity of Texas <strong>at</strong> Austin, USAren@m<strong>at</strong>h.utexas.eduWe study inverse problems to two systems of elliptic equ<strong>at</strong>ionsth<strong>at</strong> arise from quantit<strong>at</strong>ive (fluorescence) photoacoustictomography. We present some general uniquenessand stability results following the general theory developedin [Bal, arXiv:1210.0265], as well as some explicitreconstruction str<strong>at</strong>egies in simplified settings.Recent progress in electrical tissue propertyMRIJin Keun SeoYonsei University, Koreaseojyonsei.ac.krRecently, imaging techniques in science, engineering, andmedicine have evolved to expand our ability to visualizeinternal inform<strong>at</strong>ion of an object such as the human body.In particular, there has been marked progress in MRbasedelectromagnetic property imaging techniques whichuse MRI to provide cross-sectional images of conductivity,permittivity, and susceptibility distributions insidethe human body. These electromagnetic m<strong>at</strong>erial propertiesof biological tissues are important biomarkers sincethey reveal physiological and p<strong>at</strong>hological conditions ofbody tissues and organs. Since the conductivity and permittivityvalues exhibit frequency-dependent changes, itis worthwhile to perform spectroscopic imaging from almostdc to hundreds of MHz. To probe the human body,we may inject current using surface electrodes or inducecurrent using external coils. Noting th<strong>at</strong> an MRI scannercan noninvasively measure magnetic fields inside the humanbody, electrical tissue property imaging methods usingMRI have l<strong>at</strong>ely been proposed. Magnetic resonanceEIT (MREIT) performs conductivity imaging <strong>at</strong> dc orbelow 1 kHz by externally injecting current into the humanbody and measuring induced internal magnetic fluxdensity d<strong>at</strong>a using an MRI scanner. Magnetic resonanceelectrical property tomography (MREPT) produces bothconductivity and permittivity images <strong>at</strong> the Larmor frequencyof an MRI scanner based on B1-mapping techniques.Since internal d<strong>at</strong>a are only available in MREITand MREPT, we may formul<strong>at</strong>e well-posed inverse problemsfor image reconstructions. To develop rel<strong>at</strong>ed imagingtechniques, we should clearly understand the basicprinciples of MREIT and MREPT, which are based oncoupled physics of bioelectromagnetism and MRI as wellas associ<strong>at</strong>ed m<strong>at</strong>hem<strong>at</strong>ical methods. In this talk, we describethe physical principles of MREIT and MREPT ina unified way and associ<strong>at</strong>e measurable quantities withthe conductivity and permittivity. Clarifying the key rel<strong>at</strong>ionsamong them, we examine existing image reconstructionalgorithms to reveal their capabilities and limit<strong>at</strong>ions.This talk is based on our recent book " Electro-Magnetic tissue property MRI" by JK Seo, EJ Woo, KUlrich, and Y Wang.Local lens rigidityPlamen StefanovPurdue University, USAstefanov@m<strong>at</strong>h.purdue.eduWe show th<strong>at</strong> we can recover locally a sounds speed neara boundary point p from the lens rel<strong>at</strong>ion (travel times)assuming th<strong>at</strong> the boundary is strictly convex near p.This is a recent result with Gunther Uhlmann and AndrasVasy.Stochastic controllabilityXu ZhangSichuan University, Chinazhang_xu@scu.edu.cnControllability for dynamical systems is a typical ill-posedproblem. In this talk, I will explain why the formul<strong>at</strong>ionof stochastic controllability problems and the toolsto solve them may differ considerably from their deterministiccounterpart.Some efficient domain decomposition methodsfor a Class of inverse problemsJun ZouChinese University of Hong Kong, Hong Kong, Chinazou@m<strong>at</strong>h.cuhk.edu.hkIn this talk we shall present several new domain decompositionmethods for solving some linear and nonlinearinverse problems. The motiv<strong>at</strong>ions and deriv<strong>at</strong>ions of themethods will be discussed, and numerical experimentswill be demonstr<strong>at</strong>ed. This is a joint work with Xiao-Chuan Cai (University of Colorado <strong>at</strong> Boulder) and HuiFeng (Wuhan University) and Daijun Jiang (HuazhongNormal University). The work was supported by HongKong RGC grants (projects 405110 and 404611).
21 PRIMA 2013 AbstractsSpecial Session 10Kinetic Equ<strong>at</strong>ionsOn some kinetic models for Bose Einstein condens<strong>at</strong>ionRadjesvarane AlexandreFrench Naval Academy, France and Shanghai Jiao TongUniversity, Chinaradjesvarane.alexandre@ecole-navale.frWe present some models based on kinetic equ<strong>at</strong>ions fordescribing Bose Einstein condens<strong>at</strong>ion. We will discussabout possible blow up or not of some of the partial differentialequ<strong>at</strong>ions. This is a joint work with Jie LIAOand Chunjin LIN.Angular averaging, propag<strong>at</strong>ion of exponentialtails and grazing collisions for solutions ofthe Boltzmann equ<strong>at</strong>ionIrene GambaUniversity of Texas <strong>at</strong> Austin, USAgamba@m<strong>at</strong>h.utexas.eduWe will discuss the interplay on the collision kernels propertiesof the Boltzmann equ<strong>at</strong>ion and the gener<strong>at</strong>ion andpropag<strong>at</strong>ion of summability of moments of the solutionfor the homogeneous initial value problem. Such summabilityyields global bounds for the solution of the Boltzmannequ<strong>at</strong>ion by exponentially weighted norms in L 1and pointwise, where the exponent depend on the initialst<strong>at</strong>e norms, the r<strong>at</strong>e of the intra-molecular potentials aswell as the integrability properties on the sphere (angularaveraging) for the sc<strong>at</strong>tering angle cross-section. We willalso discuss the impact of these estim<strong>at</strong>es in open problems,such as the grazing collision limits to the Landauequ<strong>at</strong>ion for Coulombic interactions. We will also shownumerical simul<strong>at</strong>ions of these limits for different crosssections.L p -sc<strong>at</strong>tering and uniform stability of kineticequ<strong>at</strong>ionsSeung-Yeal HaSeoul N<strong>at</strong>ional University, Koreasyha@snu.ac.krIn this talk, we will review recent progress on the L p -sc<strong>at</strong>tering and uniform stability of several kinetic equ<strong>at</strong>ionswith self-consistent forces. For the Vlasov equ<strong>at</strong>ionwith a self-consistent force, we will show th<strong>at</strong> theCoulomb’s potential in three dimensions is critical in thesense th<strong>at</strong> if sp<strong>at</strong>ial dimension is larger than three, thereexists a L 1 -sc<strong>at</strong>tering, whereas for low dimensions lessthan equal to three, there is no L 1 -sc<strong>at</strong>tering. We alsopresent a framework for the L p -stability of kinetic equ<strong>at</strong>ions.This is a joint work with Sun-Ho Choi (NUS) andQinghua Xiao (SNU).On the sp<strong>at</strong>ially homogeneous Boltzmann andLandau equ<strong>at</strong>ionsLingbing HeTsinghua University, Chinalbhe@m<strong>at</strong>h.tsinghua.edu.cnIn this talk, I will present some recent progress on thelower and upper bounds for the Boltzmann collision oper<strong>at</strong>or.As one applic<strong>at</strong>ion, we can build a unified frameworkto establish the well-posedness results for bothBoltzmann and Landau equ<strong>at</strong>ions. As another applic<strong>at</strong>ion,we will revisit the so-called "grazing collisions limit".It is shown th<strong>at</strong> when almost all collisions are grazing,th<strong>at</strong> is, the devi<strong>at</strong>ion angle θ of the collision is limitednear zero (i.e., θ ≤ ɛ), the solution f ɛ of the Boltzmannequ<strong>at</strong>ion with initial d<strong>at</strong>a f 0 can be globally or locallyexpanded asf ɛ = f + O(ɛ),for non Coulomb potential, orf ɛ = f + O(| log ɛ| −1 ),for Coulomb potential, where the function f is the solutionof Landau equ<strong>at</strong>ion, which is associ<strong>at</strong>ed to the grazingcollisions limit of Boltzmann equ<strong>at</strong>ion, with the sameinitial d<strong>at</strong>a f 0 . These give the rigorous justific<strong>at</strong>ion ofthe Landau approxim<strong>at</strong>ion in the sp<strong>at</strong>ially homogeneouscase.New regularity estim<strong>at</strong>es for transport equ<strong>at</strong>ionsPierre-Emmanuel JabinUniversity of Maryland, USApjabin@umd.eduWe present new regularity estim<strong>at</strong>es which are propag<strong>at</strong>edby transport equ<strong>at</strong>ions with rough coefficients.Those estim<strong>at</strong>es provides compactness on the density,which is a key ingredient to obtain existence of solutionsfor models from fluid mechanics (of the compressibleNavier-Stokes type) to chemotaxis. The correspondingspaces are defined <strong>at</strong> a logarithmic scale in terms of numberof deriv<strong>at</strong>ives and can thus be seen as intermediarybetween the usual L p and Sobolev spaces.Condens<strong>at</strong>ion and regularity for Boson Boltzmannequ<strong>at</strong>ionXuguang LuTsinghua University, Chinaxglu@m<strong>at</strong>h.tsinghua.edu.cnWe study the sp<strong>at</strong>ially homogeneous Boltzmann equ<strong>at</strong>ionfor Bose-Einstein particles for the hard sphere model. Weconsider the case where the initial d<strong>at</strong>um of a solution ofthe equ<strong>at</strong>ion is a function so th<strong>at</strong> there is no condens<strong>at</strong>ion(Dirac mass) <strong>at</strong> the initial st<strong>at</strong>e. We show th<strong>at</strong> if theinitial d<strong>at</strong>um is not very singular near the origin (the zeropointof particle energy) and if the kinetic temper<strong>at</strong>ureis sufficiently high, then the solution is also a functionfor all time, and it is a unique classical mild solutionof the equ<strong>at</strong>ion; whereas if the initial d<strong>at</strong>um is singularenough near the origin but still Lebesgue integrable, thenthe condens<strong>at</strong>ion of a corresponding solution continuouslystarts to occur from the initial time to every l<strong>at</strong>er time.Hamiltonian propag<strong>at</strong>ion of mono-kineticmeasures with rough initial profilesPeter MarkowichKing Abdullah University of Science and Technology,Kingdom of Saudi ArabiaP.A.Markowich@damtp.cam.ac.ukConsider in the phase space of classical mechanics aRadon measure which is a probability density carried bythe graph of a Lipschitz continuous (or even less regular)vector field. We study the structure of the push-forwardof such a measure by a Hamiltonian flow. In particular,we provide an estim<strong>at</strong>e on the number of folds in thesupport of the transported measure th<strong>at</strong> is the image ofthe initial graph by the flow. We also study in detail thetype of singularities in the projection of the transported
22 PRIMA 2013 Abstractsmeasure in configur<strong>at</strong>ion space (averaging out the momentumvariable). We study the conditions under whichthis projected measure can have <strong>at</strong>oms, and give an examplein which the projected measure is singular withrespect to the Lebesgue measure and diffuse. Finally, wediscuss applic<strong>at</strong>ions of our results to the classical limit ofthe SchrŽdinger equ<strong>at</strong>ion.Scalar conserv<strong>at</strong>ion laws and kinetic formul<strong>at</strong>ionBenoît PerthamePierre-and-Marie-Curie University, CNRS/INRIA andInstitut Universitaire de France, Franceperthame@ann.jussieu.frWe present a theory of Scalar Conserv<strong>at</strong>ion Laws withrough fluxes. The difficulty is th<strong>at</strong>, even with BV estim<strong>at</strong>es,the equ<strong>at</strong>ions does not make sense in disctributionalsense. Our approach is based on the kinetic formul<strong>at</strong>ionof conserv<strong>at</strong>ions laws.This theory leads n<strong>at</strong>urally to consider Kinetic AvergaingLemmas with random fluxes. On simple situ<strong>at</strong>ions wewill show the differences int he gain of regularity.This talk is based on works with P.-L. Lions and P. E.Souganidis.Kinetic description of bacterial motion bychemotaxis and asymptoticsNicolas VaucheletPierre-and-Marie-Curie University, Francevauchelet@ann.jussieu.frChemotaxis is the phenomenon in which cells direct theirmotion according to a chemical present in their environment.Since experimental observ<strong>at</strong>ions have shown th<strong>at</strong>the motion of bacteria (e.g. Escherichia Coli) is due tothe altern<strong>at</strong>ion of ‘runs and tumbles’, m<strong>at</strong>hem<strong>at</strong>ical modellingthanks to a kinetic description has been proposed.The starting point of the study is the so-called Othmer-Dunbar-Alt model governing the dynamics of the distributionfunction f of cells <strong>at</strong> time t, position x and velocityv, assumed to have a constant modulus c > 0, as wellas the concentr<strong>at</strong>ion S(t, x) of the involved chemical. Ageneral formul<strong>at</strong>ion for this model can be written as⎧⎪⎨⎪⎩∂ tf + v · ∇ xf = Q(f),Q(f) = ∫ (|v ′ |=c T [S](v ′ , v)f(v ′ )−T [S](v, v ′ )f(v) ) ∫ dv ′ ,−∆S + S = ρ(t, x) := f(t, x, v) dv.|v|=cThe third equ<strong>at</strong>ion describes the dynamics of the chemicalagent which diffuses in the domain. It is producedby the cells themselves with a r<strong>at</strong>e proportional to thedensity of cells ρ and disappears with a r<strong>at</strong>e proportionalto S. The transport oper<strong>at</strong>or on the left-hand side of thefirst equ<strong>at</strong>ion stands for the unbiased movement of cells(‘runs’), while the right-hand side governs ‘tumbles’, th<strong>at</strong>is chemotactic orient<strong>at</strong>ion, or taxis, through the turningkernel T [S](v ′ , v), which is the r<strong>at</strong>e of cells changing theirvelocity from v ′ to v.In this work, we focus on positive chemotaxis whichmeans th<strong>at</strong> the involved chemical S is <strong>at</strong>tracting cells,called chemo<strong>at</strong>tractant. Existence results for this systemhas been obtained for various assumptions on the turningkernel. Macroscopic model can be derived from thissystem of equ<strong>at</strong>ions after a rescaling. When the taxis issmall compared to the unbiased movement of cells, thescaling must be of diffusive type, so th<strong>at</strong> the limit equ<strong>at</strong>ionsare of diffusion or drift-diffusion type. When taxisdomin<strong>at</strong>es the unbiased movements, a hyperbolic limitcan be derived, leading to aggreg<strong>at</strong>ion equ<strong>at</strong>ions. Moreover,experimental observ<strong>at</strong>ions have shown the form<strong>at</strong>ionof traveling pulse of bacteria in micro-channel. The abovem<strong>at</strong>hem<strong>at</strong>ical modeling allows to recover this behaviour,which motiv<strong>at</strong>es the interest on such system.Viscous wave propag<strong>at</strong>ion <strong>at</strong> interfaceShih-Hsien YuN<strong>at</strong>ional University of Singapore, Singaporem<strong>at</strong>ysh@nus.edu.sgIn this talk we implement the LY algorithm to derive <strong>at</strong>wo-sided master rel<strong>at</strong>ionship. This gives rise the oper<strong>at</strong>orto construct the surface wave <strong>at</strong> the interface and theconstruction of the Green’s function of a simple variablecoefficient problem for viscous conserv<strong>at</strong>ion laws.Special Session 11M<strong>at</strong>hem<strong>at</strong>ical Fluid Dynamics and Rel<strong>at</strong>edTopicsGlobal solutions of the equivariant he<strong>at</strong>-flowStephen GustafsonUniversity of British Columbia, Canadagustaf@m<strong>at</strong>h.ubc.caThe harmonic map he<strong>at</strong>-flow is a canonical, parabolic,geometric evolution equ<strong>at</strong>ion, which is (energy) criticalin two dimensions. I will present a global regularity resultfor the equivariant, higher-degree, above-thresholdhe<strong>at</strong>-flow into the sphere, which extends to higher energiesearlier work with Nakanishi and Tsai on the he<strong>at</strong>and Schroedinger flows. This is joint work with DimitriosRoxanas.Well-posedness of coupled kinetic-fluid modelsfor flockingSeung-Yeal HaSeoul N<strong>at</strong>ional University, Koreasyha@snu.ac.krIn this talk, I will present several kinetic-fluid models forflocking. More precisely, I will discuss the dynamics ofCucker-Smale flocking particles interacting with neighboringcompressible and incompressible fluid. For suchcoupled kinetic-fluid models, we will show global existenceof weak and strong solutions and asymptotic flockingestim<strong>at</strong>es for small initial d<strong>at</strong>a and large viscosities.This is a joint work with H.O.Bae (Ajou Univ), Young-PilChoi (Imperial College of London) and Moon-Jin Kang(SNU).Global classical and weak solutions to the 3Dfully compressible Navier-Stokes-Fourier systemXiangdi HuangAcademy of M<strong>at</strong>hem<strong>at</strong>ics and System Sciences, CAS,Chinaxdhuang@amss.ac.cnWe establish the global existence and uniqueness of classicalsolutions to the three-dimensional fully compressibleNavier-Stokes-Fourier system with smooth initial d<strong>at</strong>awhich are of small energy but possibly large oscill<strong>at</strong>ionswhere the initial density is allowed to vanish. Moreover,for the initial d<strong>at</strong>a, which may be discontinuous and containvacuum st<strong>at</strong>es, we also obtain the global existenceof weak solutions. These results generalize previous oneson classical and weak solutions for initial density being
23 PRIMA 2013 Abstractsstrictly away from vacuum, and are the first for globalclassical and weak solutions which may have large oscill<strong>at</strong>ionsand can allow vacuum st<strong>at</strong>es.Solvability of the initial value problem to amodel system for w<strong>at</strong>er wavesT<strong>at</strong>suo IguchiKeio University, Japaniguchi@m<strong>at</strong>h.keio.ac.jpThe w<strong>at</strong>er wave problem is m<strong>at</strong>hem<strong>at</strong>ically formul<strong>at</strong>edas a free boundary problem for an irrot<strong>at</strong>ional flow ofan inviscid and incompressible fluid under the gravit<strong>at</strong>ionalfield. The basic equ<strong>at</strong>ions for w<strong>at</strong>er waves arecomplic<strong>at</strong>ed due to the nonlinearity of the equ<strong>at</strong>ions togetherwith the presence of an unknown free surface.Therefore, until now many approxim<strong>at</strong>e equ<strong>at</strong>ions havebeen proposed and analyzed to understand n<strong>at</strong>ural phenomenafor w<strong>at</strong>er waves. Famous examples of such approxim<strong>at</strong>eequ<strong>at</strong>ions are the shallow w<strong>at</strong>er equ<strong>at</strong>ions, theGreen–Nagdhi equ<strong>at</strong>ions, Boussinesq type equ<strong>at</strong>ions, theKorteweg–de Vries equ<strong>at</strong>ion, the Kadomtsev–Petviashviliequ<strong>at</strong>ion, the Benjamin–Bona–Mahony equ<strong>at</strong>ion, theCamassa–Holm equ<strong>at</strong>ion, the Benjamin–Ono equ<strong>at</strong>ions,and so on. All of them are derived from the w<strong>at</strong>er waveproblem under the shallowness assumption of the w<strong>at</strong>erwaves, which means th<strong>at</strong> the mean depth of the w<strong>at</strong>er issufficiently small compared to the typical wavelength ofthe w<strong>at</strong>er surface.On the other hand, it is well-known th<strong>at</strong> the w<strong>at</strong>er waveproblem has a vari<strong>at</strong>ional structure. In fact, J. C. Luke(1967) gave a Lagrangian in terms of the velocity potentialand the surface vari<strong>at</strong>ion, and showed th<strong>at</strong> the correspondingEuler–Lagrange equ<strong>at</strong>ions are the basic equ<strong>at</strong>ionsfor w<strong>at</strong>er waves. M. Isobe (1994) and T. Kakinuma(2000) derived model equ<strong>at</strong>ions for w<strong>at</strong>er waves withoutany shallowness assumption. The model equ<strong>at</strong>ions arethe Euler–Lagrange equ<strong>at</strong>ions to an approxim<strong>at</strong>ed Lagrangian,which is obtained by approxim<strong>at</strong>ing the velocitypotential in Luke’s Lagrangian.In this talk, we consider one of the model equ<strong>at</strong>ions andreport the solvability of the initial value problem. Themodel are nonlinear dispersive equ<strong>at</strong>ions and the hypersurfacet = 0 is characteristic for the model equ<strong>at</strong>ions.Therefore, the initial d<strong>at</strong>a have to be restricted in an infinitedimensional manifold in order to the existence ofthe solution, and we show th<strong>at</strong> the manifold is invariantunder the time evolution.This talk is based on the joint research with my formerstudent Yuuta Murakami.Some new advances on modeling and algorithmsdevelopment of multiphase complexfluid system using the phase field methodChun Liu, Xiaofeng Yang & Jie ShenPennsylvania St<strong>at</strong>e University, USAliu@m<strong>at</strong>h.psu.eduWe present some efficient modeling approach for the twophase fluid system with the variable densities and viscosities.The model, derived by employing an energetic vari<strong>at</strong>ionalapproach, is thermodynamically consistent th<strong>at</strong>admits an energy law. Some decoupled, energy stableschemes are developed to solve the model efficiently. Similarapproach has been applied to the two phase complexfluid system, where one phase is considered to be thenem<strong>at</strong>ic liquid crystal. Qualit<strong>at</strong>ive agreements with experimentalresults are observed.Classical limit of some quantum Euler equ<strong>at</strong>ionsS<strong>at</strong>oshi MasakiHiroshima University, Japanmasaki@am<strong>at</strong>h.hiroshima-u.ac.jpIn this talk, we consider classical limit problem of a classof quantum Euler equ<strong>at</strong>ion. The classical limit describesthe transition between quantum mechanics and classicalmechanics (Newtonian mechanics). More specifically, weconsider the compressible Euler equ<strong>at</strong>ion with a quantumpressure, th<strong>at</strong> is,⎧∂ tρ + divρv = 0,⎪⎨( √ ) ∆ ρ∂ t(ρv)+div(ρv⊗v)+ρ∇P (ρ)= 2 ρ∇ √ , (2) ρ⎪⎩ρ(0, x) = ρ 0 (x), v(0, x) = v 0 (x),for (t, x) ∈ R + × R N , where ρ = ρ(t, x) and v = v(t, x)denote the mass density and the velocity vector, respectively.(ρ 0 , v 0 ) is a given initial d<strong>at</strong>a independent of. P stands for the pressure. In this talk, we mainlyconsider the pressure given by the Poisson equ<strong>at</strong>ion;P (ρ) = c(−∆) −1 ρ with some constant c. In this case, (2)is often referred to as an Euler-Poisson equ<strong>at</strong>ions. Theright hand side of the second line of (2) is the quantumpressure. is a positive parameter which corresponds tothe scaled Planck constant. Our problem is analysis ofthe limit → 0 (the classical limit). At least formally, asolution (ρ, v) of (2) tends to a solution of the usual Eulerequ<strong>at</strong>ion⎧⎨ ∂ tn + divnw = 0,∂ t(nw)+div(nw⊗w)+n∇P (n)=0,⎩n(0, x) = ρ 0 (x), w(0, x) = v 0 (x).for (t, x) ∈ R + ×R N . Our purpose is to establish sufficientexistence results for (2) and (3) and to justify this limit.The difficulty of (2) lies in the tre<strong>at</strong>ment of the quantumpressure term. Since this pressure contains the density ρas a denomin<strong>at</strong>or, we have to care about the existence ofvacuum (zero points of ρ).In this talk, we restrict our <strong>at</strong>tention to the irrot<strong>at</strong>ionalflow case, in which case (2) is an altern<strong>at</strong>ive formul<strong>at</strong>ionof Schrödinger equ<strong>at</strong>ion (the Madelung equ<strong>at</strong>ion), andanalyze (2) by using a complex square root of the density.This method is introduced by Grenier in 1998 in orderto justify the semiclassical limit of the cubic nonlinearSchrödinger equ<strong>at</strong>ion. Let a(t, x) be a C-valued functionand u(t, x) be an R N -valued function. We work with thefollowing system.⎧⎪⎨∂ ta + u · ∇a + 1 2 a∇ · u = i 2 ∆a,∂ tu + (u · ∇)u + ∇P (|a| 2 (4)) = 0,⎪⎩a(0, x) = √ ρ 0 (x), u(0, x) = v 0 (x).for (t, x) ∈ R + × R N . The heart of m<strong>at</strong>ter is th<strong>at</strong> if (a, u)solves this system then (ρ, ρv) = (|a| 2 , |a| 2 u + Im(a∇a))becomes a solution to (2) (<strong>at</strong> (t, x) ∉ {a(t, x) = 0}).By this method, besides the justific<strong>at</strong>ion of the limit(ρ, ρv) → (n, nw) as → 0, we obtain an asymptoticexpansion of (ρ, ρv) in the classical limit. We remarkth<strong>at</strong> the presence of vacuum makes no trouble when wesolve (4) since the quantum pressure now changes into adispersion term.(3)Asymptotic stability of mild solutions to theNavier-Stokes equ<strong>at</strong>ionsMaria SchonbekUniversity of California, Santa Cruz, USAschonbek@m<strong>at</strong>h.ucsc.eduWe consider the initial value problem for the Navier-Stokes equ<strong>at</strong>ions modeling an incompressible fluid inthree dimensions:u t + u · ∇u + ∇p = ∆u + f, (x, t) ∈ R 3 × (0, ∞),
24 PRIMA 2013 Abstractsdiv u = 0,u(x, 0) = u 0 (x)It is well-known th<strong>at</strong> this problem has a unique globalin-timemild solution for a sufficiently small initial conditionu 0 and for a small external force F in suitable scalinginvariant spaces. We show th<strong>at</strong> these global-in-timemild solutions are asymptotically stable under every (arbitrarylarge) l 2 -perturb<strong>at</strong>ion of their initial conditions.The work is joint with Grsegorz Karch and Dominika Pilarczyk.On vanishing viscosity limit for 3-Dimensionalincompressible Navier-Stokes equ<strong>at</strong>ions witha slip boundary conditionZhouping XinThe Chinese University of Hong Kong, Hong Kong, Chinazpxin@ims.cuhk.edu.hkIn this talk, we will discuss the problem of vanishingviscosity limit for 3-dimensional incompressible Navier-Stokes equ<strong>at</strong>ions in a general bounded smooth domainwith general Navier-Slip boundary conditions. The focuswill be on the convergence of viscous solutions to the inviscidones in the space C([0, T ], H 1 (Ω)). Some uniformestim<strong>at</strong>es on the r<strong>at</strong>e of convergence will be presented.Topological instability of laminar flows for thetwo-dimensional Navier-Stokes equ<strong>at</strong>ion withcircular arc no-slip boundary conditionsTsuyoshi YonedaHokkaido University, Japanyoneda@m<strong>at</strong>h.sci.hokudai.ac.jpIn this talk we show th<strong>at</strong> a diffuser-shaped boundary inducesthe reverse flow even near the entrance of the diffuser.Let us be more precise. We consider the twodimensionalNavier-Stokes equ<strong>at</strong>ion in Ω ⊂ R 2 (defineΩ l<strong>at</strong>er) with no-slip and inflow-outflow conditions on∂Ω. We need to handle a shape of the boundary ∂Ωprecisely, thus we set a parametrized smooth boundaryϕ : (0, S) → R 2 as |∂ sϕ(s)| = 1, |∂s 2 ϕ(s)| = κ (curv<strong>at</strong>ure),ϕ(0) = (0, 0), ∂ sϕ(0) = (1, 0), ∂s 2 ϕ(0) = (0, −κ).We choose S l<strong>at</strong>er (should be sufficiently small). We definen = n(s) := (∂ sϕ(s)) ⊥ as a unit normal vector andτ = τ(s) = ∂ sϕ(s) as a unit tangent vector, where ⊥represents upward direction.Global strong solution for equ<strong>at</strong>ions rel<strong>at</strong>edto the incompressible viscoelastic fluidsTing ZhangZhejiang University, Chinazhangting79@zju.edu.cnConsidering a system rel<strong>at</strong>ed to the incompressible viscoelasticfluids of Oldroyd–B type,∇ · v = 0, (t, x) ∈ R + × R N , N ≥ 2,v it +v · ∇v i +∂ i Π=µ∆v i +E jk ∂ j E ik +∂ j E ij ,E t + v · ∇E = ∇vE + ∇v,(v, E)(0, x) = (v 0 , E 0 )(x),we investig<strong>at</strong>e the global existence of the strong solutionswith some classes of large initial d<strong>at</strong>a E 0 =[E 0,ij ] i=1,...,N;j=1,...,N , v 0 = [v 01 , . . . , v 0N ] ⊤ . We obtainthe global existence and uniqueness of solution providedth<strong>at</strong> (Ē0, ¯v 0 ) are sufficient small in (Ḃ N 2 −12,1 ∩Ḃ N 22,1 ) × Ḃ N 2 −12,1 , while E 0N and v 0N are large, whereĒ 0 = [E 0,ij ] i=1,...,N−1;j=1,...,N , ¯v 0 = [v 01 , . . . , v 0,N−1 ] ⊤and E 0N = [E 0,N1 , . . . , E 0,NN ].Special Session 12M<strong>at</strong>hem<strong>at</strong>ics of String TheoryStacky resolutions of the moduli spaces of instantonson ALE spacesUgo BruzzoIntern<strong>at</strong>ional School for Advanced Studies, Italybruzzo@sissa.itModuli spaces of framed sheaves on the complex projectiveplane are a resolution of singularities of the modulispace of ideal instantons on the 4-sphere. Anotherinstance of this phenomenon is provided by the modulispace of framed sheaves on the blowup of the projectiveplane, which resolves the singularities of the moduli spaceof ideal instantons on the orient<strong>at</strong>ion-reversed projectiveplane. This fact is used extensively in super Yang-Millstopological quantum field theories, where the instantonmoduli spaces classify the classical vacua, in particular tocompute Nekrasov partition functions and other invariants.A n<strong>at</strong>ural question arises whether similar constructionscan be made in the case of other spaces. I will considerinstantons on the ALE spaces X of type A k . Here thenontrivial behaviour of the instantons <strong>at</strong> infinity makesit necessary to consider moduli spaces of framed sheaveson a DM projective stack whose coarse moduli space isa toric compactific<strong>at</strong>ion of X. In particular one needs tointroduce a so-called root stack which has a gerby behaviourover the compactifying divisor.Topology change from heterotic Narain T-dualityJarah EvslinInstitute of High Energy Physics, CAS, Chinajarah@ihep.ac.cnI will describe topology changing Narain T-dualities ontorus-fibered compactific<strong>at</strong>ions with H flux in type II andheterotic string theories. In heterotic string theories, suchT-dualities mix the topology of the gauge bundle withth<strong>at</strong> of spacetime consistently with the supersymmetryconditions. More precisely, T-duality mixes half of thefield strength of an unbroken U(1) gauge symmetry withthe antiselfdual part of the curv<strong>at</strong>ure of the fibr<strong>at</strong>ion ofcompactified circle.Equivariant Cohomology and Bismut-ChernCharacter in the Stolz-Teichner ProgramFei HanN<strong>at</strong>ional University of Singapore, Singaporem<strong>at</strong>hanf@nus.edu.sgAbstract: The Stolz-Teichner program aims to rel<strong>at</strong>e supersymmetricfield theories to generalized cohomologytheories. In this talk, we will describe our joint projectswith Chris Schommer-Pries, Stephan Stolz and Peter Teichner,rel<strong>at</strong>ing 0|1-dimensional gauged field theories tothe equivariant cohomology of manifolds with Lie groupactions and realizing the Bismut-Chern character as dimensionreduction functor.T-duality commutes with reduction
25 PRIMA 2013 AbstractsPedram Hekm<strong>at</strong>iUniversity of Adelaide, Australiapedram.hekm<strong>at</strong>i@adelaide.edu.auT-duality is a discrete symmetry in string theory th<strong>at</strong> rel<strong>at</strong>estopologically distinct torus fibr<strong>at</strong>ions and provides adictionary for transl<strong>at</strong>ing geometrical structures betweenthem. The duality is m<strong>at</strong>hem<strong>at</strong>ically well-understood intype II theories and the purpose of this talk is to explainhow it can be extended to the heterotic setting.The setup n<strong>at</strong>urally involves string structures and reductionof Courant algebroids. This is joint work with DavidBaraglia.A motivic approach to Potts modelsM<strong>at</strong>ilde MarcolliCalifornia Institute of Technology, USAm<strong>at</strong>ilde@caltech.eduThe use of motivic techniques in Quantum Field Theoryhas been widely explored in the past ten years, in rel<strong>at</strong>ionto the occurrence of periods in the comput<strong>at</strong>ion ofFeynman integrals. In this lecture, based on joint workwith Aluffi, I will show how some of these techniques canbe extended to a motivic analysis of the partition functionof Potts models in st<strong>at</strong>istical mechanics. An estim<strong>at</strong>eof the complexity of the locus of zeros of the partitionfunction, can be obtained in terms of the classesin the Grothendieck ring of the affine algebraic varietiesdefined by the vanishing of the multivari<strong>at</strong>e Tutte polynomial,based on a deletion-contraction formula for theGrothendieck classes.The Wess-Zumino-Witten model on SL (2; R)David RidoutThe Australian N<strong>at</strong>ional University, Australiadavid.ridout@anu.edu.auThe prototypical examples of string theories on targetspaces with non-trivial topologies are the Wess-Zumino-Witten (WZW) models for which the target is a compactreductive Lie group. However, the non-compact case isphysically more relevant and is m<strong>at</strong>hem<strong>at</strong>ically richer aswell. While the pioneering work of Maldacena and Ooguriproposed string spectra and proved a no-ghost theoremfor the WZW model on SL (2; R), recent work has shownth<strong>at</strong> the underlying conformal field theory is far richer, <strong>at</strong>least for certain levels, and provides an example of a socalledlogarithmic conformal field theory. This talk willreview this recent work and wh<strong>at</strong> it suggests for othertheories with non-compact target spaces.M-branes and higher bundlesHisham S<strong>at</strong>iUniversity of Pittsburgh, USAhs<strong>at</strong>i@pitt.eduWe describe the M-branes in M-theory via higher geometry,including String structures, String bundles with connections,higher (stacky) notions of Chern-Simons theory,and rel<strong>at</strong>ion to higher WZW models. This is joint workwith Domenico Fiorenza and Urs Schreiber.T-duality for circle bundles via noncommut<strong>at</strong>ivegeometryM<strong>at</strong>hai VargheseThe University of Adelaide, Australiavarghese@adelaide.edu.auIt is known th<strong>at</strong> topological T-duality can be extendedto apply not only to principal circle bundles, but also tonon-principal circle bundles. We show th<strong>at</strong> this resultcan also be recovered via the noncommut<strong>at</strong>ive geometryapproach which we previously used for principal torusbundles. This work has several interesting byproducts,including a study of the K-theory of crossed products byÕ(2) = Isom(R), the universal cover of O(2), and some interestingfacts about equivariant K-theory for Z/2. Theseresults are then extended to the case of bundles withsingular fibers, or in other words, non-free O(2)-actions.This is joint work with Jon<strong>at</strong>han Rosenberg.Special Session 13Measurable and Topological DynamicsHeight reducing problemShigeki AkiyamaUniversity of Tsukuba, Japana.h.dooley@b<strong>at</strong>h.ac.ukWe say th<strong>at</strong> an algebraic number α has height reducingproperty (HRP) if there is a positive integer B th<strong>at</strong>Z[α] = B[α], i.e., every number in Z[α] has an equivalentrepresent<strong>at</strong>ion with coefficients in {−B, . . . , B}. Thisproblem is studied for algebraic integers, since it has intim<strong>at</strong>econnection to the construction of self-affine tilings.In this talk, we consider HRP for general algebraic numbersand obtain some ‘almost’ if and only if conditionfor HRP. The proof relies on a quantit<strong>at</strong>ive version ofKronecker’s approxim<strong>at</strong>ion theorem. This is a joint workwith Toufik Zaimi.Large devi<strong>at</strong>ion principle for chaotic dynamicalsystemsYong Moo ChungHiroshima University, Japanchung@am<strong>at</strong>h.hiroshima-u.ac.jpWe will discuss a class of chaotic dynamical systems forwhich the full large devi<strong>at</strong>ion principle holds. It containsintermittent maps and quadr<strong>at</strong>ic maps on intervals,almost Anosov diffeomorphisms on tori and countableMarkov shifts with return time functions of ’gentle’slopes.Chaotic dynamics of continuous-time topologicalsemiflow on Polish spaceXiongping DaiNanjing University, Chinaxpdai@nju.edu.cnDifferently from Li-Yorke and others in liter<strong>at</strong>ure, we willintroduce the concept—chaos—for a continuous semiflowf : R + × X → X on a Polish space X without isol<strong>at</strong>edpoints, which is useful for the theory of ODE and is invariantunder topological equivalence. Our definition isweaker than Devaney’s since here f may have neitherfixed nor periodic elements; but it still implies the sensitivedependence on initial d<strong>at</strong>a similar to Devaney’schaos. We will show th<strong>at</strong> f always has a maximal chaoticsubsystem. In addition, we will consider the chaotic behavioron minimal center of <strong>at</strong>traction of a motion.Random dynamical systemsAnthony DooleyUniversity of B<strong>at</strong>h, UKa.h.dooley@b<strong>at</strong>h.ac.uk
26 PRIMA 2013 AbstractsIn joint work with Guo-Hua Zhang, we have extendedthe notion of random dynamical system from Z actionsto actions of discrete amenable groups.In this setting, we introduce local fiber topological pressureand establish a vari<strong>at</strong>ional principle rel<strong>at</strong>ed tomeasure-theoretic entropy.One can then define both topological and measuretheoreticentropy tuples, and apply the vari<strong>at</strong>ional principleto obtain a rel<strong>at</strong>ionship between them. These resultsrecover and extend many recent results in local entropytheory.Local entropy dimension for a measure and avari<strong>at</strong>ional principleDou DouNanjing University, Chinadoum<strong>at</strong>h@163.comThe notion of entropy dimension measures the subexponentialcomplexity of entropy zero dynamical systems.By considering topological entropy via hausdorff dimensionand measure-theoretical local entropy, we introduceBowen’s type entropy dimension D B (T, K) and local(lower) entropy dimension D locµ (T ) in entropy zerosystems. When restrict to a compact subset K, weprove the following vari<strong>at</strong>ional principle: D B (T, K) =sup{D locµ (T ) : µ ∈ M(X), µ(K) = 1}.Decomposition problems in symbolic dynamicsUijin JungAjou University, Koreauijin@ajou.ac.krA code is a homomorphism between shift dynamical systems.Problems concerning decompositions of one codeinto a composition of several codes were considered insymbolic dynamics for coding purpose. Although a lot isknown about the decompositions of factor codes betweensubshifts with equal entropy, not much is known for thecase of unequal entropies. The first part of the talk willbe devoted to the history and known results on the decompositionproblems. For the remaining part, our recentdevelopments will be presented. Especially we focus onthe set of possible entropies of intermedi<strong>at</strong>e subshifts arisingfrom decomposing a given code. This is a joint workwith Soonjo Hong and In-Je Lee.Overlap and strong coincidences on substitutiontilingsJeong-Yup LeeKwandong University, Koreajylee@kd.ac.krPisot number is an algebraic integer whose all the otherGalois conjug<strong>at</strong>es are less than 1 in absolute. Substitutionsequences can be constructed replacing a letter by aword from a given finite letters. Incidence m<strong>at</strong>rix is definedby the numbers of letters coming from each letter.If the largest eigenvalue of this m<strong>at</strong>rix is a Pisot number,we say th<strong>at</strong> the substitution is “Pisot”. We constructa tiling space collecting all the locally indistinguishabletiling from the given Pisot substitution tiling.It has been conjectured th<strong>at</strong> the tiling space of a Pisotsubstitution tiling whose substitution m<strong>at</strong>rix is irreduciblehas discrete dynamical spectrum. This is called“Pisot substitution conjecture” which has not been solvedfor many years. Many notions of coincidences in substitutiontilings have been introduced in the study of thediscrete dynamical spectrum of the tiling spaces.Here we consider two well-known coincidences in the area,namely overlap coincidence and strong coincidence, whoserel<strong>at</strong>ions are not completely understood. We establishone direction of the implic<strong>at</strong>ion from overlap coincidenceto strong coincidence.Subword complexity and Sturmian coloringsof treesSeonhee LimSeoul N<strong>at</strong>ional University, Koreaslim@snu.ac.krIn this talk, we introduce subword complexity of coloringsof regular trees. We characterize colorings of boundedsubword complexity and then introduce Sturmian colorings,which are colorings of minimal unbounded subwordcomplexity.We classify Sturmian colorings using their type sets. Weshow th<strong>at</strong> any Sturmian coloring is a lifting of a coloringon a quotient graph of the tree which is a geodesic or a ray,with loops possibly <strong>at</strong>tached, thus a lifting of an "infinteword". We further give a complete characteriz<strong>at</strong>ion ofthe quotient graph for eventually periodic ones. We willprovide several examples. This is a joint work with DongHan Kim.Shadowing properties with average tracing ofpseudo-orbits.Piotr OprochaAGH University of Science and Technology, Polandoprocha@agh.edu.plAverage shadowing properties generalize standard definitionsof shadowing (e.g. shadowing property, limit shadowingproperty, etc.) by controlling average error of tracinginstead of its control in each iter<strong>at</strong>ion. Clearly, thedefinition of pseudo-orbit have to be modified accordingly.This modific<strong>at</strong>ion enables applic<strong>at</strong>ion of average shadowingin dynamical systems where we cannot control errorin each step, but we can ensure th<strong>at</strong> average error is sufficientlysmall. In particular, there are maps with averageshadowing property but without shadowing property(and vice-versa).In this talk we will survey recent results on average shadowingproperties. We will present a few sufficient conditionsth<strong>at</strong> ensure average shadowing and comment onrel<strong>at</strong>ions between average shadowing and notions fromtopological dynamics, like shadowing property, mixing,specific<strong>at</strong>ion, proximality and the like.Higher order Bohr problem and rel<strong>at</strong>ed topicsSong ShaoUniversity of Science and Technology of China, Chinasongshao@ustc.edu.cnIn this talk we will discuss higher order Bohr problem andrel<strong>at</strong>ed questions. An old problem about Bohr sets saysth<strong>at</strong> for any syndetic set S, is the set S − S a Bohr 0 set?We study the higher order version of this problem: forany d does the common difference of arithmetic progressionwith length d + 1 appeared in a syndetic set coincidewith a Nil d Bohr 0 set? We show th<strong>at</strong> one side of thisquestion holds: for any Nil d Bohr 0 -set A, there exists asyndetic set S such th<strong>at</strong> A contains the common differenceof arithmetic progression with length d + 1 appearedin S. And we show th<strong>at</strong> other side of the problem can bededuced from some result by Bergelson-Host-Kra if moduloa set with zero density. This is a joint work with W.Huang and X.D. Ye.Neg<strong>at</strong>ivity of Lyapunov exponents in genericrandom dynamical systems of complex polynomialsHiroki SumiOsaka University, Japansumi@m<strong>at</strong>h.sci.osaka-u.ac.jpIn this talk, we consider random dynamical systems ofcomplex polynomial maps on the Riemann sphere Ĉ. It
27 PRIMA 2013 Abstractsis well-known th<strong>at</strong> for each r<strong>at</strong>ional map f on Ĉ withdeg(f) ≥ 2, the Julia set J(f) is a non-empty perfect compactsubset of Ĉ (thus J(f) contains uncountably manypoints), f : J(f) → J(f) is chaotic (<strong>at</strong> least in the senseof Devaney), anddim H ({x ∈ Ĉ | lim infn→∞ 1 n log ‖Df n (x)‖ > 0}) > 0,where dim H denotes the Hausdorff dimension with respectto the spherical distance on Ĉ and ‖ · ‖ denotesthe norm of the deriv<strong>at</strong>ive with respect to the sphericalmetric on Ĉ. However, we show th<strong>at</strong> for generic i.i.d.random dynamical systems of complex polynomials, allof the following (1) and (2) holds.(1) For all points x ∈ Ĉ, the orbit of the Dirac measureδ x <strong>at</strong> x under the dual of the transition oper<strong>at</strong>or ofthe system converges to a periodic cycle of probabilitymeasures on Ĉ.(2) For all but countably many points x ∈ Ĉ, for almostevery sequence γ = (γ 1 , γ 2 , γ 3 , · · · ) of polynomials,the Lyapunov exponent along γ starting with x isneg<strong>at</strong>ive. More precisely, there exists a constantc < 0, which depends only on the system, such th<strong>at</strong>for all but countably many points x ∈ Ĉ, for almostevery sequence γ = (γ 1 , γ 2 , γ 3 , · · · ) of polynomials,1χ(γ, x) := lim n→∞ log ‖D(γn ◦ · · · ◦nγ 1 )(x)‖ exists and χ(γ, x) ≤ c.Note th<strong>at</strong> each of (1) and (2) cannot hold in the usualiter<strong>at</strong>ion dynamics of a single r<strong>at</strong>ional map f withdeg(f) ≥ 2. Therefore the picture of the randomcomplex dynamics is completely different fromth<strong>at</strong> of the usual complex dynamics. We remarkth<strong>at</strong> even the chaos of the random system disappears inC 0 sense, the chaos of the system may remain in C 1 sense,and we have to consider the “grad<strong>at</strong>ion between the nonchaoticityand the chaoticity”.References[1] H. Sumi, Random complex dynamics and semigroupsof holomorphic maps, Proc. London. M<strong>at</strong>h. Soc. (2011),102 (1), 50–112.[2] H. Sumi, Cooper<strong>at</strong>ion principle, stability andbifurc<strong>at</strong>ion in random complex dynamics, preprint,http://arxiv.org/abs/1008.3995.The semi-classical zeta function for contactAnosov flowMas<strong>at</strong>o TsujiiKyushu University, Japantsujii@m<strong>at</strong>h.kyushu-u.ac.jpWe consider the semi-classical (or Gutzwiller-Voros) zetafunction for a C ∞ contact Anosov flow. This is definedby the formula⎛⎞Z sc(s) = exp ⎝− ∑ ∞∑ e −s·m·|γ|⎠m · | det(Id − Dγ∈Γ m=0γ m)|1/2 where Γ is the set of prime periodic orbits. (|γ| and D γdenote the prime period and the transversal Jacobian ofγ ∈ Γ respectively. )Investig<strong>at</strong>ing the spectrum of transfer oper<strong>at</strong>ors associ<strong>at</strong>edto the flow, we prove th<strong>at</strong> the zeros of Z sc(s) arecontained in the region{s ∈ C | |R(s)| < τ or R(s) < −χ 0 + τ}for arbitrarily small τ > 0 up to finitely many exceptions,where χ 0 is the hyperbolicity exponent of the flow. Furtherwe show th<strong>at</strong> the zeros in the strip {s ∈ C | |R(s)|
28 PRIMA 2013 AbstractsQuantum, kinetic and hydrodynamic descriptionson spin transfer torqueCarlos J. García-CerveraUniversity of California, Santa Barbara, USAcgarcia@m<strong>at</strong>h.ucsb.eduMagnetic storage devices rely on the fact th<strong>at</strong> ferromagneticm<strong>at</strong>erials are typically bistable, and th<strong>at</strong> it is possibleto switch between diïňĂerent st<strong>at</strong>es by applying amagnetic ïňĄeld. The discovery of the Giant MagnetoResistanceeïňĂect has enabled the use of layered ferromagneticm<strong>at</strong>erials in magnetic devices, such as magneticmemories (MRAMs). Even in the absence of thermaleïňĂects, there are limit<strong>at</strong>ions in the storage capacity ofsuch devices due to the fact th<strong>at</strong> as the size is decreased,the magnitude of the switching ïňĄeld increases, due toan increase in shape anisotropy. Given th<strong>at</strong> magneticïňĄelds have long range interactions, the density of suchdevices is limited.A new mechanism for magnetiz<strong>at</strong>ion reversal in multilayerswas proposed by Slonczweski and Berger. In thisnew mechanism, an electric current ïňĆows perpendicularto the layers. The current is polarized in the ïňĄrstlayer, and the polariz<strong>at</strong>ion travels with the current to thesecond layer, where it interacts with the underlying magnetiz<strong>at</strong>ion.Since currents are localized in each cell, longrange eïňĂects can be reduced.In this talk we will discuss the connection between severalmodels for the description of the spin transfer torque<strong>at</strong> different physical scales. Specifically, we connect thequantum and kinetic descriptions with the help of theWigner transform, and the kinetic and diffusion modelsby a specific parabolic scaling. Numerical examples willpresented to illustr<strong>at</strong>e the applicability and limit of thedifferent models.This is joint work with Jingrun Chen and Xu Yang <strong>at</strong>UCSB.From discrete velocity model to momentmethodRuo LiPeking Univerisity, Chinarli@m<strong>at</strong>h.pku.edu.cnIn the numerical approaches for Boltzmann equ<strong>at</strong>ion, thediscrete velocity model and the moment method are formallyvery different. The difference is so big th<strong>at</strong> thecommunities working on the two approaches are in certaincompetitive rel<strong>at</strong>ion. In this talk, I will try to show theintrinsic connection between these two approaches. Precisely,the Grad type moment method with appropri<strong>at</strong>eclosure can be regarded as a discrete velocity model withsome adaptivities in setup of the velocity points. Theglobally hyperbolic regulaz<strong>at</strong>ion of the moment methodplays an essential role in connecting both approaches together.Atomic level interpret<strong>at</strong>ion of fracture criteriaXiantao LiPennsylvania St<strong>at</strong>e University, USAxli@m<strong>at</strong>h.psu.eduFracture in brittle m<strong>at</strong>erials has been a subject of intensivestudies following the pioneering works of Griffithand Irwin. The propag<strong>at</strong>ion of a crack is often predictedbased on the energy release r<strong>at</strong>e or the stress intensityfactors. This talk will present our recent studies of crackpropag<strong>at</strong>ion in the framework of bifurc<strong>at</strong>ion theory. Thishas been motiv<strong>at</strong>ed by the fact th<strong>at</strong> structural stability isa well-defined concept in the theory of bifurc<strong>at</strong>ion. Thebifurc<strong>at</strong>ion study is based on molecular dynamics models,which provide a direct microscopic view of the criticalevents in the process of fracturing. More importantly, wewill re-interpret several important concepts in the conventionalfracture mechanics.Multiscale modeling and comput<strong>at</strong>ion of nanooptical responsesDi LiuMichigan St<strong>at</strong>e University, USArichardl@m<strong>at</strong>h.msu.eduWe introduce a new framework for the multiphysicalmodeling and multiscale comput<strong>at</strong>ion of nano-optical responses.The semi-classical theory tre<strong>at</strong>s the evolution ofthe electromagnetic field and the motion of the chargedparticles self-consistently by coupling Maxwell equ<strong>at</strong>ionswith Quantum Mechanics. To overcome the numericalchallenge of solving high dimensional many body Schrodinger equ<strong>at</strong>ions involved, we adopt the Time DependentCurrent Density Functional Theory (TD-CDFT). Inthe regime of linear responses, this leads to a linear systemof equ<strong>at</strong>ions determining the electromagnetic eld aswell as the current and electron densities simultaneously.A self-consistent multiscale method is proposed to dealwith the well separ<strong>at</strong>ed space scales. Numerical examplesarepresented to illustr<strong>at</strong>e the resonant condition.Convergence of force-based <strong>at</strong>omistic-tocontinuummethodsJianfeng LuDuke University, USAjianfeng@m<strong>at</strong>h.duke.eduThe numerical analysis of <strong>at</strong>omistic-to-continuum methods,in particular, for two or three dimensional systems,is challenging and important for understanding multiscalemethods for solids. In this talk, we will discusssome recent progress in stability and convergence analysisof force-based hybrid methods coupling together <strong>at</strong>omisticmodels and Cauchy-Born elasticity with smooth andsharp transitions. We will focus on the requirement ofstability conditions due to interfaces. (Joint work withPingbing Ming)Ghost forces for multiscale coupling methodsin solidsPingbing MingInstitute of Comput<strong>at</strong>ional M<strong>at</strong>hem<strong>at</strong>ics, ChineseAcademy of Sciences, Chinampb@lsec.cc.ac.cnIn this talk, I will report some recent progress on theghost force issue for multiscale coupling methods in solids.Quantit<strong>at</strong>ive estim<strong>at</strong>es for the influence of the ghost forcewill be presented. Examples for high dimensional problems,dynamic problem and the crack problem will bediscussed.The growing string method for saddle pointsearchWeiqing RenN<strong>at</strong>ional University of Singapore and Institute Of HighPerformance Computing, Singaporem<strong>at</strong>rw@nus.edu.sgThe string method was originally designed for findingminimum energy p<strong>at</strong>hs between two minima on a potential(or free) energy landscape. It evolves a continuouscurve in the p<strong>at</strong>h space by the steepest descent dynamics.In this talk, we discuss how the string method can bemodified to find saddle points of a potential energy usinga minima as the only input. Compared to the existingalgorithms, the new method has the advantage th<strong>at</strong> thecomputed saddle points are guaranteed to be directly connectedto the minima. We will also discuss the acceler<strong>at</strong>ionof the convergence using an inexact Newton method.Applic<strong>at</strong>ions to the diffusion of a cluster of <strong>at</strong>oms on a
29 PRIMA 2013 Abstractssolid substr<strong>at</strong>e and the wetting transition of a droplet ona rough surface will be presented.Multiscale methods for wave propag<strong>at</strong>ionproblemsOlof RunborgKTH Royal Institute of Technology, Swedenolofr@nada.kth.seMultiscale wave propag<strong>at</strong>ion problems are comput<strong>at</strong>ionallycostly to solve by traditional techniques because thesmallest scales must be represented over a domain determinedby the largest scales of the problem. We considernumerical methods for multiscale wave propag<strong>at</strong>ion inthe framework of the heterogeneous multiscale method.These methods couple simul<strong>at</strong>ions on macro- and microscalesfor problems with rapidly oscill<strong>at</strong>ing coefficients.The complexity is significantly lower than th<strong>at</strong> of traditionaltechniques with a comput<strong>at</strong>ional cost th<strong>at</strong> is essentiallyindependent of the microscale. In this talk weshow analysis of how the method works in the long timecase, where the macroscale solution show dispersive behavior,and how the method, although designed for waveproblems, can be beneficial for solving multiscale ellipticproblems.Modeling and simul<strong>at</strong>ion of three-componentflows on solid surfaceXiao-Ping WangHong Kong University of Science and Technology, HongKong, Chinaxpwhk63@gmail.comWe propose a phase field model for the study of threecomponentimmiscible flows with boundary. The modelis a generaliz<strong>at</strong>ion of the two-component model. We firststudy certain consistency conditions for the forms of thebulk free energy and surface energy. We then developan adaptive mesh refinement(AMR) technique to solvethe system in order to improve the efficiency of the problem.Several numerical results are given, including theliquid lens spreads between two phases, the buoyancydrivendroplet through a fluid-fluid interface, spreadingof a compound droplet on a st<strong>at</strong>ionary substr<strong>at</strong>e, andshear flows of a compound droplet on a channel.A p<strong>at</strong>h way based mean field model for E. colichemotaxisXu YangUniversity of California, SantaBarbara, USAxuyang@m<strong>at</strong>h.ucsb.eduIn this talk, we give a m<strong>at</strong>hem<strong>at</strong>ical deriv<strong>at</strong>ion of ap<strong>at</strong>hway- based mean-field model for E. coli chemotaxisbased on the moment closure in kinetic theory. The p<strong>at</strong>hwaybased model incorpor<strong>at</strong>e the most recent intracellularchemical dynamics. The derived moment system,under some assumptions, gets to the chemotaxis modelproposed in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys.Rev. Lett., 109 (2012), 048101], especially an importantphysical assumption made in which can be understoodexplicitly in this new moment system. We obtain theKeller-Segal limit by considering the moment system inthe regime of long time and strong tumbling r<strong>at</strong>e. Numericalexperiments are presented to show the agreementof the moment system with (individual based) signalingp<strong>at</strong>hway- based E. coli chemotaxis simul<strong>at</strong>or ([L. Jiang,Q. Ouyang and Y. Tu, PLoS Comput. Biol., 6 (2010),e1000735]).Generalized Irving-Kirkwood formula for thecalcul<strong>at</strong>ion of continuum quantities in moleculardynamics modelsZhijian YangWuhan University, Chinazjyang.m<strong>at</strong>h@whu.edu.cnContinuum mechanics quantities can be computed frommolecular dynamics (MD) models based on the classicalIrving-Kirkwood (IK) formalism. Practical implement<strong>at</strong>ionsof IK formulas involve a sp<strong>at</strong>ial averaging usinga smooth kernel function. The obtained results usuallyneed to be further processed to reduce the fluctu<strong>at</strong>ion,e.g., by ensemble or time averaging. In this talk the IKformalism is extended to system<strong>at</strong>ically incorpor<strong>at</strong>e bothsp<strong>at</strong>ial and temporal averaging into the expression of continuumquantities. We will present the results both inLagrangian and Eulerian coordin<strong>at</strong>es.Special Session 15Number Theory and Represent<strong>at</strong>ion TheoryOn a classific<strong>at</strong>ion of irreducible modulo p represent<strong>at</strong>ionsof p-adic groupsNoriyuki AbeHokkaido University, Japanabenori@m<strong>at</strong>h.sci.hokudai.ac.jpBarthel-Livné introduced the notion of modulo p supersingularrepresent<strong>at</strong>ions of GL 2 . It is generalized to splitgroups by Herzig and to connected reductive groups byHenniart and Vignéras. In this talk, we discuss about aclassific<strong>at</strong>ion of irreducible modulo p represent<strong>at</strong>ions interms of supersingular represent<strong>at</strong>ions.This is joint work with G. Henniart, F. Herzig and M.-F.Vignéras.Parity sheaves on the affine Grassmannianand the Mirković–Vilonen conjecturePramod N. AcharLouisiana St<strong>at</strong>e University, USApramod@m<strong>at</strong>h.lsu.eduThe geometric S<strong>at</strong>ake equivalence gives a realiz<strong>at</strong>ion ofthe c<strong>at</strong>egory of represent<strong>at</strong>ions of a split reductive algebraicgroup over any field in terms of perverse sheaves onthe affine Grassmannian for the dual group. In this setting,Mirković and Vilonen conjectured th<strong>at</strong> the perversesheaves corresponding to Weyl modules should enjoy aparity-vanishing property, similar to th<strong>at</strong> of l-adic intersectioncohomology complexes. This conjecture has nowbeen proved (with a few exceptions in small characteristics)in joint work with Laura Rider. I will discuss theingredients in the proof, along with potential applic<strong>at</strong>ionsof our techniques to questions in modular represent<strong>at</strong>iontheory.Rectifiers and the local Langlands correspondenceMoshe AdrianUniversity of Utah, USAmadrian@m<strong>at</strong>h.utah.eduAbstract: In this talk, I will recall the notion of a rectifieras in the work of Bushnell/Henniart in the localLanglands correpsondence for GL(n). I will then proposea definition for rectifier for general unramified groups G.I will describe rectifiers in this setting, and show th<strong>at</strong> ourdefinition agrees with Bushnell/Henniart’s in the depthzero case. This is joint work with David Roe.Uniform in p estim<strong>at</strong>es for orbital integralsJulia GordonUniversity of British Columbia, Canadagor@m<strong>at</strong>h.ubc.ca
30 PRIMA 2013 AbstractsThis talk is about a method, based on model theory, th<strong>at</strong>can be used to get some uniform in p estim<strong>at</strong>es for integralsover p-adic fields in the cases when it is hard to seedirectly how such integrals behave for different places p.One example of such a situ<strong>at</strong>ion is orbital integrals onp-adic groups. Let G be a reductive p-adic group. It wasproved by Harish-Chandra th<strong>at</strong> the orbital integrals, normalizedby the discriminant, are bounded (for a fixed testfunction). However, it is not easy to see how this boundbehaves if we let the p-adic field vary (for example, if thegroup G is defined over a number field F , and we considerthe family of groups G v = G(F v), as v runs over the set offinite places of F ), and how it varies for a family of testfunctions. Using a method based on model theory andmotivic integr<strong>at</strong>ion, we prove th<strong>at</strong> the bound on orbitalintegrals can be taken to be a fixed power (dependingon G) of the cardinality of the residue field. This st<strong>at</strong>ementhas an applic<strong>at</strong>ion to the recent work of S.-W. Shinand N. Templier on counting zeroes of L-functions. Thisproject is joint work with R. Cluckers and I. Halupczok.On the center of Lie algebrasMasoud KamgarpourUniversity of Queensland, Australiamasoud@uq.edu.auI will discuss the center of the universal enveloping algebraof four different kinds of Lie algebras:(1) Harish-Chandra’s description of the centre of a simplealgebra g.(2) Duflo-Kirillov’s description of the centre of an arbitraryfinite dimensional algebra.(3) Center of the algebra of jets g[[t]] and g((t)).(4) Feigin-Frenkel description of center of the vertex Liealgebra associ<strong>at</strong>ed to g, via Langlands dual group.I will then define the notion of quasi-Verma modules forthe abovementioned vertex algebra, and stipul<strong>at</strong>e how theFeigin-Frenkel Center should act on these modules.A homological study of Green polynomialsSyu K<strong>at</strong>oKyoto University, Japansyuchan@m<strong>at</strong>h.kyoto-u.ac.jpWe first explain how to c<strong>at</strong>egorify the Green/Kostka polynomialsof reductive groups. Then, we discuss how theyare rel<strong>at</strong>ed to the relevant orthogonality rel<strong>at</strong>ion of somemodules of affine Hecke algebras and p-adic groups, andtheir consequences.On the structure of Selmer groupsMas<strong>at</strong>o KuriharaKeio University, Japankurihara@m<strong>at</strong>h.keio.ac.jpAs a refinement of Iwasawa theory, which gives a refinedrel<strong>at</strong>ionship than the usual main conjecture betweenSelmer groups and p-adic L-functions, I describethe structure as an abelian group of the classical Selmergroup of an elliptic curve, using modular symbols. I alsotalk on Euler systems and Kolyvagin systems of Gausssum type, which give nontrivial elements in Galois cohomologygroups.On the first Betti number of hyperbolic arithmeticmanifoldsJianshu LiHong Kong University of Science and Technology, HongKong, Chinam<strong>at</strong>om@ust.hkIn the 1970’s Thurston conjectured th<strong>at</strong> every hyperbolicmanifold admits a finite cover with non-zero first Bettinumber. In the arithmetic case, this property is rel<strong>at</strong>edto the congruence subgroup problem for SO(n, 1). Forarbitrary dimension n there are two types of arithmetichyperbolic manifolds, which arise from either quadr<strong>at</strong>icforms over totally real number fields, or skew-hermitianforms over certain qu<strong>at</strong>ernion algebras. In 1976 Millsonproved Thurston’s conjecture for the first type of arithmetichyperbolic manifolds using geometric methods. Forthe second type of manifolds, similar results were establishedin the 1990’s .In this talk we will briefly review this history, and discussan improved version of an old construction which leads tosome modest rel<strong>at</strong>ed results. We will also discuss somerel<strong>at</strong>ed open problems.On the elliptic part of the trace formula for˜Sp(2n)Wen-Wei LiChinese Academy of Sciences, Chinawwli@m<strong>at</strong>h.ac.cnIn this talk, I will introduce the stabiliz<strong>at</strong>ion of Arthur-Selberg trace formula for reductive groups and its applic<strong>at</strong>ions,then proceed to its generaliz<strong>at</strong>ion to the metaplectictwofold cover ˜Sp(2n) of Sp(2n). Based on therecent progress on geometric transfer and the invarianttrace formula for metaplectic group, I will explain thestabiliz<strong>at</strong>ion of the elliptic terms in the trace formula of˜Sp(2n).Endoscopic classific<strong>at</strong>ion of automorphic represent<strong>at</strong>ionsof classical groupsChung Pang MokMcMaster University, Canadacpmok@m<strong>at</strong>h.mcmaster.caWe will give an exposition of the recent works on endoscopicclassific<strong>at</strong>ion of automorphic represent<strong>at</strong>ions forclassical groups. Some recent arithmetic applic<strong>at</strong>ions ofthe endoscopic classific<strong>at</strong>ion will be discussed.Twisted spectral transfer for real groupsPaul MezoCarleton University, Canadamezo@m<strong>at</strong>h.carleton.caKottwitz and Shelstad generalized the framework of endoscopyto include twisting by group automorphisms orcentral characters. This generaliz<strong>at</strong>ion contained conjecturalidentities between orbital integrals, constituting <strong>at</strong>ransfer from functions on a group to functions on oneof its endoscopic groups. This geometric transfer has recentlybeen proven by Shelstad. Dual to geometric transferis spectral transfer, which is a collection identities betweencharacters of L-packets of a group and one of itsendoscopic groups. We show how some work of Bouaziz,Duflo and Shelstad may be adapted to the twisted endoscopyof real reductive groups in order to achieve spectraltransfer.Zelevinsky involution and l-adic cohomologyof Rapoport-Zink spacesYoichi MiedaKyoto University, Japanmieda@m<strong>at</strong>h.kyoto-u.ac.jp
31 PRIMA 2013 AbstractsRapoport-Zink spaces are certain moduli spaces of quasiisogeniesof p-divisible groups with additional structures,and can be regarded as local analogues of Shimura varieties.It is conjectured th<strong>at</strong> the l-adic cohomology ofRapoport-Zink spaces can be precisely decribed by meansof the local Langlands correspondence for general reductivegroups. In this talk, I will give results on rel<strong>at</strong>ionshipbetween the l-adic cohomology of Rapoport-Zink spacesand the Zelevinsky involution. I will also explain someapplic<strong>at</strong>ions to compute the l-adic cohomology.Geometrizing characters of toriDavid RoeUniversity of Calgary, Canadaroed.m<strong>at</strong>h@gmail.comThe passage from functions to sheaves has proven a valuabletool in the geometric Langlands program. In thistalk I’ll describe a “geometric av<strong>at</strong>ar” for the group ofcharacters of T (K), where T is an algebraic torus over alocal field K. I will then give some potential applic<strong>at</strong>ionsto the classical Langlands correspondence. This is jointwork with Clifton Cunningham.Twisted Bhargava cubesGordan SavinUniversity of Utah, USAsavin@m<strong>at</strong>h.utah.eduLet G be a reductive group and P = MN a maximalparabolic subgroup. The group M acts, by conjug<strong>at</strong>ion,on N/[N, N]. It is well known th<strong>at</strong>, over an algebraicallyclosed field, the group M acts transitively on a Zariskiopen set. However, over a general field, the structure oforbits may be quite non-trivial. A description my involveunexpected invariants. A notable example is when G isa split, simply connected group of type D 4 , and P is themaximal parabolic corresponding to the branching pointof the Dynkin diagram. The space N/[N, N] is also knownas the Bhargava cube, and it was the starting point of hisinvestig<strong>at</strong>ions of prehomogeneous spaces. We consider aversion of this problem for the triality D 4 . This is a jointwork with Wee Teck Gan.Stability and sign changes in p-adic harmonicanalysisLoren SpiceTexas Christian University, USAl.spice@tcu.eduReeder has described a conjectural candid<strong>at</strong>e for thepartition of certain supercuspidal represent<strong>at</strong>ions constructedby Yu (the so called toral, unramified supercuspidals)into L-packets, and verified th<strong>at</strong> it s<strong>at</strong>isfies most ofthe necessary properties. However, the problem of stabilityof the appropri<strong>at</strong>e character sums remained outstanding.In this talk, I will discuss joint work with DeBackerth<strong>at</strong> shows the necessary stability. A key ingredient isthe study of a sign associ<strong>at</strong>ed to combin<strong>at</strong>orial d<strong>at</strong>a involvingGalois orbits on a root system, which we computeunconditionally in the unramified case.Conserv<strong>at</strong>ion rel<strong>at</strong>ions for local theta correspondenceBinyong SunAcademy of M<strong>at</strong>hem<strong>at</strong>ics and Systems Science, CAS,Chinasun@m<strong>at</strong>h.ac.cnI will introduce Kudla-Rallis conjecture on first occurrencesof local theta correspondence, and explain the ideaof its proof. This is a report of a joint work with Chen-BoZhu.L-functions and theta correspondenceShunsuke YamanaKyushu University, Japanyamana@m<strong>at</strong>h.kyushu-u.ac.jpThe doubling method of Pi<strong>at</strong>etski-Shapiro and Rallis appliesin the local situ<strong>at</strong>ion to define local factors of represent<strong>at</strong>ionsof classical groups. On the one hand, theL-factor is defined as a g.c.d. of the local zeta integralsfor all good sections. On the other hand, it is definedfrom the gamma factor by using the Langlands classific<strong>at</strong>ion.In this talk I develop a theory of the zeta integraland prove th<strong>at</strong> the two candid<strong>at</strong>es of the L-factor agree.Applic<strong>at</strong>ions include a characteriz<strong>at</strong>ion of nonvanishing ofglobal theta liftings in terms of the analytic properties ofthe complete L-functions and the occurrence in the localtheta correspondence.Special Session 16Oper<strong>at</strong>or Algebras and Harmonic AnalysisUncertainty principles for infinite abeliangroupsLiming Ge, Jingsong Wu, Wenming Wu & Wei YuanUniversity of New Hampshire, USAliming@unh.eduIn this paper, we shall revisit uncertainty principle onfinite abelian groups and determine the functions th<strong>at</strong>give Tao’s lower bound in above inequality. Our mainfocus then moves to the additive integer group Z. Itsdual is identified with R/Z (= [0, 1)). Since there is nocountably additive invariant (probability) measure on Z,we shall use von Neumann’s invariant mean which is afinitely additive for any disjoint subsets. With respectto a given mean on Z and Lebesgue measure on R/Z,we show th<strong>at</strong> there is a subset S of Z with mean 1 soth<strong>at</strong> any square summable functions f supported on Shave “full” supported Fourier transform in the sense th<strong>at</strong>the closure of supp(f) is equal to [0, 1]. Symmetrical, weshow th<strong>at</strong> there is subset G of Z with mean 0 so th<strong>at</strong>, forany x ∈ [0, 1] and any ɛ > 0, all functions supported onG together with those f with supp( ˆf) ⊂ [x, x + ɛ] spana dense subset of l 2 (Z), the Hilbert space of all squaresummable functions.Oper<strong>at</strong>or theoretic analogue for Lehmer’sproblemKunyu GuoFudan Unversity, Chinakyguo@fudan.edu.cnIn this talk, we will establish a fascin<strong>at</strong>ing connectionbetween Lehmer’s problem and oper<strong>at</strong>or theory. This isa joint work with Jiayang Yu.Convolution algebras associ<strong>at</strong>ed with locallycompact quantum groupsZhiguo HuUniversity of Windsor, Canadazhiguohu@uwindsor.caWe consider the convolution algebras L 1 (G) andT (L 2 (G)) associ<strong>at</strong>ed with a locally compact quantum
32 PRIMA 2013 Abstractsgroup G, where T (L 2 (G)) is the space of trace class oper<strong>at</strong>orson L 2 (G) with the convolution induced by theright fundamental unitary of G. We obtain a n<strong>at</strong>ural isomorphismbetween the completely bounded right multiplieralgebras of L 1 (G) and T (L 2 (G)), and characterizethe regularity of the quantum group G in terms of theconvolution on T (L 2 (G)). We show th<strong>at</strong> T (L 2 (G)) isstrongly Arens irregular in the sense of Dales and Lauif and only if G is finite. Some commut<strong>at</strong>ion rel<strong>at</strong>ionsof completely bounded multipliers of L 1 (G) will also bediscussed. This is joint work with M<strong>at</strong>thias Neufang andZhong-Jin Ruan.Complex geometry and similarity of Cowen-Douglas oper<strong>at</strong>orsChunlan JiangHebei Normal University, Chinacljiang@hebtu.edu.cnIn this talk, we discuss the similarity invariant of the geometryoper<strong>at</strong>or induced by the holomorphic bundle. Wegive a complete similarity invariant of this kind of geometryoper<strong>at</strong>or by using K-group and curv<strong>at</strong>ure.Minimum phase oper<strong>at</strong>ors and the Polya-Schur problemMichael P. LamoureuxUniversity of Calgary, Canadamikel@ucalgary.caWe set a m<strong>at</strong>hem<strong>at</strong>ical framework for understanding minimumphase preserving physical processes and obtain thefollowing. The n<strong>at</strong>ural analytic setting for these timelimitedsignals is Hilbert-Hardy space. The minimumphase (or impulsive) signals correspond to the outer functionsin Hardy space. The minimum phase preservingprocesses correspond to linear oper<strong>at</strong>ors which preservethe set of shifted outer functions.Our main result shows these linear oper<strong>at</strong>ors on Hardyspace are completely characterized as a combin<strong>at</strong>ion ofa multiplic<strong>at</strong>ion and a composition oper<strong>at</strong>or involvingholomorphic functions of a specific form. The proof ofthis result makes essential use of Hadamard’s Theoremand the Weierstrass product represent<strong>at</strong>ion. Remarkably,this result also extends to provide constructive solutionsto the Polya-Schur problem of finding linear oper<strong>at</strong>orsth<strong>at</strong> preserve the zero-sets of families of complex polynomials.Returning to the physical problem, these processesthus consist of a st<strong>at</strong>ionary filtering combined witha frequency-dependent Q-<strong>at</strong>tenu<strong>at</strong>ion.Joint with Peter. C. Gibson and Gary F. MargraveKishimoto’s conjugacy theorems in simple C ∗ -algebras of tracial rank oneHuaxin LinUniversity of Oregon, USAhlin@uoregon.eduLet A be a unital separable simple amenable C*-algebrawith finite tracial rank which s<strong>at</strong>isfies the UCT. Supposeα and β are two automorphisms with the Rokhlin property.We show th<strong>at</strong> α and β are strongly co-cycle conjug<strong>at</strong>eand uniformly approxim<strong>at</strong>ely conjug<strong>at</strong>e, i.e., thereexists a sequence of unitaries {u n} ⊂ A and a sequence ofstrong asymptotically inner automorphisms σ n such th<strong>at</strong>α = Ad u n ◦ σ n ◦ β ◦ βn −1 and lim ‖un − 1‖ = 0,n→∞provided th<strong>at</strong> they induce the same K-theoretical d<strong>at</strong>a.We also show th<strong>at</strong> converse also holds. We also give aK-description as exactly when α and β are co-cycle conjug<strong>at</strong>e.We also show th<strong>at</strong> given a K-theoretical d<strong>at</strong>a,there is an automorphism α with the Rokhlin propertywhich has th<strong>at</strong> given K-theoretical d<strong>at</strong>a.Spectral gap actions and invariant st<strong>at</strong>esChi-Keung NgNankai University, Chinackng@nankai.edu.cnWe define spectral gap actions of discrete groups on vonNeumann algebras and study their rel<strong>at</strong>ions with invariantst<strong>at</strong>es. We will show th<strong>at</strong> a finitely gener<strong>at</strong>ed ICCgroup Γ is inner amenable if and only if there exist morethan one inner invariant st<strong>at</strong>es on the group von Neumannalgebra L(Γ). Moreover, a countable discrete groupΓ has property (T ) if and only if for any action α of Γ ona von Neumann algebra N, every α-invariant st<strong>at</strong>e on Nis a weak- ∗ -limit of a net of normal α-invariant st<strong>at</strong>es.Quantum correl<strong>at</strong>ions and Tsirelson’s problemNarutaka OzawaKyoto University, Japannarutaka@kurims.kyoto-u.ac.jpThe EPR paradox tells us quantum theory is incomp<strong>at</strong>iblewith classic realistic theory. Indeed, Bell has shownth<strong>at</strong> quantum correl<strong>at</strong>ions of independent bipartite systemshave more possibility than the classical correl<strong>at</strong>ions.To study wh<strong>at</strong> the possibilities are, Tsirelson has introducedthe set of quantum correl<strong>at</strong>ion m<strong>at</strong>rices, but dependingon the interpret<strong>at</strong>ion of independence, there aretwo plausible definitions of it. Tsirelson’s problem askswhether these definitions are equivalent. It turned outth<strong>at</strong> this problem in quantum inform<strong>at</strong>ion theory is infact equivalent to Connes’s embedding conjecture, one ofthe most important open problems in theory of oper<strong>at</strong>oralgebras. I will talk some recent progress on Tsirelson’sproblem.Ergodic theory over locally compact quantumgroupsVolker RundeUniversity of Alberta, Canadavrunde@ualberta.caWe develop the elements of an ergodic theory over locallycompact quantum (semi)groups and extend resultsby Zsidó et al.. This is joint work with Ami Viselter.Extending deriv<strong>at</strong>ions to dual Banach algebrasEbrahim SameiUniversity of Sask<strong>at</strong>chewan, Canadasamei@m<strong>at</strong>h.usask.caIf D : A → X is a deriv<strong>at</strong>ion from a Banach algebra toa contractive, Banach A-bimodule, then one can equipX ∗∗ with an A ∗∗ -bimodule structure, such th<strong>at</strong> the secondtranspose D ∗∗ : A ∗∗ → X ∗∗ is again a deriv<strong>at</strong>ion.I present an analogous extension result, where A ∗∗ is replacedby the enveloping dual Banach algebra F(A) (as introducedby V. Runde), and X ∗∗ by an appropri<strong>at</strong>e kindof universal, enveloping, normal dual bimodule of X. Ourapproach is motiv<strong>at</strong>ed by earlier results of F. Gourdeau.I apply these constructions to obtain some new characteriz<strong>at</strong>ionsof Connes-amenability of F(A). In particular, weshow th<strong>at</strong> F(A) is Connes-amenablity if and only if A admitsa so-called WAP-virtual diagonal. Also, in the casewhere A = L 1 (G), we show by modifying arguments ofRunde th<strong>at</strong> existence of a WAP-virtual diagonal is equivalentto the existence of a virtual diagonal in the usual
33 PRIMA 2013 Abstractssense. Our approach does not involve invariant means forG.p-vari<strong>at</strong>ions of Fourier algebrasNico SpronkUniversity of W<strong>at</strong>erloo, Canadanspronk@uw<strong>at</strong>erloo.caLet G be a compact group and A(G) its Fourier algebra.About a half decade ago, an invesitg<strong>at</strong>ion of B. Forrest,E. Samei and the speaker brought up a curious Banachalgebra A ∆ (G) which plays a role rel<strong>at</strong>ive to oper<strong>at</strong>oramenability problems for A(G), in the same manner as acertain algebra A γ(G) of B. Johnson plays to amenabilityproblems. The algebra A γ(G) may be understoodas a type of “Beurling-Fourier algebra" on G, in a mannerwhich has been recently invesig<strong>at</strong>ed by H.H. Lee, E.Samei, J. Ludwig, L. Turowska and the speaker, in variousarticles.I will present a context in which we may understandA ∆ (G) as the case p = 2 in a class of Banach algebrasA p (G) (1 ≤ p ≤ ∞). Here A 1 (G) = A(G), but the rest ofthe algebras may be understood via interpol<strong>at</strong>ion. Thesealgebras do not exhibit the same functorial properties asFourier algebras, and hence allow us to exhibit some unusualBanach algebras on tori.This talk represents joint work with H.H. Lee and E.Samei.Zero products and norm preserving orthogonallyadditive homogeneous polynomials onC*-algebrasNgai-Ching WongN<strong>at</strong>ional Sun Y<strong>at</strong>-sen University, Taiwanwong@m<strong>at</strong>h.nsysu.edu.twLet P : A → B be a bounded orthogonally additiveand zero product preserving n-homogeneous polynomialbetween C*-algebras. We show th<strong>at</strong>, in the commut<strong>at</strong>ivecase th<strong>at</strong> A = C 0 (X) and B = C 0 (Y ), there exista bounded continuous function h in C(Y ) and a mapϕ : Y → X such th<strong>at</strong> P f = h · (f ◦ ϕ) n . In the generalcase, we show th<strong>at</strong> there is a central invertible multiplierh of B and a surjective Jordan homomorphism J : A → Bsuch th<strong>at</strong> P a = hJ(a) n , provided th<strong>at</strong> P (A) ⊇ B + . SimilarBanach-Stone type theorems also hold for orthogonallyadditive n-homogeneous polynomials which are n-isometries. Using these results, we provide the full structureof orthogonally additive and orthogonally multiplic<strong>at</strong>iveholomorphic functions on commut<strong>at</strong>ive C*-algebras.This is a joint work with Qingying Bu (Univ. of Mississippi)and Ming-Hsiu Hsu (N<strong>at</strong>’l Sun Y<strong>at</strong>-sen Univ.)Recent development of analysis on noncommut<strong>at</strong>ivetoriQuanhua XuWuhan University, China and University of Franche-Comté, FranceNoncommut<strong>at</strong>ive tori are fundamental examples in oper<strong>at</strong>oralgebras and noncommut<strong>at</strong>ive geometry. This talkwill present a survey on the recent development of analysison noncommut<strong>at</strong>ive tori. The results presented willinclude those on harmonic analysis and Sobolev embeddinginequalities on quantum tori. This talk is based onjoint works with Zeqian Chen, Xiao Xiong and Zhi Yin.Amenability properties of weighted group algebrasYong ZhangUniversity of Manitoba, Canadazhangy@cc.umanitoba.caLet G be a locally compact group and ω a continuousweight on G. It is well-known th<strong>at</strong> the weightedgroup algebra L 1 (G, ω) is amenable as a Banach algebraif and only if G is an amenable group and the functionΩ(t) = ω(t)ω(t −1 ) is bounded on G. We show th<strong>at</strong>, foran abelian locally compact group G, L 1 (G, ω) is weaklyamenable if and only if there is no nontrivial continuousgroup homomorphism φ: G → (C, +) such th<strong>at</strong>|φ(t)|supt∈G Ω(t) < ∞.In other words, Ω(t) shall grow slower then any φ in orderL 1 (G, ω) to be weakly amenable.We will also consider the weak amenability of L 1 (G, ω)and its center ZL 1 (G, ω) for non-commut<strong>at</strong>ive locallycompact groups G, discussing some special cases. In general,how to characterize the weak amenability of a noncommut<strong>at</strong>iveL 1 (G, ω) and how to characterize the weakamenability of its center algebra are still open problems.Special Session 17Optimiz<strong>at</strong>ionRegularized interior proximal altern<strong>at</strong>ing directionsmethodFelipe AlvarezUniversidad de Chile, Chilefalvarez@dim.uchile.clWe consider convex constrained optimiz<strong>at</strong>ion problemswith a special separable structure. We propose a class ofaltern<strong>at</strong>ing directions methods (ADM) where their subproblemsare regularized with a general interior proximalmetric which covers the double regulariz<strong>at</strong>ion proposed bySilva and Eckstein. Under standard assumptions, globalconvergence of the primal-dual sequences produced by thealgorithm is established.Linear conic programming and interior-pointalgorithmsYanqin BaiShanghai University, Chinayqbai@shu.edu.cnLinear conic programming extends the popularly used linearprogramming models from linearity to non-linearityas well as from convexity to non-convexity in polynomialtimecomput<strong>at</strong>ions. Linear conic programming problemsare linear programming models with the additional constraintof products of nonlinear cones which include twoclasses of important cones. One class is symmetric conewhich leads to symmetric cone optimiz<strong>at</strong>ion problemssuch as linear, semideąěnite and second-order cone programmingproblems in which the cone constraints are selfdualand homogeneous. These symmetric conic programmingcan be solved eąÀciently using polynomial-timeinterior-point methods. Another class is nonsymmetriccone optimiz<strong>at</strong>ion problems such as copositive cone programmingproblems and the cone programming of nonneg<strong>at</strong>ivequadr<strong>at</strong>ic function over a set. For these conicprogramming the cone constraints are not self-dual andin particular requires special purpose algorithm. The proposeof this talk is to introduce a very rich formul<strong>at</strong>ion oflinear conic programming and present the general model,the conjug<strong>at</strong>e duality theory, p<strong>at</strong>h-following interior pointapproaches and illustr<strong>at</strong>ive applic<strong>at</strong>ions of linear conicprogramming.
34 PRIMA 2013 AbstractsDesign of robust truss structures for minimumweight using the sequential convex approxim<strong>at</strong>ionmethodAlfredo CanelasUniversidad de la República, Uruguayacanelas@fing.edu.uyMiguel CarrascoUniversidad de los Andes, Chilemigucarr@uandes.clJulio LopezUniversidad Diego Portales, Chilejulio.lopez@udp.clTrusses are mechanical structures in R d , where d is 2 forplanar trusses or 3 for three-dimensional ones. They consistof an ensemble of N nodes joint by m ≥ 2 bars whichare made of a linear elastic, isotropic and homogeneousm<strong>at</strong>erial. Long bars overlapping small ones are not allowed,and therefore m ≤ N(N − 1)/2 for a mesh fullof bars. Trusses are designed to support some externalnodal loads taking into account the properties of the barm<strong>at</strong>erial. We assume th<strong>at</strong> there exists a set of primaryexternal loads, applied only in the nodes of the truss, andth<strong>at</strong> there exists a set of secondary nodal ones th<strong>at</strong> areuncertain in size and direction, which can be viewed asa perturb<strong>at</strong>ion of the main loads. Our main objective isto minimize the total amount of m<strong>at</strong>erial or weight, withthe purpose of finding the most economic structure, th<strong>at</strong>is robust under load perturb<strong>at</strong>ions.We formul<strong>at</strong>e a model in order to include the mechanicalequilibrium constraint and stress constraints, as well asbounds on displacements, considering also stability constraintsunder perturb<strong>at</strong>ion of the main load. More precisely,we will study the properties of the following non–convex semi-infinite m<strong>at</strong>hem<strong>at</strong>ical programming problem(P w) minx≥0m∑x ii=1|u j (ξ, x)| ≤ ū j j ∈ J ⊆ {1, . . . , n},|σ i (ξ, x)| ≤ ¯σ i i ∈ I ⊆ {1, . . . , m},ξ ∈ E,where x i represents the volume of each bar, u is the vectorof displacements, and σ i the stress of the i-th bar. Theset E ⊆ R n corresponds to the set of secondary loads,and we implicitly assume the mechanical equilibrium constraintK(x)u(ξ, x) = f + ξ. To address the infinite numberof constraints we reformul<strong>at</strong>e (P w) as a non–convexbilevel m<strong>at</strong>hem<strong>at</strong>ical program. The main idea is to solvethis problem assuming th<strong>at</strong> the set E of secondary loadstakes the form of a particular ellipsoid, similar to the approachedby Ben-Tal and Nemirovski . Based on the workof Beck et al., we have obtained encouraging preliminarynumerical results for this altern<strong>at</strong>ive, which approach consistson approxim<strong>at</strong>ing some non–convex constraints andsolving a sequence of parametric conic problems.Expected residual minimiz<strong>at</strong>ion for stochasticvari<strong>at</strong>ional inequalitiesXiaojun ChenThe Hong Kong Polytechnic University, Hong Kong,Chinamaxjchen@polyu.edu.hkThis talk discusses a variety of comput<strong>at</strong>ional approachesfor stochastic vari<strong>at</strong>ional inequalities and presents a newexpected residual minimiz<strong>at</strong>ion formul<strong>at</strong>ion for a classof stochastic vari<strong>at</strong>ional inequalities by using the gapfunction. The objective function of the expected residualminimiz<strong>at</strong>ion problem is nonneg<strong>at</strong>ive and Lipschitzcontinuous. Moreover, it is convex for some stochasticlinear vari<strong>at</strong>ional inequalities, which helps us guaranteethe existence of a solution and convergence of approxim<strong>at</strong>ionmethods. We propose a globally convergent(a.s.) smoothing sample average approxim<strong>at</strong>ion (SSAA)method to minimize the expected residual function. Weshow th<strong>at</strong> the residual minimiz<strong>at</strong>ion problem and itsSSAA problems have minimizers in a compact set andany cluster point of minimizers and st<strong>at</strong>ionary points ofthe SSAA problems is a minimizer and a st<strong>at</strong>ionary pointof the expected residual minimiz<strong>at</strong>ion problem (a.s.). Ourexamples come from applic<strong>at</strong>ions involving traffic flowproblems. We show th<strong>at</strong> the conditions we impose ares<strong>at</strong>isfied and th<strong>at</strong> the solutions, efficiently gener<strong>at</strong>ed bythe SSAA procedure, have desirable properties.Joint work with Roger Wets and Yangfan Zhang.Stability of two-stage stochastic programswith quadr<strong>at</strong>ic continuous recourseZhiping ChenXi’an Jiaotong Universityzchen@mail.xjtu.edu.cnYoupan HanXi’an Polytechnic UniversityWe consider the stability of the two-stage quadr<strong>at</strong>icstochastic programming problem with quadr<strong>at</strong>ic continuousrecourse when the underlying probability distributionis perturbed. For the case th<strong>at</strong> all the coefficientsin the objective function and the right-hand side vectorin second-stage constraints are random, we firstly showthe locally Lipschtiz continuity of the optimal value functionof the recourse problem; then under suitable probabilitymetric, we derive the Lipschitz continuity of theexpected optimal value function with respect to the firststagevariable and the probability distribution; and furthermore,we establish the qualit<strong>at</strong>ive and quantit<strong>at</strong>ivestability results of the optimal value function and theoptimal solution set with respect to the Fortet-Mourierprobability metric. For the more complex situ<strong>at</strong>ion th<strong>at</strong>the recourse costs, the recourse m<strong>at</strong>rix, the technologym<strong>at</strong>rix and the right-hand side vector in the second-stageproblem are all random, and th<strong>at</strong> the second-stage objectivefunction might be non-convex, we obtain the uniformlyboundedness and locally Lipschtiz continuity ofthe second-stage feasible solution set when it is regularand bounded; we also establish the locally Lipschtizcontinuity of the corresponding optimal value function;then we show the Lipschitz continuity of the expectedvalue function of the second-stage problem with respectto both the first-stage variables and the probability metricinvolved in the second-stage problem; utilizing theseresults, we finally derive the qualit<strong>at</strong>ive and quantit<strong>at</strong>ivestability results of the optimal value function andthe optimal solution set of two-stage quadr<strong>at</strong>ic stochasticprograms with respect to the Fortet-Mourier probabilitymetric.Existence of minimizers on dropsRafael CorreaUniversidad de Chile, Chilercorrea@dim.uchile.clFor a boundedly gener<strong>at</strong>ed drop [a, E] (property whichholds, for instance, whenever E is bounded), where abelongs to a real Banach space X and E ⊂ X is anonempty convex set, we show th<strong>at</strong> for every lower semicontinuousfunction h : X −→ R ∪ {+∞} th<strong>at</strong> s<strong>at</strong>isfiessup δ > 0 infx ∈ E + δBx h(x) > h(a)(B X being the unitaryopen ball in X), there exists x ∈ [a, E] such th<strong>at</strong>h(a) ≥ h(x) and x is a strict minimizer of h on the drop[x, E].The robust stability of every equilibrium ineconomic models of exchangeAlejandro JofreUniversity de Chile, Chileajofre@dim.uchile.cl
35 PRIMA 2013 AbstractsIn an economic model of exchange of goods, the structurecan be specified by utility functions. Under utility conditionsidentified here even more broadly than usual, exceptfor concavity in place of quasi-concavity, every equilibriumwill simultaneously be stable with respect to shiftsin the associ<strong>at</strong>ed holdings of the agents and with respectto the dynamic Walrasian t<strong>at</strong>onnement process of priceadjustment. This fact, seemingly contrary to widespreadbelief, is revealed by paying close <strong>at</strong>tention not only toprices but also to the proximal st<strong>at</strong>us of initial holdings.The conditions on the concave utility functions are standardfor stability investig<strong>at</strong>ions, in th<strong>at</strong> they invoke propertiescoming from second deriv<strong>at</strong>ives, but significantlyrelaxed in not forcing all goods to be held only in positiveamounts. Recent advances in vari<strong>at</strong>ional analysisprovide the support needed for working in th<strong>at</strong> context.The stability results also point the way toward furtherdevelopments in which an equilibrium might evolve inresponse to exogenous inputs to the agents’ holdings, orextractions.Solving m<strong>at</strong>hem<strong>at</strong>ical programs with equilibriumconstraints as constrained equ<strong>at</strong>ionsGui-Hua LinShanghai University, Chinaguihualin@shu.edu.cnLei GuoDalian University of Technology, Chinaguolayne@gmail.comJane J. YeUniversity of Victoria, Canadajaneye@uvic.caThis paper aims <strong>at</strong> developing effective numerical methodsfor solving m<strong>at</strong>hem<strong>at</strong>ical programs with equilibriumconstraints. Due to the complementarity constraints, theusual constraint qualific<strong>at</strong>ions such as the Mangasarian-Fromovitz constraint qualific<strong>at</strong>ion do not hold <strong>at</strong> any feasiblepoint and there are various st<strong>at</strong>ionarity conceptssuch as Clarke/Mordukhovich/strong st<strong>at</strong>ionarity suggestedin the liter<strong>at</strong>ure. In this paper, we reformul<strong>at</strong>ethese st<strong>at</strong>ionarity conditions as smooth equ<strong>at</strong>ions withbox constraints. We then present a modified Levenberg-Marquardt method for solving these constrained equ<strong>at</strong>ions.We show th<strong>at</strong>, under some weak local error boundconditions, the method is locally and superlinearly convergent.Furthermore, we give some sufficient conditionsfor local error bounds to hold and show th<strong>at</strong> these conditionsare not very stringent by a number of examples.A feasible direction algorithm for nonlinearsecond-order cone optimiz<strong>at</strong>ion problemsJulio LópezUniversidad Diego Portales, Chilejulio.lopez@udp.clIn this work, we propose a feasible direction algorithmfor solving nonlinear convex second-order cone programs.This kind of problems consists of minimizing a convexfunction over the Cartesian product of second-ordercones. Our approach computes feasible descend directionsby using the same formul<strong>at</strong>ion as in FDIPA proposed byHerskovitz [J. Optim. Theory Appl., vol. 99 (1998), pp.53–58]. Under suitable assumptions, some results preliminariesof convergence are obtained. Finally, to show howour algorithm works in practice, comput<strong>at</strong>ional resultsapplied to support vector machines under uncertainty ispresented.A dynamical approach to an inertial forwardbackwardalgorithm for convex minimiz<strong>at</strong>ionJuan PeypouquetUniversidad Técnica Federico Santa María, Chilejuan.peypouquet@usm.clWe introduce a new class of forward-backward algorithmsfor structured convex minimiz<strong>at</strong>ion problems in Hilbertspaces. Our approach relies on the time discretiz<strong>at</strong>ion ofa second-order differential system with two potentials andHessian-driven damping. This system can be equivalentlywritten as a first order-system in time and space, each ofthe two constitutive equ<strong>at</strong>ions involving only one of thetwo potentials. Its time dicretiz<strong>at</strong>ion n<strong>at</strong>urally leads tothe introduction of forward-backward splitting algorithmswith inertial fe<strong>at</strong>ures. Using a Liapunov analysis, weshow the convergence of the algorithm under conditionsimproving the classical step size limit<strong>at</strong>ion. Then, wespecialize our results to gradient-projection algorithms,and give some illustr<strong>at</strong>ion to sparse signal recovery andfeasibility problems.Second-order analysis in conic programming:Applic<strong>at</strong>ions to stabilityHéctor Ramírez C.Universidad de Chilehramirez@dim.uchile.clIn this talk we review some recent results obtained forconic programs from the applic<strong>at</strong>ion of a second-ordergeneralized differential approach. It is used to calcul<strong>at</strong>eappropri<strong>at</strong>e deriv<strong>at</strong>ives and coderiv<strong>at</strong>ives of the correspondingsolution maps. These developments allow usto obtain verifiable conditions for the strong regularity,the Aubin property and isol<strong>at</strong>ed calmness of the consideredsolution maps. The main results obtained in thegeneral conic programming setting are specified for andillustr<strong>at</strong>ed by the second-order cone programming[1] J. F. Bonnans and H. Ramírez C., Perturb<strong>at</strong>ion analysisof second-order cone programming problems. M<strong>at</strong>h.Program., 104 (2005), pp. 205-227.[2] J. V. Outr<strong>at</strong>a and H. Ramírez C., On the Aubin propertyof critical points to perturbed second-order cone programs,SIAM J. Optim., 21 (2011), pp. 798-823.[3] B. Mordukhovich, J. V. Outr<strong>at</strong>a and H. Ramírez C.,Second-order vari<strong>at</strong>ional analysis in conic programmingwith applic<strong>at</strong>ion to optimality and stability. Submitted(2013).Facially exposed cones are not always niceVera RoshchinaUniversity of Ballar<strong>at</strong>, Australiavroshchina@ballar<strong>at</strong>.edu.auWe show th<strong>at</strong> Gabor P<strong>at</strong>aki’s conjecture th<strong>at</strong> facially exposedcones are nice is true in three-dimensional case,but does not hold for higher dimensions by presenting afour-dimensional counterexample. We also discuss implic<strong>at</strong>ionsof this result and st<strong>at</strong>e some open problems.Asymptotic convergence analysis for distributionalrobust optimiz<strong>at</strong>ion and equilibriumproblemsHailin SunHarbin Institute of Technology, Chinam<strong>at</strong>hhlsun@gmail.comHuifu XuCity University of London, UKHuifu.Xu.1@city.ac.ukIn this paper, we study distributional robust optimiz<strong>at</strong>ionapproaches for a one stage stochastic minimiz<strong>at</strong>ion problem,where the true distribution of the underlying randomvariables is unknown but it is possible to constructa set of probability distributions which contains the truedistribution and optimal decision is taken on the basis ofworst possible distribution from th<strong>at</strong> set. We consider thecase when the distributional set is constructed through
36 PRIMA 2013 Abstractssamples and investig<strong>at</strong>e asymptotic convergence of optimalvalues and optimal solutions as sample size increases.The analysis provides a unified framework for asymptoticconvergence of some d<strong>at</strong>a-driven problems and extendsthe classical asymptotic convergence analysis in stochasticprogramming. The discussion is extended to a stochasticNash equilibrium problem where each player takes arobust action on the basis of their subjective expectedobjective value.Special Session 18ProbabilityThe motion of a tagged particle in the simpleexclusion processDayue Chen & Peng ChenPeking University, Chinadayue@pku.edu.cnThe simple exclusion process is an interacting particlesystem. There is no birth or de<strong>at</strong>h of particles. Eachparticle perform an independent random walk. The walkis suspended when a particle jumps to the site of anotherparticle. Therefore a tagged particle behaviors very muchlike a random walk with a fixed r<strong>at</strong>e of slow down. Inthis talk we shall review some limit theorems of a taggedparticle in the simple exclusion and report our progressin this direction.Multivari<strong>at</strong>e normal approxim<strong>at</strong>ion by Stein’smethod: the concentr<strong>at</strong>ion inequality approachLouis H. Y. ChenN<strong>at</strong>ional University of Singapore, Singaporem<strong>at</strong>chyl@nus.edu.sgIn this talk we will describe Stein’s method for normalapproxim<strong>at</strong>ion and explain the role of concentr<strong>at</strong>ion inequalitiesin proving Kolmogorov bounds in one dimension.We will then discuss multivari<strong>at</strong>e extensions of boththe normal approxim<strong>at</strong>ion and the concentr<strong>at</strong>ion inequalities.The multivari<strong>at</strong>e concentr<strong>at</strong>ion inequalities are thenapplied to multivari<strong>at</strong>e normal approxim<strong>at</strong>ion for independentsummands as well as for locally dependent summands.This talk is based on joint work with Xiao Fang.Stable processes with driftZhen-Qing ChenUniversity of Washington, USAzqchen@uw.eduSuppose th<strong>at</strong> d ≥ 1 and α ∈ (1, 2). Let Y be a rot<strong>at</strong>ionallysymmetric α-stable process on R d and b an R d -valued measurable function on R d belonging to a certainK<strong>at</strong>o class of Y . We show th<strong>at</strong> dX t = dY t + b(X t)dt withX 0 = x has a unique weak solution for every x ∈ R d . LetL b = −(−∆) α/2 + b · ∇, which is the infinitesimal gener<strong>at</strong>orof X b . Denote by Cc∞ (R d ) the space of smooth functionson R d with compact support. We further show th<strong>at</strong>the martingale problem for (L b , Cc∞(Rd )) has a uniquesolution for each initial value x ∈ R d . Moreover, sharptwo-sided estim<strong>at</strong>es for the transition density function ofX can be obtained as well as th<strong>at</strong> of its subprocess killedupon leaving a C 2 -smooth open set. This talk is basedon a joint work with Longmin Wang.Brownian motion in a heavy tailed PoissonianpotentialRyoki FukushimaKyoto University, Japanryoki@kurims.kyoto-u.ac.jpConsider the d-dimensional Brownian motion in a randompotential defined by <strong>at</strong>taching a non-neg<strong>at</strong>ive and polynomiallydecaying potential around Poisson points. Weintroduce a repulsive interaction between the Brownianp<strong>at</strong>h and the Poisson points by weighting the measureby the Feynman-Kac functional. Under the (annealed)weighted measure, it is shown th<strong>at</strong> the Brownian motiontends to localize around the origin and the properly scaledprocess converges in law to a Ornstein-Uhlenbeck process.Martingale problem under non-linear expect<strong>at</strong>ionsXin GuoUniversity of California, Berkeley, USAxinguo@berkeley.eduWe consider the martingale problem under the frameworkof nonlinear expect<strong>at</strong>ions, analogous to th<strong>at</strong> in a probabilityspace in the seminal paper of Stroock and Varadhan(1969).We first establish an appropri<strong>at</strong>e comparison theorem andthe existence result for the associ<strong>at</strong>ed st<strong>at</strong>e-dependentfully non-linear parabolic PDEs. We then construct theconditional expect<strong>at</strong>ion from the viscosity solution of thePDEs, and solve the existence of martingale problems.Under this non-linear expect<strong>at</strong>ion space, we further developthe stochastic integral and the Itô’s type formula,which are consistent with Peng’s G-framework. As anapplic<strong>at</strong>ion, we introduce the notion of weak solution ofSDE under the non-linear expect<strong>at</strong>ion.Scaling limits of interacting particle systemsin high dimensions.Mark HolmesUniversity of Auckland, New Zealandm.holmes@auckland.ac.nzA number of (interacting) particle systems <strong>at</strong> criticality,such as the voter model, the contact process, orientedpercol<strong>at</strong>ion, and l<strong>at</strong>tice trees, have been conjectured orproved to behave like the critial branching random walk,when the dimension is high enough so th<strong>at</strong> the interactionis weak. One version of this st<strong>at</strong>ement is th<strong>at</strong> appropri<strong>at</strong>elyrescaled versions of these models converge to super-Brownian motion. We will discuss wh<strong>at</strong> is known and notknown about these models in the context of convergenceto super-Brownian motion.Parabolic Littlewood-Paley inequality forφ(−∆)-type oper<strong>at</strong>ors and applic<strong>at</strong>ions tostochastic integro-differential equ<strong>at</strong>ionsPanki KimSeoul N<strong>at</strong>ional University, Koreapkim@snu.ac.krIn this talk we introduce a parabolic version of theLittlewood-Paley inequality for the oper<strong>at</strong>ors of the typeφ(−∆), where φ is a Bernstein function. As an applic<strong>at</strong>ion,we construct an L p-theory for the stochastic integrodifferentialequ<strong>at</strong>ions of the type du = (−φ(−∆)u+f) dt+g dW t. This is a joint work with Ildoo Kim and Kyeong-Hun Kim.Quenched invariance principles for randomwalks and random divergence forms in randommedia with a boundaryTakashi Kumagai
37 PRIMA 2013 AbstractsKyoto University, Japankumagai@m<strong>at</strong>h.kyoto-u.ac.jpWe will consider the following two models and establishquenched invariance principles;1. Simple random walks on the infinite clusters for supercriticalpercol<strong>at</strong>ions on half and quarter planes in d-dimensional Euclidean spaces.2. Uniform elliptic divergence forms with random st<strong>at</strong>ionarycoefficients on cones in Euclidean spaces.Note th<strong>at</strong> because of the lack of transl<strong>at</strong>ion invariancewe cannot apply the method of the ’corrector’. ÂăInsteadwe make full use of the he<strong>at</strong> kernel estim<strong>at</strong>es andDirichlet form techniques to resolve the problem. This isa joint work with Z.Q. Chen (Se<strong>at</strong>tle) and D.A. Croydon(Warwick).Ultrametric potentialsJaime San MartinUniversidad de Chile, Chilejsanmart@dim.uchile.clIn m<strong>at</strong>rix theory an important question is the so calledinverse M-m<strong>at</strong>rix problem. Recall th<strong>at</strong> an M-m<strong>at</strong>rix is anonsingular m<strong>at</strong>rix whose off diagonal elements are nonpositiveand whose inverse is non-neg<strong>at</strong>ive. So, the questionis which nonneg<strong>at</strong>ive m<strong>at</strong>rices are inverses of M-m<strong>at</strong>rices?.The inverse of an M-m<strong>at</strong>rix is n<strong>at</strong>urally linked to thepotential of a transient Markov chain and then one canuse a Theorem of Choquet-Deny to characterize these m<strong>at</strong>rices.The main drawback of this result is th<strong>at</strong> the characteriz<strong>at</strong>ionis difficult to check for a given m<strong>at</strong>rix.We connect this problem with the notion of ultrametricm<strong>at</strong>rices and filtered m<strong>at</strong>rices. Using these conceptswe provide a large class of inverse M-m<strong>at</strong>rices th<strong>at</strong> are describedin combin<strong>at</strong>orial terms. Special <strong>at</strong>tention is givento one dimensional random walks and random walks ontrees. We also discuss extensions to diffusions.Some of the useful bibliography is given below.[1] C. Dellacherie, S. Martínez and J. San Martín, Ultrametricm<strong>at</strong>rices and induced Markov chains. Advancesin Applied M<strong>at</strong>hem<strong>at</strong>ics, 17 (1996), 169–183.[2] C. Dellacherie, S. Martínez and J. San Martín, Descriptionof the Sub-Markov kernel associ<strong>at</strong>ed to generalizedultrametric m<strong>at</strong>rices. An algorithmic approach.Linear Algebra and its Applic<strong>at</strong>ions, 318 (2000), 1-21.[3] C. Dellacherie, S. Martínez, J. San Martín,Hadamard functions of inverse M-M<strong>at</strong>rices. SIAM Journalon M<strong>at</strong>rix Analysis and Applic<strong>at</strong>ions (2009) 31, 2,289–315.[4] C. Dellacherie, S. Martínez S., J. San Martín, Ultrametricand tree potential. Journal of Theoretical Probability(2009) 22, 2, 311–347.[5] F.R. Gantmacher and M.G. Krein, Oszill<strong>at</strong>ionsm<strong>at</strong>rizen,Oszill<strong>at</strong>ionskerne und kleine Schwingungen mechanischerSysteme, (1960) Akademie-Verlag, Berlin.[6] T.L. Markham, Nonneg<strong>at</strong>ive m<strong>at</strong>rices whose inversesare M-m<strong>at</strong>rices. Proceedings of the AmericanM<strong>at</strong>hem<strong>at</strong>ical Society, 36 (1972), 326–330.[7] S. Martínez, G. Michon and J. San Martín, Inversesof ultrametric m<strong>at</strong>rices are of Stieltjes types, SIAM JournalM<strong>at</strong>rix Analysis and its Applic<strong>at</strong>ions, 15 (1994), 98–106.[8] S. Martínez, J. San Martín, X. Zhang. A new classof inverse M-m<strong>at</strong>rices of tree-like type. SIAM Journalon M<strong>at</strong>rix Analysis and Applic<strong>at</strong>ions, 24-4 (2003), 1136–1148.[9] S. Martínez, J. San Martín, X. Zhang. A class ofM-m<strong>at</strong>rices whose graphs are trees. Linear and MultilinearAlgebra 52-5 (2004), 303–319.[10] J.J. McDonald, M. Neumann, H. Schneider,M.J. Ts<strong>at</strong>someros, Inverse M-m<strong>at</strong>rix inequalities and generalizedultrametric m<strong>at</strong>rices. Linear Algebra and its Applic<strong>at</strong>ions,220 (1995), 321–341.[11] J.J. McDonald, R. Nabben, M. Neumann,H.Schneider, M.J. Ts<strong>at</strong>someros Inverse tridiagonalZ-m<strong>at</strong>rices. Linear and Multilinear Algebra 45 (1998),75–97.[12] R. Nabben, On Green’s m<strong>at</strong>rices of trees. SIAMJournal M<strong>at</strong>rix Analysis and its Applic<strong>at</strong>ions, 22, no. 4,(2001), 1014–1026.From Stein’s method to self-normalized moder<strong>at</strong>edevi<strong>at</strong>ionsQi-Man ShaoThe Chinese University of Hong Kong, Hong Kong, Chinaqmshao@cuhk.edu.hkIn this talk we shall review recent developments onStein’s method and self-normalized limit theory. The focuswill be on randomized concentr<strong>at</strong>ion inequalities andtheir applic<strong>at</strong>ions to self-normalized Cramer type moder<strong>at</strong>etheorems.Backward stochastic differential equ<strong>at</strong>ionsdriven by G-Brownian motionYongsheng SongChinese Academy of Sciences, Chinayssong@amss.ac.cnIn this paper, we study the backward stochastic differentialequ<strong>at</strong>ions driven by G-Brownian motion inthe following form: Y t = ξ + ∫ Tt f(s, Y s, Z s)ds +∫ Tt g(s, Y s, Z s)d〈B〉 s − ∫ Tt Z sdB s − K T + K t. Under aLipschitz condition of f and g in Y and Z, the existenceand uniqueness of the solution (Y, Z, K) is proved, whereK is a decreasing G-martingale.Symmetric rearrangements around infinitywith applic<strong>at</strong>ions to Lévy processesRongfeng SunN<strong>at</strong>ional University of Singapore, Singaporem<strong>at</strong>sr@nus.edu.sgWe prove a new rearrangement inequality for multipleintegrals, which partly generalizes a result of Friedbergand Luttinger (1976) and can be interpreted as involvingsymmetric rearrangements of domains around infinity.As applic<strong>at</strong>ions, we prove two comparison results forgeneral Lévy processes and their symmetric rearrangements.The first applic<strong>at</strong>ion concerns the survival probabilityof a point particle in a Poisson field of moving trapsfollowing independent Lévy motions. We show th<strong>at</strong> thesurvival probability can only increase if the point particledoes not move, and the traps and the Lévy motions aresymmetrically rearranged. This essentially generalizes anisoperimetric inequality of Peres and Sousi (2011) for theWiener sausage. In the second applic<strong>at</strong>ion, we show th<strong>at</strong>the q-capacity of a Borel measurable set for a Lévy processcan only increase if the set and the Lévy processare symmetrically rearranged. This result generalizes aninequality obtained by W<strong>at</strong>anabe (1983) for symmetricLévy processes. Based on joint work with Alex Drewitzand Perla Sousi.Bismut formula and gradient estim<strong>at</strong>es forSDEs driven by multiplic<strong>at</strong>ive Lévy noiseFeng-Yu Wang, Lihu Xu & Xicheng ZhangBeijing Normal University, Chinawangfy@bnu.edu.cnBismut formula and Gradient estim<strong>at</strong>es are derived forthe semigroup associ<strong>at</strong>ed to a class of stochastic differentialequ<strong>at</strong>ions driven by multiplic<strong>at</strong>ive Lévy noise, where
38 PRIMA 2013 Abstractsthe noise is realized as a subordin<strong>at</strong>ion of the Brownianmotion. In particular, the estim<strong>at</strong>es are sharp forα-stable type noises. To derive these estim<strong>at</strong>es, a newderiv<strong>at</strong>ive formula is established for the semigroup by usingthe Malliavin calculus and a finite-jump approxim<strong>at</strong>ionargument.Viscosity solutions of p<strong>at</strong>h dependent PDEsJianfeng ZhangUniversity of Southern California, USAjianfenz@usc.eduP<strong>at</strong>h Dependent PDEs (PPDEs, for short) is a convenienttool to characterize the value functions of varioustypes of stochastic control problems in non- Markovianframework. Its typical examples include Backward SDEs(semi- linear PPDEs), second order BSDEs (p<strong>at</strong>h dependentHJB equ<strong>at</strong>ions), p<strong>at</strong>h dependent Bellman-Isaacsequ<strong>at</strong>ions, and Backward Stochastic PDEs. PPDEs canrarely have classical solutions. In this talk we shall proposea notion of viscosity solutions for PPDEs and establishits wellposedness. Our definition relies heavily on theFunctional Ito formula initi<strong>at</strong>ed by Dupire. Unlike theviscosity theory of standard PDEs, the main difficultyin p<strong>at</strong>h dependent case is th<strong>at</strong> the st<strong>at</strong>e space is not locallycompact. To overcome such difficulty, we replacethe pointwise maximiz<strong>at</strong>ion in standard theory with anoptimal stopping problem under Peng’s nonlinear expect<strong>at</strong>ion.The talk will be based on joint works with NizarTouzi, and Ibrahim Ekren, Christian Keller, Triet Pham.Special Session 19Represent<strong>at</strong>ion Theory and C<strong>at</strong>egorific<strong>at</strong>ionGeometric reciprocity for algebraic tori overnon-Archimedean local fieldsClifton CunninghamUniversity of Calgary, Canadacunning@m<strong>at</strong>h.ucalgary.caRecent work with David Roe has shown th<strong>at</strong> the geometriz<strong>at</strong>ionof admissible characters of T (K), where Tis an algebraic torus over a non-Archimedean field K, isachieved by introducing the tensor c<strong>at</strong>egory of charactersheaves on the Greenberg transform of the Neron modelof T . On the other hand, earlier worth with Achar, Kamgarpourand Salmasian, closely rel<strong>at</strong>ed to ideas of Vogan,shows th<strong>at</strong> the geometriz<strong>at</strong>ion of Langlands parametersfor T is achieved by passing to the c<strong>at</strong>egory of equivariantperverse sheaves on an ind-variety formed from L T .In this talk I will use the class field theory of Serre andHazewinkel to rel<strong>at</strong>e these two c<strong>at</strong>egories.Schubert calculus and cohomology of LiegroupsHaibao DuanInstitute of M<strong>at</strong>hem<strong>at</strong>ics, Chinese Academy of Sciences,Chinadhb@m<strong>at</strong>h.ac.cnThe problem of determining the cohomology of Lie groupswas raised by E. Cartan in 1929, and has been a focus ofalgebraic topology for the fundamental roles of Lie groupsplaying in geometry and topology. On the other handSchubert calculus begun with the intersection theory ofthe 19 century, and clarifying this calculus had been amajor theme of the 20 century algebraic geometry.We bring a connection between these two topics bothwith distinguished historical backgrounds, and demonstr<strong>at</strong>ehow Schubert calculus is extended as to give anexplicit and unified construction of the integral cohomologyrings of all compact and 1-connected Lie groups.Vanishing properties of Jack polynomialsStephen GriffethUniversidad de Talca, Chilesgriffeth@inst-m<strong>at</strong>.utalca.cl(Joint work with Christine Berkesch and Steven Sam)We describe some interactions between represent<strong>at</strong>ionsof r<strong>at</strong>ional Cherednik algebra, especially unitary represent<strong>at</strong>ions,and questions arising in combin<strong>at</strong>orial commut<strong>at</strong>ivealgebra and m<strong>at</strong>hem<strong>at</strong>ical physics. These questionsall have to do with highly symmetric linear subspacearrangements and the ideals of polynomials vanishingon them. Among other things, we will indic<strong>at</strong>e howto use represent<strong>at</strong>ion theory to prove a number of conjecturesof Bernevig and Haldane on the order of vanishingof certain Jack polynomials along these arrangements,and present our own conjecture describing a Bernstein-Gelfand-Gelfand type resolutions of unitary represent<strong>at</strong>ionsof the Cherednik algebra. Any such resolution isautom<strong>at</strong>ically a minimal free resolution for the ideal ofthe corresponding linear arrangement, so we predict acombiantorial formula for the graded equivariant Bettinumbers of these ideals.The modular generalized Springer correspondenceAnthony HendersonUniversity of Sydney, Australiaanthony.henderson@sydney.edu.auGiven a connected reductive algebraic group G with Weylgroup W , the Springer correspondence realizes the c<strong>at</strong>egoryof represent<strong>at</strong>ions of W as a quotient of the c<strong>at</strong>egoryof G-equivariant perverse sheaves on the nilpotentcone. In the original definition, the represent<strong>at</strong>ions andsheaves were over a field of characteristic zero, but wehave recently shown th<strong>at</strong> the same formalism works withmodular coefficients, where the c<strong>at</strong>egories are no longersemisimple. In the characteristic-zero case, Lusztig defineda generalized Springer correspondence to interpretthe whole c<strong>at</strong>egory of G-equivariant perverse sheaves onthe nilpotent cone in terms of represent<strong>at</strong>ions of rel<strong>at</strong>iveWeyl groups. We define and determine a modular generalizedSpringer correspondence in the case G = GL(n).This gives a geometric explan<strong>at</strong>ion for the fact th<strong>at</strong>, inthe modular case, the c<strong>at</strong>egory of modules over the Schuralgebra can be obtained by successive recollements of c<strong>at</strong>egoriesof represent<strong>at</strong>ions of suitable products of symmetricgroups.Knot invariants and their c<strong>at</strong>egorific<strong>at</strong>ions viaHowe dualityAaron LaudaUniversity of Southern California, USAlauda@usc.eduIt is a well understood story th<strong>at</strong> one can extract linkinvariants associ<strong>at</strong>ed to simple Lie algebras. These invariantsare called Reshetikhin-Turaev invariants and thefamous Jones polynomial is the simplest example. Kauffmanshowed th<strong>at</strong> the Jones polynomial could be describedvery simply by replacing crossings in a knot diagram byvarious smoothings. In this talk we will explain Cautis-Kamnitzer-Lic<strong>at</strong>a’s simple new approach to understandingthese invariants using basic represent<strong>at</strong>ion theory andthe quantum Weyl group action. Their approach is basedon a version of Howe duality for exterior algebras calledskew-Howe duality. Even the graphical (or skein theory)description of these invariants can be recovered in an elementaryway from this d<strong>at</strong>a. The advantage of this approachis th<strong>at</strong> it suggests a ‘c<strong>at</strong>egorific<strong>at</strong>ion’ where knothomology theories arise in an elementary way from higherrepresent<strong>at</strong>ion theory and the structure of c<strong>at</strong>egorifiedquantum groups.Center <strong>at</strong> the critical level and commut<strong>at</strong>ivesubalgebras
39 PRIMA 2013 AbstractsAlexander MolevUniversity of Sydney, Australiaalexander.molev@sydney.edu.auFor each simple Lie algebra g the vacuum module overthe corresponding affine Kac-Moody algebra has a vertexalgebra structure. For each Lie algebra g of classicaltype, we use explicit gener<strong>at</strong>ors of the center of this vertexalgebra to produce explicit constructions of maximalcommut<strong>at</strong>ive subalgebras of the universal enveloping algebrasU(g).Cluster algebras and singular supports of perversesheavesHiraku NakajimaKyoto University, Japannakajima@kurims.kyoto-u.ac.jpWe propose an approach to Geiss-Leclerc-Schroer’s conjectureon the cluster algebra structure on the coordin<strong>at</strong>ering of a unipotent subgroup and the dual canonical base.It is based on singular supports of perverse sheaves onthe space of represent<strong>at</strong>ions of a quiver, which give thecanonical base.On orbits in double flag varieties for symmetricpairsHiroyuki OchiaiKyushu University, Japanochiai@imi.kyushu-u.ac.jpLet G be a connected, simply connected semisimple algebraicgroup over the complex number field, and let K bethe fixed point subgroup of an involutive automorphism ofG so th<strong>at</strong> (G, K) is a symmetric pair. We take parabolicsubgroups P of G and Q of K respectively and considerthe product of partial flag varieties G/P and K/Q withdiagonal K-action, which we call a double flag variety fora symmetric pair. It is said to be of finite type if thereare only finitely many K-orbits on it. In this paper, wegive a parameteriz<strong>at</strong>ion of K-orbits on G/P × K/Q interms of quotient spaces of unipotent groups without assumingthe finiteness of orbits. As a result, we get severaluseful criteria for the finiteness of orbits. If one ofP ⊂ G or Q ⊂ K is a Borel subgroup, the finiteness of orbitsis closely rel<strong>at</strong>ed to spherical actions. In such cases,the criteria enable us to obtain a complete classific<strong>at</strong>ionof double flag varieties of finite type. As a consequence,we obtain classific<strong>at</strong>ions of K-spherical flag varieties G/Pand G-spherical homogeneous spaces G/Q.Elementary subalgebras of modular Lie algebrasJulia PevtsovaUniversity of Washington, USAjulia@m<strong>at</strong>h.washington.eduLet g be a p-Lie algebra. We call a subalgebra E of gelementary of rank r if it is an abelian Lie algebra withtrivial p-restriction of dimension r. For a fixed r we considera projective variety E(r, g) th<strong>at</strong> parameterizes allelementary subalgebras of g of rank r. This variety is an<strong>at</strong>ural generaliz<strong>at</strong>ion of the rank variety introduced byCarlson for elementary abelian p-groups and the supportvariety for Lie algebras of Friedlander and Parshall.We’ll identify this projective variety in various classicalcases. We’ll also show how represent<strong>at</strong>ions of g with specialproperties lead to constructions of families of vectorbundles on E(r, g), thereby extending the study of “modulesof constant Jordan type" and their geometric applic<strong>at</strong>ionsto this more general context.Support varieties for reductive groupsPaul SobajeUniversity of Melbourne, Australiapaul.sobaje@unimelb.edu.auLet G be a reductive algebraic group over an algebraicallyclosed field of characteristic p, and denote by G (r) itsr-th Frobenius kernel. Each G (r) -module M has associ<strong>at</strong>edto it a cohomological support variety, which canbe shown in most cases to be homeomorphic to a closedsubset of the variety of commuting r-tuples of p-nilpotentelements in the Lie algebra of G. We will give some ofthe details about this homeomorphism, and also discussexplicit comput<strong>at</strong>ions in the case th<strong>at</strong> M is the restrictionof either a simple G-module or a Weyl module.Decomposition numbers for the symmetricgroups and Schur algebrasKai Meng TanN<strong>at</strong>ional University of Singapore, Singaporetankm@nus.edu.sgThe complete determin<strong>at</strong>ion of the decomposition numbersfor the symmetric groups and Schur algebras in positivecharacteristic p is a famous open problem; a completesolution of which does not seem to be forthcomingin the near future. In this talk, we present our recentresults which provide closed formulas for the decompositionnumber d λµ when the partition λ is obtained fromµ by moving some nodes whose p-residues are pairwisenon-adjacent.Hodge theory and represent<strong>at</strong>ion theoryKari VilonenNorthwestern University, USAvilonen@northwestern.eduI will explain how Hodge theory can be used in the represent<strong>at</strong>iontheory of real groups to <strong>at</strong>tack the problem ofthe unitary dual.Globalizing crystal basis for quantum superalgebrasWeiqiang WangUniversity of Virginia, USAww9c@virginia.eduCanonical basis (or global crystal basis) for quantumgroups and their integrable modules was introduced anddeveloped by Lusztig and subsequently by Kashiwara.We will present a construction for the first time, motiv<strong>at</strong>edby c<strong>at</strong>egorific<strong>at</strong>ion, of canonical basis for a classof quantum superalgebras and their integrable modules.This is joint work with Sean Clark and David Hill.Special Session 20Singularities in Geometry and TopologyThe topology of real suspension singularitiesof type fḡ + z nHaydée Aguilar CabreraN<strong>at</strong>ional Autonomous University of Mexico, Mexicolangeh@gmail.comIn this talk we present some results on the topology ofthe family of real analytic germs F : (C 3 , 0) → (C, 0)with isol<strong>at</strong>ed critical point <strong>at</strong> 0, given by F (x, y, z) =f(x, y)g(x, y)+z r , where f and g are holomorphic,r ∈ Z+
40 PRIMA 2013 Abstractsand r ≥ 2. We describe the link L F as a graph manifoldusing its n<strong>at</strong>ural open book decomposition, rel<strong>at</strong>ed tothe Milnor fibr<strong>at</strong>ion of the map-germ fḡ and the descriptionof its monodromy as a quasi-periodic diffeomorphismthrough its Nielsen invariants. Furthermore, such a germF gives rise to a Milnor fibr<strong>at</strong>ionF : S |F | 5 \L F → S 1 .We present a join theorem, which allows us to describethe homotopy type of the Milnor fibr<strong>at</strong>ion of F and weshow some cases where the open book decomposition ofS 5 given by the Milnor fibr<strong>at</strong>ion of F cannot come fromthe Milnor fibr<strong>at</strong>ion of a complex singularity in C 3 .On Griffiths numbers for higher dimensionalisol<strong>at</strong>ed singularitiesRong DuEast China Normal University, Chinardu@m<strong>at</strong>h.ecnu.edu.cnWe will discuss some numerical invariants for isol<strong>at</strong>ed singularitiesand their rel<strong>at</strong>ions. In particular, we will showth<strong>at</strong> S. Yau’s conjecture on inequalities for (n−1)-th Griffithsnumber and (n − 1)-th Hironaka number holds forirregular singularities and it is not true in general.Equisingularity and integral closure of idealsand modules: two partners in a danceTerence GaffneyNortheastern University, USAt.gaffney@neu.eduA family of sets or mappings is equisingular if the singularitiesof the family are similar, in a well defined sensedepending on the equisingularity condition. The theory ofintegral closure is an important tool for studying equisingularityconditions. It provides invariants which describethe condition, and provide means of proving the conditionshold for a family. In this talk we will quickly repriseresults for Whitney equisingularity, then discuss how toapply the same ideas to construct an infinitesimal theoryof bi-Lipschitz equivalence.Improved bounds on the ranks of the Milnorfiber cohomologyDavid B. MasseyNortheastern University, USAd.massey@neu.eduAs we showed 25 years ago, the Lê numbers provide upperbounds on the ranks of the cohomology of the Milnorfiber of a function with a critical locus of arbitrary dimension.Our new results deal with when the maps in the Lêcomplex can be zero, and so give us improved bounds onthe Milnor fiber cohomology. Our results in the classicalcase follow from more general results on the vanishingcycles of perverse sheaves.Characteristic classes of singular toric varietiesLaurentiu MaximUniversity of Wisconsin-Madison, USAmaxim@m<strong>at</strong>h.wisc.eduWe discuss the comput<strong>at</strong>ion of the homology Hirzebruchcharacteristic classes of (possibly singular) toric varieties.We present two different perspectives for the comput<strong>at</strong>ionof these characteristic classes. First, we take advantage ofthe torus-orbit decomposition and the motivic propertiesof the homology Hirzebruch classes to express the l<strong>at</strong>terin terms of the (dual) Todd classes of closures of orbits.The obtained formula is then applied to weighted l<strong>at</strong>ticepoint counting in l<strong>at</strong>tice polytopes. Secondly, in the caseof simplicial toric varieties, we make use of the Lefschetz-Riemann-Roch theorem in the context of the geometricquotient description of such varieties. In this setting, wedefine mock Hirzebruch classes of simplicial toric varietiesand investig<strong>at</strong>e the difference between the (actual) homologyHirzebruch class and the mock Hirzebruch class. Weshow th<strong>at</strong> this difference is localized on the singular locus,and we obtain a formula for it in which the contributionof each singular cone is identified explicitly. This is jointwork with Jörg Schürmann.On the topology of real analytic mapsJosé Luis Cisneros MolinaN<strong>at</strong>ional Autonomous University of Mexico, Mexicojlcm@m<strong>at</strong>cuer.unam.mxJoint work with Nivaldo G. Grulha Jr. and José Seade.In this talk we present some recent results on the topologyof real analytic maps. Every real analytic map germf : R n → R p , p ≥ 1, with arbitrary critical set, has aMilnor-Lê type fibr<strong>at</strong>ion. Now assume also th<strong>at</strong> f hasthe Thom a f -property, and its zero-locus has positive dimension.Also consider another real analytic map germg : R n → R k with an isol<strong>at</strong>ed critical point <strong>at</strong> the origin.We have Milnor-Lê type fibr<strong>at</strong>ions for f and for(f, g): R n → R p+k , and we prove for these the analogousof the classical Lê-Greuel formula, expressing the differenceof the Euler characteristics of the fibers F f and F f,gin terms of an invariant associ<strong>at</strong>ed to these maps.Intersection theory on mixed curvesMutsuo OkaTokyo University of Science, Japanoka@rs.kagu.tus.ac.jpWe consider two mixed curve C, C ′ ⊂ C 2 which are definedby mixed functions of two variables Z = (z 1 , z 2 ). Wehave shown in our previu paper th<strong>at</strong> they have canonicalorient<strong>at</strong>ions. If C and C ′ are smooth and intersecttransversely <strong>at</strong> P , the intersection number I top(C, C ′ ; P )is topologically defined. We will generalize this definitionto the case when the intersection is not necessarilytransversal or either C or C ′ may be singular <strong>at</strong> P usingthe defining mixed polynomials.Newton-Puiseux analysisLaurentiu PaunescuThe University of Sydney, Australialaurent@m<strong>at</strong>hs.usyd.edu.auComplex analysis is extended to the Newton-Puiseuxfield. We give analogues of several clasic results and, asa corollary, a short proof of the Kuo-Lu theorem.Singularities of several geometric objects rel<strong>at</strong>edto null curves in Minkowski 3-spaceDonghe PeiNortheast Normal University, Chinapeidh340@nenu.edu.cnIn this article, we investig<strong>at</strong>e the singularities of nullDarboux developables, Gaussian surfaces and pseudosphericalDarboux Images associ<strong>at</strong>ed with a null Cartancurve in Minkowski 3−space. This is a joint work withZhi-Gang Wang.Broken Lefschetz fibr<strong>at</strong>ions and their moves
41 PRIMA 2013 AbstractsOsamu SaekiKyushu University, Japansaeki@imi.kyushu-u.ac.jpA broken Lefschetz fibr<strong>at</strong>ion (BLF, for short) is a smoothmap of a closed oriented 4-manifold onto a closed surfacewhose singularities consist of Lefschetz critical points(w.r.t. local complex coordin<strong>at</strong>es comp<strong>at</strong>ible with theorient<strong>at</strong>ions) together with indefinite folds. Such aclass of maps was first introduced by Auroux-Donaldson-K<strong>at</strong>zarkov in rel<strong>at</strong>ion to near-symplectic structures, andnow it is known th<strong>at</strong> every closed oriented 4-manifold admitsa BLF over the 2-sphere. In this talk, we give aset of explicit moves for BLFs which can connect any twohomotopic BLFs, and give an elementary and constructiveproof to the fact th<strong>at</strong> any map into the 2-sphere ishomotopic to a BLF whose indefinite fold has embeddedimage. This is a joint work with R. İnanç Baykur (MaxPlanck Institute for M<strong>at</strong>hem<strong>at</strong>ics).Geometry of non-tame polynomial mapsKiyoshi TakeuchiUniversity of Tsukuba, Japantakemicro@nifty.comFor a polynomial map f = (f 1 , . . . , f k ): C n −→ C k (1 ≤k ≤ n), it is well-known th<strong>at</strong> there exists a proper subsetB ⊂ C k such th<strong>at</strong> the restrictionC n \ f −1 (B) −→ C k \ B (5)of f is a locally trivial fibr<strong>at</strong>ion. We denote by B f thesmallest subset B ⊂ C k s<strong>at</strong>isfying this condition. Theelements of B f are called bifurc<strong>at</strong>ion points of f. Whenk = 1 many m<strong>at</strong>hem<strong>at</strong>icians obtained various subsets ofC k = C containing B f . In particular, Némethi and Zaharia[8] showed th<strong>at</strong> for a non-convenient polynomialf = (f 1 ) such a subset is obtained by the bad faces of itsNewton polyhedron <strong>at</strong> infinity Γ ∞(f). In this talk, wefirst introduce the following analogue of their result forgeneral k ≥ 1 (see also Nguyen [9] for a rel<strong>at</strong>ed result).Theorem: (Chen-Dias-T-Tibăr [2]) Assume th<strong>at</strong> f =(f 1 , . . . , f k ): C n −→ C k is non-degener<strong>at</strong>e <strong>at</strong> infinity.Let N f , K f ⊂ C k be the subsets of C k defined by theNewton polyhedra <strong>at</strong> infinity of f 1 , . . . , f k in [2]. Thenwe haveB f ⊂ f(singf) ∪ N f ∪ K f . (6)Note th<strong>at</strong> if k = 1 this result coincides with th<strong>at</strong> of [8].When k = 1 and n = 2, Némethi and Zaharia [8] provedthe equality B f = f(singf)∪N f ∪K f and conjectured itsvalidity also in the higher-dimensional case n ≥ 3. In thistalk, we next introduce our approach to this conjecture.By using the results in [5] we will show th<strong>at</strong> it can beverified in many cases. Finally, we restrict ourselves to thecase k = 1. If f = (f 1 ) is convenient and non-degener<strong>at</strong>e<strong>at</strong> infinity, then by a result of Broughton [1] we have thecohomological concentr<strong>at</strong>ionH j (f −1 (R); C) = 0 (j ≠ 0, n − 1) (7)for the generic fiber f −1 (R) (R ≫ 0) of f. However,many polynomials th<strong>at</strong> we usually encounter are not convenient.They are not tame <strong>at</strong> infinity. The study ofnon-tame polynomials is important also for the Jacobianconjecture since they are the only interesting objects for it(see [2] etc.). The main reason why non-tame polynomialscould not be studied successfully before is th<strong>at</strong> one cannotexpect to have the cohomological concentr<strong>at</strong>ion for them.Here we partially overcome this difficulty on non-tamepolynomials by improving the above-mentioned result ofBroughton [1] as follows. Let C R = {x ∈ C | |x| = R}(R ≫ 0) be a sufficiently large circle in C such th<strong>at</strong>B f ⊂ {x ∈ C | |x| < R}. Then by restricting thelocally trivial fibr<strong>at</strong>ion C n \ f −1 (B f ) −→ C \ B f toC R we obtain a geometric monodromy automorphismΦ ∞ f : f −1 (R) ≃ f −1 (R) and the linear mapsΦ ∞ j : Hj (f −1 (R); C) ≃ H j (f −1 (R); C) (j = 0, 1, . . .)(8)associ<strong>at</strong>ed to it. We call Φ ∞ j ’s the (cohomological) monodromies<strong>at</strong> infinity of f. Recently in [10], by using theNewton polyhedron <strong>at</strong> infinity Γ ∞(f) of f we defined afinite subset A f ⊂ C of “bad" eigenvalues which we call<strong>at</strong>ypical engenvalues of f. Then we have the following refinementof the main result of Broughton [1]. For λ ∈ Cand j ∈ Z let H j (f −1 (R); C) λ ⊂ H j (f −1 (R); C) be thegeneralized eigenspace for the eigenvalue λ of the monodromy<strong>at</strong> infinity Φ ∞ j .Theorem: (T-Tibăr [10]) Let f ∈ C[x 1 , . . . , x n] be anon-convenient polynomial such th<strong>at</strong> dim Γ ∞(f) = n.Assume th<strong>at</strong> f is non-degener<strong>at</strong>e <strong>at</strong> infinity. Then forany non-<strong>at</strong>ypical eigenvalue λ /∈ A f of f we have theconcentr<strong>at</strong>ionH j (f −1 (R); C) λ ≃ 0 (j ≠ n − 1) (9)for the generic fiber f −1 (R) ⊂ C n (R ≫ 0) of f.With this theorem <strong>at</strong> hand, we can extend the results in[4], [6] and [7] etc. to non-convenient polynomials. Inparticular, as in [7] and [3] by using the motivic Milnorfiber <strong>at</strong> infinity of f we completely determine the Jordannormal forms of Φ ∞ n−1 for non-<strong>at</strong>ypical eigenvalues λ /∈A f of f. See [10] for the details.[1] Broughton, S. A. “Milnor numbers and the topologyof polynomial hypersurfaces", Invent. M<strong>at</strong>h., 92 (1988):217-241.[2] Chen, Y., Dias, R., Takeuchi, K. and Tibăr,M. “Invertible polynomial mappings via Newton nondegeneracy",arXiv:1303.6879.[3] Esterov, A. and Takeuchi, K. “Motivic Milnor fibersover complete intersection varieties and their virtual Bettinumbers", Int. M<strong>at</strong>h. Res. Not., Vol. 2012, No. 15(2012): 3567-3613.[4] Libgober, A. and Sperber, S. “On the zeta functionof monodromy of a polynomial map", Compositio M<strong>at</strong>h.,95 (1995): 287-307.[5] M<strong>at</strong>sui, Y. and Takeuchi, K. “Milnor fibers oversingular toric varieties and nearby cycle sheaves", TohokuM<strong>at</strong>h. J., 63 (2011): 113-136.[6] M<strong>at</strong>sui, Y. and Takeuchi, K. “Monodromy zetafunctions <strong>at</strong> infinity, Newton polyhedra and constructiblesheaves", M<strong>at</strong>hem<strong>at</strong>ische Zeitschrift, 268 (2011): 409-439.[7] M<strong>at</strong>sui, Y. and Takeuchi, K. “Monodromy <strong>at</strong> infinityof polynomial maps and Newton polyhedra, withAppendix by C. Sabbah", Int. M<strong>at</strong>h. Res. Not., Vol.2013, No. 8 (2013): 1691-1746.[8] Némethi, A. and Zaharia, A. “On the bifurc<strong>at</strong>ion setof a polynomial function and Newton boundary", Publ.Res. Inst. M<strong>at</strong>h. Sci., 26 (1990): 681-689.[9] Nguyen, T. T., “Bifirc<strong>at</strong>ion set, M-tameness,asymptotic critical values and Newton polyhedrons",arXiv:1205.0939v5, to appear in Kodai M<strong>at</strong>h. J.[10] Takeuchi, K. and Tibăr, M. “Monodromies <strong>at</strong> infinityof non-tame polynomials", arXiv:1208.4584.Characteristic points, fundamental cubicform and Euler characteristic of projectivesurfacesRicardo Uribe-VargasUniversité de Bourgogne, Francer.uribe-vargas@u-bourgogne.fr
42 PRIMA 2013 AbstractsJoint work with M. Kazarian. Generic surfaces in projective3-space have isol<strong>at</strong>ed characteristic points (invariantunder projective trasform<strong>at</strong>ions and stable under smallperturb<strong>at</strong>ions of the surface) called elliptic nodes, hyperbolicnodes and godrons (also known as cusps of Gauss).These characteristic points have interesting propertiesand deserve special <strong>at</strong>tention. We give a geometric definitionof the characteristic points (there are several equivalentdefinitions) and we define n<strong>at</strong>ural local invariants forthem (a sign ±).Our formulas for global counting of these invariants onthe surface (or on domains in it) involve the Euler characteristicof the surface (or of the respective domains)providing restrictions on the coexistence of characteristicpoints.One way to prove our counting formulas (we know threeways) is considering the fundamental cubic form: in thesame way as the second fundamental quadr<strong>at</strong>ic form measuresthe quadr<strong>at</strong>ic devi<strong>at</strong>ion of a surface from its tangentplane, the cubic fundamental form measures the cubic devi<strong>at</strong>ionof the surface from its quadr<strong>at</strong>ic part. The fundamentalcubic form is a local intrinsic invariant definedfor every point of the surface, which vanish <strong>at</strong> the characteristicpoints.Our exposition will be r<strong>at</strong>her geometrical and for a wideaudience.Topological classific<strong>at</strong>ion of multiaxial U(n)-actionsMin Yan (joint with S. Cappell and S. Weinberger)Hong Kong University of Science and Technology, HongKong, Chinamamyan@ust.hkA manifold under the action of the unitary group U(n)is multiaxial if all the isotropy groups are unitary subgroups.Such manifolds are often modeled on kC n ⊕ jR,where C n has the canonical U(n)-action and R has trivialU(n)-action. One of the major achievements aboutmultiaxial manifolds was M. Davis and W.C. Hsiang’sconcordance classific<strong>at</strong>ion in l<strong>at</strong>e 1970s for the smoothc<strong>at</strong>egory and under the assumption k ≤ n.We study the structure set S U(n) (M) of a multiaxialU(n)-manifold M, which is the homeomorphism classesof the topological U(n)-manifolds equivariantly homotopyequivalent to M. We show th<strong>at</strong> S U(n) (M) can be decomposedinto simpler structure sets. We discuss the implic<strong>at</strong>ionof the decomposition and compute explicitly for thecase M is the canonical represent<strong>at</strong>ion sphere. All theresults do not assume k ≤ n.Milnor fibers of real line arrangementsMasahiko YoshinagaHokkaido University, Japanyoshinaga@m<strong>at</strong>h.sci.hokudai.ac.jpThe Milnor fiber of a line arrangement is a certain cycliccovering space of the complexified complement equippedwith monodromy action. We will discuss the monodromyaction on the first homology group. We will present anew algorithm computing multiplicities of monodromyeigenvalues, which uses real and combin<strong>at</strong>orial structures(chambers). I will also give an upper bounds and severalconjectures.Special Session 21Symplectic Geometry and Hamiltonian DynamicsContacting the moonUrs FrauenfelderSeoul N<strong>at</strong>ional University, Koreafrauenf@snu.ac.krThe restricted three body problem has an intriguing dynamics.In joint work with Peter Albers, Gabriel P<strong>at</strong>ernainand Otto van Koert we showed th<strong>at</strong> below andslightly the first critical level energy hypersurfaces ofthe restricted three body problem are of contact type.This result allows us to apply global methods comingfrom Gromov-Witten theory, Floer theory, and SymplecticField theory to this old problem. I will explain howwe can use these global methods to detect global surfacesof section were the perturb<strong>at</strong>ive methods used so far fail.Mean Euler characteristic:caseViktor L. GinzburgUniversity of California, Santa Cruz, USAginzburg@ucsc.eduthe degener<strong>at</strong>eThe mean Euler characteristic (MEC) is an invariant ofa contact manifold, which is on the one hand sensitiveenough to distinguish interesting contact structures and,on the other, rel<strong>at</strong>ively easily computable in terms of thedynamics of the Reeb flow. This invariant was introducedby van Koert. As has been shown by Kerman and thespeaker, the MEC can be expressed in terms of local,purely topological, invariants of closed Reeb orbits wheneverthe Reeb flow is non-degener<strong>at</strong>e and has finitely ofsuch orbits. This expression generalizes the resonancerel<strong>at</strong>ion for the mean indices of closed characteristics establishedby Viterbo for convex hypersurfaces, and it hasbeen further refined and generalized by Espina.In this talk, based on a joint work with Yusuf Goren, wewill discuss a version of such a local formula for the MECwhen the closed orbits are degener<strong>at</strong>e. This work buildson the previous results of Long et al. and Hryniewicz andMacarini, and its main new fe<strong>at</strong>ure is th<strong>at</strong>, as in the nondegener<strong>at</strong>ecase, the contributions of individual orbits arepurely topological. We will also touch upon applic<strong>at</strong>ionsof this resonance rel<strong>at</strong>ion to dynamics.The Hill-type formula and Krein-type traceformulaXijun HuShandong University, Chinaxjhu@sdu.edu.cnIn the study of the motion of lunar perigee, Hill got a formulawhich rel<strong>at</strong>es the characteristic polynomial of themonodromy m<strong>at</strong>rix for a periodic orbit and a kind of infinitedeterminant. Hill’s formula is useful in understandingthe property of the monodromy m<strong>at</strong>rix. Motiv<strong>at</strong>edby the previous works, we build up the Hill-type formulafor S-periodic solutions for first-order ordinary differentialequ<strong>at</strong>ions and Lagrangian systems. The S-periodic solutionis a solution such th<strong>at</strong> x(t) = Sx(t + T ) for some orthogonalm<strong>at</strong>rix S, which comes n<strong>at</strong>urally from the studyof symmetry periodic orbits in n-body problem. Basedon it, we get the Trace formula for linear ODE, includethe case of standard Sturm-Liouville systems, which canbe consider as a generaliz<strong>at</strong>ion of Krein’s work in 1950’s.Especially, for the eigenvalue problem Lu + λR(x)u = 0,where L is the Sturm-Liouville oper<strong>at</strong>or, ∑ 1/λ k j can becomputed by the trace formula. Some applic<strong>at</strong>ions forthe stability problem is given.The extremal Kahler metrics on toric manifoldsAn-Min LiSichuan University, Chinam<strong>at</strong>h_li@yahoo.com.cnWe study the prescribed scaler curv<strong>at</strong>ure problem on toricmanifolds, following Donaldson’s program. Let ∆ be an
43 PRIMA 2013 Abstractsopen Delzant polytope in R n with ¯∆ compact. The prescribedscalar curv<strong>at</strong>ure problem reduces then to findinga smooth convex solution in ∆ for the 4-th order PDE∑i,j∂ 2 u ij∂ξ i ∂ξ j= −A. (10)subjecting to the Guillemin’s boundary conditions. Thisis the Abreu’s equ<strong>at</strong>ion. It is well known th<strong>at</strong> the solutionu gives an extremal metric if and only if A is a linearfunction in ∆.Denote by S the set of continuous convex functions u on ¯∆such th<strong>at</strong> u s<strong>at</strong>isfies the Guillemin’s boundary conditions.For a fixed point p o ∈ ∆, we setS po = {u ∈ S : u ≥ u(p o) = 0}.Donaldson introduced a stronger version of stability,which we call the uniform stability. We show th<strong>at</strong> theuniform stability is a necessary condition for existing asmooth solution.Theorem 1(Bohui Chen, An-Min Li and Li Sheng) Ifthe Abreu equ<strong>at</strong>ion (1) has a smooth solution in S, then(∆, A) is uniform stable.We would suggest a modific<strong>at</strong>ion on the original conjectureposed by Donaldson:Conjecture 2 (M, ω) has a metric within the class [ω]th<strong>at</strong> solves the Abreu equ<strong>at</strong>ion (1) if and only if (∆, A)is uniformly K-polystable.We derived interior estim<strong>at</strong>es for any dimension:Theorem 3(Bohui Chen, Qing Han, An-Min Li and LiSheng) Let ∆ be a bounded open polytope in R n and A bea smooth function on ¯∆. Suppose (∆, A) is uniformly K-stable and u is a solution in S po of the Abreu’s equ<strong>at</strong>ion(1). Then, for any Ω ⊂⊂ ∆, any nonneg<strong>at</strong>ive integer kand any constant α ∈ (0, 1),‖u‖ C k+3,α (Ω) ≤ C‖A‖ C k ( ¯∆) ,where C is a positive constant depending only on n, k, α,Ω, and λ in the uniform K-stability. For n=2, Donaldsonsolved the conjecture 2 for A = constant, we are able toprove the conjecture 2 for almost any A.Definition Let A be a smooth function on ¯∆. It is callededge-nonvanishing if it does not vanish on any edge of ∆.Theorem 4(Bohui Chen, An-Min Li and Li Sheng) LetM be a compact toric surface and ∆ be its Delzant polytope.Let A ∈ C ∞ ( ¯∆) be an edge-nonvanishing function.If (M, A) is uniformly stable, then there is a smooth T 2 -invariant metric on M th<strong>at</strong> solves the Abreu equ<strong>at</strong>ion.Canonical connection and analysis of contactCauchy-Riemann equ<strong>at</strong>ionYong-Geun OhUniversity of Wisconsin-Madison, USA & IBS-Center forGeometry and Physics, Koreaoh@m<strong>at</strong>h.wisc.eduIn this talk, we explain the analysis of the following systemof (degener<strong>at</strong>e) elliptic equ<strong>at</strong>ion ∂ π w = 0, d(w ∗ λ ◦j) = 0 associ<strong>at</strong>ed for each given contact triad (Q, λ, J) ona contact manifold (Q, ξ), which was first introduced byHofer. We directly work with this equ<strong>at</strong>ion on the contactmanifolds without involving the symplectiz<strong>at</strong>ion process.We explain the basic analytical ingredients towards theconstruction of moduli space of solutions, which we callcontact instantons. For the needed tensorial calcul<strong>at</strong>ions,we introduce a canonical affine connection on the contactmanifold (Q, ξ), which is associ<strong>at</strong>ed to each contact triad(Q, λ, J) where λ is a contact form and J : ξ → ξ is anendomorphism with J 2 = −id comp<strong>at</strong>ible to dλ. We callit the contact triad connection of (Q, λ, J) which existsuniquely. This is partially a joint work with Rui Wang.Anti-symplectic involution and Floer theoryKaoru OnoKyoto University, Japanono@kurims.kyoto-u.ac.jpI will present the work on anti-symplectic involution andits effect on Floer theory for Lagrangian submanifoldsbased on a joint work with K. Fukaya, Y.-G. Oh andH. Ohta. There are interesting example of Lagrangiansubmanifolds, which appear as the fixed point set of ananti-symplectic involution. Then we study when theyare unobstructed in Floer theoretical sense and its consequences.We can identify the quantum cohomology of(X, ω) and Lagrangian Floer thoery on the diagonal in(X × X, −ω ⊕ ω) and define higher oper<strong>at</strong>ions on quantumcohomology.Witten equ<strong>at</strong>ion and the geometry of LGmodelYongbin RuanUniversity of Michigan, Ann Arbor, USAruan@umich.eduThe study of moduli space of solutions of nonlinearPDE has revolutionized the geometry and topologyfor last twenty years. The famous examples areDonaldson/Seiberg-Witten theory and Gromov-Wittentheory. In the talk, I will discuss another family of PDEintroduced by Witten in the context of so called Landau-Ginzburg model. As expected, it is revolutionizing thesubject of Landau-Ginzburg model right now.Isotopy of Lagrangian tori revisitedMei-Lin YauN<strong>at</strong>ional Central University, Taiwanyau@m<strong>at</strong>h.ncu.edu.twOver the last twenty years, isotopy problems of Lagrangiantori (and more generally, Lagrangian submanifolds)have been under investig<strong>at</strong>ions from many differentapproaches. Yet it seems th<strong>at</strong> more can be explored, evenfor Lagrangian tori in R 4 .In this talk I will review the construction of monodromygroups for Lagrangian submanifolds and reporton some recent results concerning the three types (Hamiltonian/Lagrangian/smooth)of monodromy groups Cliffordtori and Chekanov tori in R 4 .If time permits, i will also talk about some very recentwork in progress on the construction of Lagrangian surfacesvia surgery, as well as a potentially new symplecticinvariant of Lagrangian surfaces to detect the surgery effecton the Hamiltonian isotopy class of Lagrangian surfaces.Special Session 22Symplectic Geometry and M<strong>at</strong>hem<strong>at</strong>icalPhysicsA classifying space for commut<strong>at</strong>ivityAlejandro AdemUniversity of British Columbia, Canadaadem@pims.m<strong>at</strong>h.ca
44 PRIMA 2013 AbstractsLet G denote a Lie group. In this talk we will discussa classifying space constructed from the commuting elementsin G. We compute its cohomology and describe itsgeometry and homotopy type.Virtual neighborhood techniques in Gromov-Witten theoryBohui ChenSichuan University, Chinabohui@cs.wisc.edu>Abstract: In this talk, I will explain the construction ofvirtual orbifolds for the moduli spaces of stable curves.In particular, I will explain how to deal with the nonsmoothnessissues arised from the infinite dimensionalset-ups.Algebra of Legendrian surgeryYakov EliashbergStanford University, USAeliash m<strong>at</strong>h.stanford.eduI will discuss algebraic structures arising in connectionwith Legendrian surgery, which enter the comput<strong>at</strong>ion ofholomorphic curve invariants of Weinstein domains andtheir boundaries. This is a joint work with F. Bourgeoisand T. Ekholm.Fock sheaf of Givental quantiz<strong>at</strong>ionHiroshi IritaniKyoto University, Japaniritani@m<strong>at</strong>h.kyoto-u.ac.jpI will talk about joint work with Tom Co<strong>at</strong>es (ImperialCollege London) on a global version of Givental quantiz<strong>at</strong>ion.Based on a generalized vari<strong>at</strong>ion of Hodge structure(the so-called semi-infinite vari<strong>at</strong>ion of Hodge structure),we construct a sheaf of Fock spaces which can be identifiedwith Givental’s Fock space infinitesimally. An oppositesubspace which yields a Frobenius structure on thebase plays a role of polariz<strong>at</strong>ion in the context of geometricquantiz<strong>at</strong>ion. As applic<strong>at</strong>ions, we discuss modularityof Gromov-Witten potential of local projective plane, andalso holomorphic anomaly equ<strong>at</strong>ion.C<strong>at</strong>egories and dynamical systemsLudmil K<strong>at</strong>zarkovUniversity of Miami, USA and University of Vienna, Austrial.k<strong>at</strong>zarkov@m<strong>at</strong>h.miami.eduIn this talk we will discuss recent developments in thetheory of stability conditions of c<strong>at</strong>egories. We will outlinesome parallels with classical results from dynamicalsystems.Quasimap invariants and mirror mapsBumsig KimKorea Institute for Advanced Study, Koreabumsig@kias.re.krThe moduli spaces of stable quasimaps unify various moduliappearing in the study of Gromov-Witten Theory.We introduce big I-functions as the quasimap version ofJ-functions, generalizing Givental’s small I-functions ofsmooth toric complete intersections. The J-functions arethe GW counterparts of periods of mirror families. Wediscuss some advantages of I-functions, in particular anexplan<strong>at</strong>ion of mirror maps. This is joint work with I.Ciocan-Fontanine.The Eynard-Orantin recursion in singularitytheoryTodor MilanovKavli Institute for the Physics and M<strong>at</strong>hem<strong>at</strong>ics of theUniverse, Japantodor.milanov@ipmu.jpIt was proved recently th<strong>at</strong> the correl<strong>at</strong>ion functions ofa semi-simple cohomological field theory s<strong>at</strong>isfy the socalled local Eynard–Orantin topological recursion. In mytalk, I would like to explain this result in the settings ofsingularity theory. In my earlier work with B. Bakalov,we have constructed a certain twisted represent<strong>at</strong>ion ofthe Heisenberg vertex oper<strong>at</strong>or algebra associ<strong>at</strong>ed withthe vanishing cohomology of the singularity. The kernel ofthe Eynard-Orantin recursion is essentially obtained fromthe so called oper<strong>at</strong>or product expansion of the fields th<strong>at</strong>define the represent<strong>at</strong>ion. Finally, I would like to reportmy progress on finding the global recursion, which seemsto be rel<strong>at</strong>ed to the theory of W -algebras.Orbifold Hurwitz numbers and Eynard-Orantin invariantsPaul NorburyUniversity of Melbourne, Australianorbury@unimelb.edu.auI will describe a generalis<strong>at</strong>ion of simple Hurwitz numbersdue to Johnson, Pandharipande and Tseng and proveth<strong>at</strong> they s<strong>at</strong>isfy the topological recursion of Eynard andOrantin. This generalises the Bouchard-Marino conjectureand places Hurwitz-Hodge integrals, which arise inthe Gromov-Witten theory of target curves with orbifoldstructure, in the context of the Eynard-Orantin topologicalrecursion.Transl<strong>at</strong>ed points and contact rigiditySheila SandonUniversité de Nantes, Francesheila.sandon@univ-nantes.frI will discuss the role played by transl<strong>at</strong>ed points ofcontactomorphisms in contact rigidity phenomena suchas non-squeezing, orderability and the existence of biinvariantmetrics on the contactomorphism group. I willthen either concentr<strong>at</strong>e on presenting the construction ofthe discriminant metric on the contactomorphism group(which is joint work with Vincent Colin) or discuss ananalogue for transl<strong>at</strong>ed points of the Arnold conjectureon fixed points of Hamiltonian symplectomorphisms, anda joint work in progress with Yasha Savelyev and EgorShelukhin to prove this conjecture by constructing a Floerhomology theory for transl<strong>at</strong>ed points.On a certain generaliz<strong>at</strong>ion of Virasoro constraintsfor Frobenius manifoldsYoujin ZhangTsinghua University, Chinayoujin@mail.tsinghua.edu.cnWe show th<strong>at</strong> the Virasoro oper<strong>at</strong>ors associ<strong>at</strong>ed to anarbitray Frobenius manifold admit certain deform<strong>at</strong>ionswhich give additional constraints for the genus zero freeenergy of the Frobenius manifold. We discuss applic<strong>at</strong>ionsof such additional constraints and their analoguesfor higher genus free energies.Gopakumar-Vafa invariants of local Calabi-Yau 3-Folds
45 PRIMA 2013 AbstractsJian ZhouTsinghua University, Chinajzhou@m<strong>at</strong>h.tsinghua.edu.cnWe will present a formula for Gopakumar-Vafa BPSinvariants of local Calabi-Yau geometries given by thecanonical line bundles of toric surfaces under some technicalconditions. This verifies and extends a conjecturemade by K<strong>at</strong>z-Klemm-Vafa based on M-theory.Special Session 23Triangul<strong>at</strong>ed C<strong>at</strong>egories in Represent<strong>at</strong>ionTheory of AlgebrasDerived simple algebrasLidia Angeleri HügelUniversity of Verona, Italylidia.angeleri@univr.itAn algebra is said to be derived simple if its derived c<strong>at</strong>egorycannot be deconstructed into ‘smaller’ derived c<strong>at</strong>egories,more precisely, it is not the middle term of a nontrivialrecollement where the two outer terms are againderived c<strong>at</strong>egories of algebras.We will see th<strong>at</strong> being derived simple strongly dependson the choice of derived c<strong>at</strong>egories: whether <strong>at</strong> boundedor unbounded level, whether considering finitely gener<strong>at</strong>edor arbitrary modules. We will clarify the connectionbetween the different choices by discussing when recollementscan be lifted or restricted between different levelsof derived c<strong>at</strong>egories. We will then characterize derivedsimpleness on each level in terms of the height of ladders,th<strong>at</strong> is, the number of adjacent recollements <strong>at</strong> unboundedlevel. This is joint work with Steffen Koenig,Qunhua Liu, Dong Yang.The decor<strong>at</strong>ed mapping class group of amarked surfaceThomas BrüstleBishops’s University and Université de Sherbrooke,Canad<strong>at</strong>bruestl@ubishops.caThe main character of this talk is the decor<strong>at</strong>ed mappingclass group MCG p(S, M) of a marked surface (S, M). Weshow th<strong>at</strong> (in most cases) it is isomorphic to a groupformed by automorphisms of the cluster algebra associ<strong>at</strong>edto (S, M), which can also be interpreted as a groupof auto-equivalences of the corresponding cluster c<strong>at</strong>egoryC(S, M). Moreover we describe the suspension functor ofC(S, M) geometrically, as an element in the decor<strong>at</strong>edmapping class group of (S, M).Autoequivalences under derived equivalencesRagnar-Olaf BuchweitzUniversity of Toronto Scarboroughragnar@utsc.utoronto.caThere are many examples where derived c<strong>at</strong>egories ofcoherent sheaves on some smooth projective variety areequivalent to the derived c<strong>at</strong>egory of finite length modulesover an artinian algebra, or to the singularity c<strong>at</strong>egoryof graded modules over a graded Gorenstein algebra,or both.In these case, often one of the partners in the derivedequivalences carries obvious autoequivalences, such astwists by line bundles on the geometric side or degreeshifts in the graded case, th<strong>at</strong> are quite mysterious onthe equivalent incarn<strong>at</strong>ions.We will review this situ<strong>at</strong>ion and explain some classicalexamples where the "obvious" autoequivalences on oneside can now be understood on the other side. Part ofthis is joint work in progress with Lutz Hille.Singular equivalences with examplesXiao-Wu ChenUniversity of Science and Technology of China, Chinaxwchen@mail.ustc.edu.cnTwo finite dimensional algebras are said to be singularlyequivalent if there is a triangle equivalence between theirsingularity c<strong>at</strong>egories in the sense of Buchweitz and Orlov;this triangle equivalence is called a singular equivalence.We will report recent progress on singular equivalenceswith examples.The represent<strong>at</strong>ion type of non-degener<strong>at</strong>eQPsChristof GeissN<strong>at</strong>ional Autonomous University of Mexico, Mexicochristof@m<strong>at</strong>em.unam.mxLet Q be a 2-acyclic quiver, and W a non-degener<strong>at</strong>epotential for Q. We show, th<strong>at</strong> up to a few exceptionsthe Jacaobian algebra P(Q, W ) is tame if and only if thequiver is mut<strong>at</strong>ion finite.The exceptions are the following: The mut<strong>at</strong>ion finitequivers X 6 , X 7 (found by Derksen and Owen) and the m-Kronecker quiver for m ≥ 3 yield wild Jacobian algebras.The mut<strong>at</strong>ion finite quivers T 1 and T 2 corresponding totriangul<strong>at</strong>ions of a torus with one puncture resp. withone marked point admit non-degener<strong>at</strong>e potentials whichcan be either tame or wild.The tame cases include virtually all known "derivedtamephenomena": (extended) Dynkin, tubular, skewedclannishand deform<strong>at</strong>ions. Thus we obtain many examplesof "tame" triangulal<strong>at</strong>ed 2-CY c<strong>at</strong>egories.If time permits we discuss the uniqueness of nondegener<strong>at</strong>epotentials for most mut<strong>at</strong>ion finite quivers.Geigle-Lenzing spaces and canonical algebrasof dimension d (I)Martin HerschendNorwegian University, Norwaymartinh@m<strong>at</strong>h.nagoya-u.ac.jpThis is the first half of a report on ongoing joint workwith Osamu Iyama, Hiroyuki Minamoto, and Steffen Oppermann.The second half will be given by Osamu Iyama.Weighted projective lines were introduced by Geigle andLenzing. One key property of these is th<strong>at</strong> they give riseto hereditary c<strong>at</strong>egories with tilting objects, whose endomorphismrings are canonical algebras. Both weightedprojective lines and canonical algebras have proven tobe interesting objects in represent<strong>at</strong>ion theory, and beenstudied intensively. In our talks we will introduce the notionof d-dimensional Geigle-Lenzing spaces, generalizingthe concept of weighted projective lines. Also in this casewe obtain a nice tilting bundle, whose endomorphism ringwe call a d-canonical algebra. We will then focus on someproperties of weighted projective lines which generalizenicely to the d-dimensional setup.Geigle-Lenzing spaces and canonical algebrasin dimension d (II)Osamu IyamaNagoya University, Japaniyama@m<strong>at</strong>h.nagoya-u.ac.jpThis is the second half of a report on ongoing joint workwith Martin Herschend, Hiroyuki Minamoto and Steffen
46 PRIMA 2013 AbstractsOppermann. The first half will be given by Steffen Oppermann.Weighted projective lines were introduced by Geigle andLenzing. One key property of these is th<strong>at</strong> they give riseto hereditary c<strong>at</strong>egories with tilting objects, whose endomorphismrings are canonical algebras. Both weightedprojective lines and canonical algebras have proven tobe interesting objects in represent<strong>at</strong>ion theory, and beenstudied intensively. In our talks we will introduce the notionof d-dimensional Geigle-Lenzing spaces, generalizingthe concept of weighted projective lines. Also in this casewe obtain a nice tilting bundle, whose endomorphism ringwe call a d-canonical algebra. We will then focus on someproperties of weighted projective lines which generalizenicely to the d-dimensional setup.Cohomological length functionsHenning KrauseUniversität Bielefeld, Germanyhkrause@m<strong>at</strong>h.uni-bielefeld.deA cohomological functor from a triangul<strong>at</strong>ed c<strong>at</strong>egoryinto the c<strong>at</strong>egory of finite length modules over some ringgives rise to an integer valued function on the set of all objects.One might ask: Wh<strong>at</strong> are the characteristic propertiesof such a function, and can one recover the functorfrom the corresponding function? Somewh<strong>at</strong> surprisingly,we can offer fairly complete answers to both questions.Examples from represent<strong>at</strong>ion theory will illustr<strong>at</strong>e theseanswers, and we discuss some cases when all cohomologicallength functions can be classified.Invariant flags for nilpotent oper<strong>at</strong>ors, andweighted projective linesHelmut LenzingPaderborn University, Germanyhelmut@m<strong>at</strong>h.uni-paderborn.deThis is joint work with Dirk Kussin and Hagen Meltzerextending a previous analysis of the invariant subspaceproblem for nilpotent oper<strong>at</strong>ors (of finite dimensional vectorspaces over an algebraically closed field k). The problemitself goes back to G. Birkhoff (1934) and was tre<strong>at</strong>edin detail by C.M. Ringel and M. Schmidmeier (2006-2008); it is further rel<strong>at</strong>ed to research by D. Simson (2007)and Pu Zhang (2011). In previous work with Kussin andMeltzer we did establish a rel<strong>at</strong>ionship of the invariantsubspace problem to singularity theory, more specificallywe showed a link to the theory of weighted projectivelines X of special weight type (2, 3, c). In this talk, weshow th<strong>at</strong> for arbitrary triple weight type (a, b, c), a suitablefactor c<strong>at</strong>egory S of the c<strong>at</strong>egory of vector bundleson X, is equivalent to the c<strong>at</strong>egory of graded represent<strong>at</strong>ionsof nilpotency degree bounded by c, equipped withtwo invariant flags of graded sub-represent<strong>at</strong>ions , wherethe flag lengths are determined by the integers a and b.The c<strong>at</strong>egory S carries a n<strong>at</strong>ural exact structure which isalmost-Frobenius, but in general not Frobenius. It’s associ<strong>at</strong>edstable c<strong>at</strong>egory S is triangul<strong>at</strong>ed and shown tobe equivalent to the singularity c<strong>at</strong>egory of the (suitablygraded) triangle singularity x a + y b + z c .Cluster c<strong>at</strong>egories and independence resultsfor exchange graphsPierre-Guy PlamondonUniversity of Paris-Sud, Francepierre-guy.plamondon@m<strong>at</strong>h.u-psud.frCluster c<strong>at</strong>egories are triangul<strong>at</strong>ed c<strong>at</strong>egories th<strong>at</strong> havebeen used to study S.Fomin and A.Zelevinsky’s cluster algebras.They come equipped with special objects, calledcluster-tilting objects, th<strong>at</strong> are obtained from one anotherby a process called mut<strong>at</strong>ion; this gives rise to an exchangegraph. In this talk, we will study properties ofthis exchange graph, and see how it is rel<strong>at</strong>ed to the exchangegraph of a cluster algebra. We will then applythese results to a conjecture of Fomin-Zelevinsky st<strong>at</strong>ingth<strong>at</strong> the exchange graph of a cluster algebra does not dependon the choice of the ring of coefficients over whichthe algebra is defined. (This is joint work with G.CerulliIrelli, B.Keller and D.Labardini-Fragoso.)Triangul<strong>at</strong>ed c<strong>at</strong>egories and tau-tilting theoryIdun ReitenNorwegian University of Science and Technology, Norway)idun.reiten@m<strong>at</strong>h.ntnu.noThis talk is based upon work with Adachi and Iyama.We explain how work on triangul<strong>at</strong>ed c<strong>at</strong>egories (clusterc<strong>at</strong>egories and more generally, 2-Calabi-Yau c<strong>at</strong>egories)inspired an extension of some aspects of classical tiltingtheory, which we have called tau-tilting theory.From submodule c<strong>at</strong>egories to preprojectivealgebrasClaus Michael RingelBielefeld University, Germany and Shanghai Jiao TongUniversity, Chinaringel@m<strong>at</strong>h.uni-bielefeld.deLet S(n) be the c<strong>at</strong>egory of invariant subspaces of nilpotentoper<strong>at</strong>ors with nilpotency index <strong>at</strong> most n. Suchsubmodule c<strong>at</strong>egories have been studied already in 1936by Birkhoff, they have <strong>at</strong>tracted a lot of <strong>at</strong>tention in recentyears, for example in connection with some weightedprojective lines (Kussin, Lenzing, Meltzer). On the otherhand, we consider the preprojective algebra of type A n;the preprojective algebras were introduced by Gelfandand Ponomarev, they are now of gre<strong>at</strong> interest, for examplethey form an important tool to study quantum groups(Lusztig) or cluster algebras (Geiss, Leclerc, Schroeer).Direct connections between the submodule c<strong>at</strong>egory S(n)and the module c<strong>at</strong>egory of the preprojective algebra oftype A n−1 have been established quite a long time ago byAuslander and Reiten, and recently also by Li and Zhang,but apparently this remained unnoticed. The lecture isbased on joint investig<strong>at</strong>ions with Zhang Pu and will providedetails on this rel<strong>at</strong>ionship. As a byproduct we seeth<strong>at</strong> here we deal with ideals I in triangul<strong>at</strong>ed c<strong>at</strong>egoriesT such th<strong>at</strong> I is gener<strong>at</strong>ed by an idempotent and T/I isabelian.Exact c<strong>at</strong>egories over Cohen–Macaulay ringsRyo TakahashiNagoya University, Japantakahashi@m<strong>at</strong>h.nagoya-u.ac.jpIt is known th<strong>at</strong> the following full subc<strong>at</strong>egories of finitelygener<strong>at</strong>ed modules are Frobenius c<strong>at</strong>egories:• the c<strong>at</strong>egory of maximal Cohen–Macaulay modulesover a Gorenstein ring,• the c<strong>at</strong>egory of totally reflexive ( = finitely gener<strong>at</strong>edGorenstein projective) modules over a noetherianring,• the c<strong>at</strong>egory of special Cohen–Macaulay modulesover a r<strong>at</strong>ional surface singularity.In this talk, we give a system<strong>at</strong>ic generaliz<strong>at</strong>ion of thisfact over a Cohen–Macaulay ring. More precisely, westudy certain full subc<strong>at</strong>egories of finitely gener<strong>at</strong>ed modules,and investig<strong>at</strong>e when they are exact c<strong>at</strong>egories withenough projectives and enough injectives. This talk isbased on joint work with Osamu Iyama.Toward repetitive equivalences
47 PRIMA 2013 AbstractsJiaqun WeiNanjing Normal University, Chinaweijiaqun@njnu.edu.cnWe say two artin algebras R and S are repetitive equivalentprovided th<strong>at</strong> their repetitive algebras are stablyequivalent. By Happel’s result, repetitive equivalencesbetween artin algebras of finite globe dimension implyderived equivalences. On the other hand, by results ofRickard, Chen etc., if two artin algebras are derived equivalent,then their repeptitive algebras are derived equivalent,and hence stably equivalent. Thus, repetitive equivalencesare more general than derived equivalences. Thepaper will suggest a way teward the Morita theory ofrepetitive equivalences.Some results rel<strong>at</strong>ed to Poisson (co)homologyQuanshui WuFudan University, Chinaqswu@fudan.edu.cnPoisson (co)homologies of some Poisson polynomial algebrasare used to calcul<strong>at</strong>e the Hochschild (co)homologiesof some Artin-Schelter regular algebras recently. In thistalk, I will concentr<strong>at</strong>e on some recent work on Poisson(co)homologies.Rigid morphisms, exact pairs and applic<strong>at</strong>ionsChangchang XiCapital Normal University, Chinaxicc@cnu.edu.cnIn this talk, we shall introduce rel<strong>at</strong>ively exact pairsof ring homomorphisms, define non-commut<strong>at</strong>ive tensorproducts over such pairs, which generalize the usual notionof tensor products over commut<strong>at</strong>ive rings, and constructrecollements of derived module c<strong>at</strong>egories of ringsinvolving those non-commut<strong>at</strong>ive tensor products. Thisconsider<strong>at</strong>ion is then used to understand the rel<strong>at</strong>ionshipof finitistic dimensions and algebraic K-theory of rings ina recollement.The content of this talk is taken from a joint work withHongxing Chen <strong>at</strong> CNU.T -structures and torsion pairs in a 2−Calabi-Yau triangul<strong>at</strong>ed c<strong>at</strong>egoryBin ZhuTsinghua University, Chinazhubin@m<strong>at</strong>h.tsinghua.edu.cnFor an indecomposable 2−Calabi-Yau triangul<strong>at</strong>ed c<strong>at</strong>egoryC with a cluster tilting object, we prove th<strong>at</strong>there are no non-trivial t-structures or non-trivial co-tstructuresin C. This allows us to give a classific<strong>at</strong>ion oftorsion pairs in this triangul<strong>at</strong>ed c<strong>at</strong>egory C. Furthermorewe determine the hearts of torsion pairs in the sense ofNakaoka: They are equivalent to the module c<strong>at</strong>egoriesover the endomorphism algebras of the cores of the torsionpairs.This is a joint work with Yu Zhou.4 Contributed TalksContributed Talks Group 1Geometry and AnalysisBounded oper<strong>at</strong>ors on Hilbert C ∗ -modulesMassoud AminiInstitute for Research in Fundamental Sciences, Iranmamini@modares.ac.irWe study the problem of amenability for the C ∗ -algebraB(E) of bounded oper<strong>at</strong>ors in a Hilbert C ∗ -module E ona C ∗ -algebra A. When A is a von Neumann algebra andE is full and self dual, we show th<strong>at</strong> B(E) is amenable(nuclear) if and only if A is injective and E is finitelygener<strong>at</strong>ed. We find similar results for the case where A isa C ∗ -algebra and E is weakly self dual. We briefly studythe predual and type theory of B(E) when it is a vonNeumann algebra. This is a joint work with M. BagherAsadi.Gromov-Hausdorff hyperspaces of R nSergey AntonyanN<strong>at</strong>ional University of Mexico, Mexicoantonyan@unam.mxThe Gromov-Hausdorff distance d GH was introduced in1981 by M. Gromov. It turns the set GH of all isometryclasses of compact metric spaces into a metric space.For two compact metric spaces X and Y the numberd GH (X, Y ) is defined to be the infimum of all Hausdorffdistances d H (i(X), j(Y )) for all metric spaces Mand all isometric embeddings i : X → M and j : Y → M.Clearly, the Gromov-Hausdorff distance between isometricspaces is zero; it is a metric on the set GH of isometryclasses of compact metric spaces. The metric space(GH, d GH ) is called the Gromov-Hausdorff hyperspace. Itis a challenging open problem to understand the topologicalstructure of this metric space. The talk contributestowards this problem. We denote by GH(R n ) the subspaceof GH consisting of the classes [E] whose represent<strong>at</strong>iveE is a metric subspace of R n . We are interestedin the Gromov-Hausdorff hyperspaces GH(R n ) andGH(R n , d) = {X ∈ GH(R n ) | diam X ≤ d}, d > 0. Inparticular, we will prove th<strong>at</strong> GH(R n ) is homeomorphicto the Hilbert cube with a removed point.Developments of harmonic maps into biharmonicmapsYuan-Jen ChiangUniversity of Mary Washington, Virginia, USAychiang@umw.eduHarmonic maps between Riemannian manifolds was firstestablished by Eells and Sampson [11] (Chiang’s PhDadvisor) in 1964. Biharmonic maps (generalizing harmonicmaps) were first studied by Jiang [12]–[14] in 1986.We present an overview of the developments of harmonicmaps into biharmonic maps based on [1]–[10]. We firstdiscuss the developments of harmonic maps on crucialtopics including regularity, maps of surfaces, maps intoKähler manifolds, maps into groups and Grassmannians,loop groups and integrable systems, harmonic morphisms,maps of singular spaces, and transversally harmonicmaps. We then present the developments of biharmonicmaps on topics including Riemannian immersionsand submersions, conformally biharmonic maps, biharmonicmorphisms, biharmonic homogeneous real hypersurfaces,regularity, transversally biharmonic maps, conserv<strong>at</strong>ionlaw, and biharmonic maps into Lie groups andintegrable systems.
48 PRIMA 2013 Abstracts[1] Y.-J. Chiang, Developments of harmonic maps,wave maps and Yang-Mills fields into biharmonicmaps, biwave maps and bi-Yang-Mills fields, Birkhäuser,Springer, Basel, in the series of “Frontiers in M<strong>at</strong>hem<strong>at</strong>ics,"XXII+399, 2013, in press.[2] Y. J. Chiang, Harmonic maps of V-manifolds, Ann.Global Anal. and Geom., Vol. 8 (1990), no. 3, 315–344.[3] Y.-J. Chiang, Spectral geometry of V-manifolds andits applic<strong>at</strong>ions to harmonic maps, Proc. Symp. PureM<strong>at</strong>h., Amer. M<strong>at</strong>h. Soc., Vol. 54 (1993), Part 1, 93-99.[4] Y.-J. Chiang, f-biharmonic maps between Riemannianmanifolds, J. of Geom. and Symmetry in Physics, Vol.27 (2012), 45–58.[5] Y. J. Chiang, Harmonic and biharmonic maps of Riemannsurfaces, Global J. of Pure and Applied M<strong>at</strong>h., Vol.9 (2013), no. 2, 109-124.[6] Y.-J. Chiang and A. R<strong>at</strong>to, Harmonic maps on spaceswith conical singularities, Bull. Soc. M<strong>at</strong>h. France, Vol.120 (1992), no. 3, 251–262.[7] Y.-J. Chiang and H. Sun, 2-harmonic totally realsubmanifolds in a complex projective space, Bull. Inst.M<strong>at</strong>h. Acad. Sinica, Vol. 27 (1999), no. 2, 99–107.[8] Y.-J. Chiang and H. Sun, Biharmonic maps on V-manifolds, Inter. J. M<strong>at</strong>h. M<strong>at</strong>h. Sci., Vol. 27 (2001),no. 8, 477–484.[9] Y.-J. Chiang and R. Wolak, Transversally biharmonicmaps between foli<strong>at</strong>ed Riemannian manifolds, Intern<strong>at</strong>.J. of M<strong>at</strong>h., Vol. 19 (2008), no. 8, 981–996.[10] Y.-J. Chiang and R. Wolak, Transversally f-harmonicand transversally f-biharmonic maps between foli<strong>at</strong>edRiemannian manifolds, JP J. of Geom. and Top., Vol.13 (2013), no. 1, 93–117.[11] J. Eells and J. H. Sampson, Harmonic mappingsof Riemannian manifolds, Amer. J. of M<strong>at</strong>h., Vol. 86(1964), 109–160.[12] G. Y. Jiang, 2-harmonic maps and their first andsecond vari<strong>at</strong>ional formulas Annals of M<strong>at</strong>h., China, Ser.A7 (1986), no. 4, 389-402.[13] G. Y. Jiang, 2-harmonic isometric immersions betweenRiemannian manifolds, Annals of M<strong>at</strong>h., China,Ser. A7 (1986), no. 2, 130-144.[14] G. Y. Jiang, The conserv<strong>at</strong>ion law of biharmonicmaps between Riemannian manifolds, Acta M<strong>at</strong>h. Sinica,Vol. 30 (1987), no. 2, 220–225.Hamiltonian group of self productShengda HuWilfrid Laurier University, Canadashu@wlu.caLet (X, ω) be a symplectic manifold and consider theself product (M, Ω) = (X × X, ω ⊕ −ω). We considerthe Hamiltonian groups Ham(X, ω) × Ham(X, −ω) andHam(M, Ω). There is a n<strong>at</strong>ural inclusion from the firstgroup into the second. We give an example where theinclusion map induces a proper inclusion of the fundamentalgroups. This is joint work with F. Lalonde.A McShane-type identity for closed surfacesYi HuangThe University of Melbourne, Australiahuay@ms.unimelb.edu.auWe prove a McShane-type identity— a series, expressedin terms of geodesic lengths, th<strong>at</strong> sums to 2π for anyclosed hyperbolic surface with one distinguished point.To do so, we prove a generalized Birman-Series theoremshowing th<strong>at</strong> the set of complete geodesics on a hyperbolicsurface with large cone-angles is sparse.A new gluing recursive rel<strong>at</strong>ion for LinearSigma Model of P 1 -orbifoldXiaobin LiSouthwest Jiaotong University, Chinalixiaobin@home.swjtu.edu.cnThe study of the moduli space plays an important role inenumer<strong>at</strong>ive geometry, symplectic geometry and m<strong>at</strong>hem<strong>at</strong>icalphysics. Given X = [P 1 /Z r] and let x ′ =([0] a, [∞] b ) be the 2-tuple of twisted sectors on X. Inthis talk, we construct two different compactific<strong>at</strong>ions ofthe moduli space M 0,2 (X, d[P 1 /Z r], x ′ ): Nonlinear SigmaModel M x′dx′and Linear Sigma Model Nd . Rel<strong>at</strong>ions be-x′and Ndare studied and a new gluing recur-tween M x′dsive rel<strong>at</strong>ion on N x′dis discussed.Cb-frames and the completely bounded approxim<strong>at</strong>ionproperty for oper<strong>at</strong>or spacesRui LiuNankai University, Chinaruiliu@nankai.edu.cnWe introduce the concept of cb-frames for oper<strong>at</strong>orspaces, and give characteriz<strong>at</strong>ions of completely complementedsubspaces of oper<strong>at</strong>or spaces with cb-bases. Weapply the results to discrete group C ∗ -algebras. In particular,we show th<strong>at</strong> there is a n<strong>at</strong>ural cb-frame for thereduced free group C ∗ -algebra C ∗ r (F n) of n-gener<strong>at</strong>orswhich is derived from the infinite convex decompositionof the biorthogonal system (λ s, δ s) s∈Fn . We show th<strong>at</strong>there is a separable Hilbert oper<strong>at</strong>or space which can notbe a subspace of an oper<strong>at</strong>or space with a cb-basis, thenwe introduce a n<strong>at</strong>ural question to ask for an essentialcharacteriz<strong>at</strong>ion of subspaces of oper<strong>at</strong>or spaces with cbbases.This is joint work with Zhong-Jin Ruan.Some inequalities for unitarily invariantnormsJagjit Singh M<strong>at</strong>haruGuru Nanak Dev University, Indiam<strong>at</strong>harujs@yahoo.comWe shall prove the inequalities|||(A+B)(A+B) ∗ |||≤|||AA ∗ +BB ∗ +2AB ∗ |||≤|||(A−B)(A−B) ∗ +4AB ∗ |||for all n × n complex m<strong>at</strong>rices A, B and all unitarily invariantnorms |||·|||. If furhter A, B are Hermitian positivedefinite it is proved th<strong>at</strong>k∏λ j (A♯ αB) ≤j=1k∏λ j (A 1−α B α ),j=11 ≤ k ≤ n,0 ≤ α ≤ 1,where ♯ α denotes the oper<strong>at</strong>or means considered by Kuboand Ando and λ j (X), 1 ≤ j ≤ n, denote the eigenvaluesof X arranged in the decreasing order whenever theseall are real. A number of inequalities are obtained asapplic<strong>at</strong>ions.On automorphism groups of Hua domainsFeng RongShanghai Jiao Tong University, Chinafrong@sjtu.edu.cnHua domains are the generaliz<strong>at</strong>ion of Cartan-Hartogsdomains, which were introduced by Weiping Yin around
49 PRIMA 2013 Abstractsthe end of 20th century (named after Chinese m<strong>at</strong>hem<strong>at</strong>icianLuogeng Hua). We will first give a brief introductionto Hua domains, and then give a complete description oftheir automorphism groups.Weighted harmonic spacesLuis Manuel Tovar Sánchez ∗ , Lino Feliciano Reséndis∗ N<strong>at</strong>ional Polytechnic Institute, Mexicotovar@esfm.ipn.mxIn 1994, R. Aulaskari and Peter Lappan introduced theQ p spaces p > 0, of analytic functions defined in theunit disk of the complex plane. Considering th<strong>at</strong> analyticfunctions f(z) = u(x, y) + iv(x, y) consist of a pairof harmonic conjug<strong>at</strong>e functions, in this paper we considerweighted harmonic spaces, consisting of real harmonicfunctions defined in the unit disk of the plane. Westudy their basic properties and rel<strong>at</strong>ionships with someother weighted function spaces.Variable equ<strong>at</strong>ion of st<strong>at</strong>e for a dark energymodel with linearly varying deceler<strong>at</strong>ion parameterMing ShenFuzhou University, Chinashenming0516@fzu.edu.cnWe present a dark energy model in an inhomogeneousplane symmetric space-time by considering a linearlyvarying deceler<strong>at</strong>ion parameter. In the model, the equ<strong>at</strong>ionof st<strong>at</strong>e (EoS) parameter ω is found to be time dependent.For different cosmic times, we obtain quintessence,vacuum energy and phantom fluid domin<strong>at</strong>ed universe.The universe we described has finite lifetime and endswith a big-rip which is a result consistent with recentcosmological observ<strong>at</strong>ions.Diversities and the geometry of hypergraphsPaul Tupper, David BryantSimon Fraser University, Canadapft3@sfu.caThere are well-known connections between certain combin<strong>at</strong>orialoptimiz<strong>at</strong>ion problems and the geometry of metricembeddings of graphs. Instead of metrics, we considerdiversities, which are a generaliz<strong>at</strong>ion of the conceptof metrics to functions of finite sets of points, r<strong>at</strong>herthan just pairs of points. We show th<strong>at</strong> analogous to therel<strong>at</strong>ion between flow problems and combin<strong>at</strong>orial optimiz<strong>at</strong>ionin graphs, there are intim<strong>at</strong>e rel<strong>at</strong>ions betweendiversities and a different set of flow problems, includingfractional Steiner tree packing and optimal flows in hypergraphs.We discuss polynomial approxim<strong>at</strong>ion algorithmsth<strong>at</strong> would result from a effective theory of embedding diversitiesinto l 1 .On the potential function of gradient steadyRicci solitonsPeng WuCornell University, USAwupenguin@m<strong>at</strong>h.cornell.eduWe prove th<strong>at</strong> the infimum of the potential function ofa gradient steady Ricci soliton decays linearly. As consequences,a gradient steady Ricci soliton with bounded potentialfunction must be Ricci-fl<strong>at</strong>, and no gradient steadyRicci soliton admits uniformly positive scalar curv<strong>at</strong>ure.New he<strong>at</strong> kernel estim<strong>at</strong>es on manifolds withneg<strong>at</strong>ive Ricci curv<strong>at</strong>ure lower boundXiangjin XuBinghamton University, USAxxu@m<strong>at</strong>h.binghamton.eduApply the new Li-Yau type Harnack estim<strong>at</strong>es for thehe<strong>at</strong> equ<strong>at</strong>ions on manifolds with Ric(M) ≥ −K, K ≥ 0,which established by Junfang Li and the author [Advancein M<strong>at</strong>hem<strong>at</strong>ics 226(5) (2011), 4456-4491], I prove a newupper bound estim<strong>at</strong>e for the he<strong>at</strong> kernel H(x, y, t) ofmanifolds with Ric(M) ≥ −K,H(x, y, t) ≤ A K (t)Vx −1/2 (δ(t))Vy−1/2 (δ(t))[]· exp − d2 (x, y)+ [1 + d 2 (x, y)]B K (t) ,4twhere A K (t), B K (t) : [0, ∞) → [0, ∞) are bounded functions,and δ(t) ∼ t as t → 0 and δ(t) ∼ 1 as t → ∞.While in the seminal work of Li-Yau [Acta M<strong>at</strong>h. 156(1986) 153-201.], the he<strong>at</strong> kernel upper bound estim<strong>at</strong>eshad δ-loss:H(x, y, t) ≤C(δ, n)Vx −1/2 ( √ t)Vy −1/2 ( √ t)[]· exp − d2 (x, y)(4 + δ)t + C 1δKt ,[ ]cwhere constant C(δ, n) ∼ exp 1δ as δ → 0, due th<strong>at</strong>there was non-sharp Harnack estim<strong>at</strong>es on manifolds withRic(M) ≥ −K.Contributed Talks Group 2Algebra and Number TheoryUniversal objects for free G-spacesN<strong>at</strong>ella AntonyanMonterrey Institute of Technology, Mexiconantonya@itesm.mxThroughout G is assumed to be a compact Lie group.A G-space U is called universal for a given class of G-spaces G-P, if U ∈ G-P and U contains as a G-subspacea G-homeomorphic copy of any G-space X from the classG-P.In this talk we shall present universal G-spaces in the classof all paracompact (respectively, metrizable, and separablemetrizable) free G-spaces. Recall th<strong>at</strong> for a G-spaceX and a point x ∈ X the stabilizer (or st<strong>at</strong>ionary subgroup)of x is defined by G x = {g ∈ G | gx = x}. IfG x = {e} for all x ∈ X then we say th<strong>at</strong> the action ofG is free and X is a free G-space. Denote by Cone Gthe cone over G endowed with the n<strong>at</strong>ural action of G inducedby left transl<strong>at</strong>ions. Let J ∞(G) be the infinite joinG ∗ G ∗ . . . ; it is just the subset of the countable product(Cone G) ∞ consisting of all those points (t 1 g 1 , t 2 g 2 , . . . )for which only a finite number of t i ≠ 0 and ∑ ∞i=1 t i = 1.We let G act coordin<strong>at</strong>e-wise on J ∞(G). Denote by Ithe unit interval [0, 1] and by I τ the Tychonoff cube of agiven infinite weight τ endowed with the trivial action ofG.We prove th<strong>at</strong> for every infinite cardinal number τ, theproduct J ∞(G) × I τ is universal in the class of all paracompactfree G-spaces of weight ≤ τ. A similar result formetrizable free G-spaces of weight ≤ τ is also obtained.C<strong>at</strong>egorific<strong>at</strong>ion in topology, geometry andcombin<strong>at</strong>orics
50 PRIMA 2013 AbstractsIgor BakovićUniversity of Warsaw, Polandbakovic@mimuw.edu.plC<strong>at</strong>egorific<strong>at</strong>ion become an essential tool in many areas ofmodern m<strong>at</strong>hem<strong>at</strong>ics. By generalizing algebraic conceptsfrom the classical set theory to the context of higher c<strong>at</strong>egorytheory, a program of higher dimensional algebra isiniti<strong>at</strong>ed as an <strong>at</strong>tempt to unify quantum field theory withtraditional algebraic topology. The purpose of the talk isto reflect on one of the central themes of Grothendieck’swork about the deep rel<strong>at</strong>ion between topos theory andhomotopy theory, where he emphasized the importanceof the sheaf theoretical objects corresponding to higherc<strong>at</strong>egorical structures. Such sheaf-theoretical and cohomologicalstructures associ<strong>at</strong>ed to higher c<strong>at</strong>egories areubiquitous in many areas of m<strong>at</strong>hem<strong>at</strong>ics like (algebraic)topology, geometry and combin<strong>at</strong>orics. We will shed morelight on author’s work on fibr<strong>at</strong>ions of bic<strong>at</strong>egories, stemingfrom mostly unpublished work by Bénabou, in hisinvestig<strong>at</strong>ions of logical aspects of fibred c<strong>at</strong>egories, andhis <strong>at</strong>tempt to give found<strong>at</strong>ions of naive c<strong>at</strong>egory theoryby using fibred c<strong>at</strong>egories. We will briefly describe theoryof 2-fibr<strong>at</strong>ions, Grothendieck construction for bic<strong>at</strong>egories,fibered bic<strong>at</strong>egorical Yoneda lemma and homotopytheoretic view of 2-fibr<strong>at</strong>ions, connecting the wholetheory to Lurie’s cartesian fibr<strong>at</strong>ions. Finally, we rel<strong>at</strong>ethe 2-dimensional fibr<strong>at</strong>ions with Joyal theory of speciesof structures in combin<strong>at</strong>orics. The basis for this connectionis Zawadowski’s interpret<strong>at</strong>ion of amalgam<strong>at</strong>edsign<strong>at</strong>ures by means of lax monidal fibr<strong>at</strong>ions of c<strong>at</strong>egories.By c<strong>at</strong>egorifying the l<strong>at</strong>ter notion, we describelax monoidal fibr<strong>at</strong>ions of bic<strong>at</strong>egories as a n<strong>at</strong>ural organiz<strong>at</strong>ionaltool for c<strong>at</strong>egorified sign<strong>at</strong>ures which appear ina work of Cheng and Hermida, Makkai and Power, andwhich consequently give a basis for generalized species ofstructures.Realising Galois groups via Galois represent<strong>at</strong>ionsShuvra GuptaUniversity of Iowa, USAshuvra@m<strong>at</strong>h.upenn.eduGabor Wiese first realised families of finite simple groupsas Galois groups over the field of r<strong>at</strong>ional numbers, Q,by controlling the images of certain Galois represent<strong>at</strong>ions.Since then, Galois represent<strong>at</strong>ions have been usedto realise various other families of finite simple groups asGalois groups over Q. We will discuss results which enableus to realise some new families of finite simple groupsand new techniques which enable us to realise non-simplefinite groups as Galois groups over Q. Some of this workis joint work and still in progress.L-functions from Langlands-Shahidi methodfor GSpin groups and the generic Arthur L-packet conjectureYeansu KimPurdue University, USAkim407@m<strong>at</strong>h.purdue.eduL-functions are very interesting tools th<strong>at</strong> number theoristshave been using since 18th century. Those also appearin the local Langlands conjecture. Briefly, the localLanglands conjecture asserts th<strong>at</strong> there exists a ‘n<strong>at</strong>ural’bijection between two different sets of objects: Arithmetic(Galois or Weil-Deligne) side and analytic (represent<strong>at</strong>iontheoretic) side. In each side, we can definethe L-functions of those objects. The L-functions fromanalytic side are defined by Shahidi (Langlands-Shahidimethod) and the L-functions from arithmetic side areArtin L-functions. The n<strong>at</strong>ural question is whether twoL-functions are equal through the local Langlands correspondence.If it is, we can use the properties of localL-functions from arithmetic side to study local L-packet,the object in the analytic side, which is the set of irreducibleadmissible represent<strong>at</strong>ions of quasi split group Gover p-adic field. The equality of local L-functions hasan interesting applic<strong>at</strong>ion in proving the generic ArthurL-packet conjecture. The generic Arthur L-packet conjecturest<strong>at</strong>es th<strong>at</strong> if the L-packet <strong>at</strong>tached to Arthur parameterhas a generic member, then it is tempered. Thisconjecture can be considered as local version of generalizedRamanujan conjecture. In this talk, I will explainthose in the case of split GSpin groups. Furthermore, Iwill explain the classific<strong>at</strong>ion of strongly positive discreteseries represent<strong>at</strong>ions of GSpin groups over p-adic fieldwhich is one of the main tools in the proof of the equalityof L-functions. If time permits, I will explain the generalizedRamanujan conjecture for GSpin groups.Derived equivalences and Gorenstein dimensionHirotaka KogaUniversity of Tsukuba, Japankoga@m<strong>at</strong>h.tsukuba.ac.jpA ring A is said to be left (resp., right) coherent if everyfinitely gener<strong>at</strong>ed left (resp., right) ideal of it is finitelypresented (see [3]). Let A, B be derived equivalent leftand right coherent rings (see [5]). In [4] K<strong>at</strong>o showedth<strong>at</strong> a standard derived equivalence induces an equivalencebetween the triangul<strong>at</strong>ed c<strong>at</strong>egories consisting ofcomplexes of finite Gorenstein dimension and th<strong>at</strong> a derivedequivalence induces an equivalence between the projectivelystable c<strong>at</strong>egories of modules of Gorenstein dimensionzero (see [1] and [2]) if either inj dim A < ∞or inj dim A op < ∞. In this talk, we provide altern<strong>at</strong>iveproofs of these results from another point of view.Also, we do not assume the existence of standard derivedequivalence or finiteness of selfinjective dimension.[1] M. Auslander and M. Bridger, Stable module theory,Mem. Amer. M<strong>at</strong>h. Soc., 94, Amer. M<strong>at</strong>h. Soc.,Providence, R.I., 1969.[2] R.-O. Buchweitz, Maximal Cohen-Macaulay modulesand T<strong>at</strong>e-cohomology over Gorenstein rings(1987), 155, unpublished manuscript, available <strong>at</strong>https://tspace.library.utoronto.ca/handle/1807/16682.[3] S. U. Chase, Direct products of modules, Trans.Amer. M<strong>at</strong>h. Soc. 97 (1960), 457–473.[4] Y. K<strong>at</strong>o, On derived equivalent coherent rings,Comm. Algebra 30 (2002), no. 9, 4437–4454.[5] J. Rickard, Morita theory for derived c<strong>at</strong>egories, J.London M<strong>at</strong>h. Soc. (2) 39 (1989), no. 3, 436–456.A generalized Koszul theoryLiping LiUniversity of California, Riverside, USAlipingli@m<strong>at</strong>h.ucr.eduLet A be a positively graded, locally finite k-algebrawhere A 0 is a finite-dimensional algebra whose finitisticdimension is 0. In this talk we introduce a generalizedKoszul theory preserving many classical results, and describean explicit correspondence between this generalizedtheory and the classical theory. Applic<strong>at</strong>ions in represent<strong>at</strong>ionsof certain c<strong>at</strong>egories and extension algebras ofstandard modules of standardly str<strong>at</strong>ified algebras will bedescribed if time allows.On symmetric associ<strong>at</strong>ion schemes with k 1 = 3and m i = 3
51 PRIMA 2013 AbstractsJongyook ParkUniversity of Science and Technology of China, Chinajongyook@hanmail.netIn 2006, Bannai and Bannai classified primitive symmetricassoci<strong>at</strong>ion schemes with m 1 = 3. In their paper, thehardest case was k 1 = 3. Even though, (primitive) symmetricassoci<strong>at</strong>ion schemes with k 1 = 3 were classified byYamazaki in 1998, they avoided the use of the difficultand deep result of Yamazaki. In this talk, we generalizethe result of Bannai and Bannai.Triangul<strong>at</strong>ed c<strong>at</strong>egories from c<strong>at</strong>egories ofspecail exact squencesKeyan Song, Yuehui ZhangShanghai Jiao Tong University, Chinazyh@sjtu.edu.cnLet A be an artinian algebra over an algebraically closedfield k. Let F be the c<strong>at</strong>egory consisting of all four-termexact sequences in modA. Let C be the full subc<strong>at</strong>egory ofF consisting of all exact sequences with two middle termsprojective modules in modA. It is proved th<strong>at</strong> C is contravariantlyfinite. As applic<strong>at</strong>ions, it is proved th<strong>at</strong> C is aFrobenius c<strong>at</strong>egory and has Auslander-Reiten sequencesprovided A is an selfinjective algebra. Furthermore, it isproved th<strong>at</strong> the stable c<strong>at</strong>egory C equals to C/H as factorc<strong>at</strong>egories, where H is the set of all homotopic rel<strong>at</strong>ions,and they are both equivalent to the stable c<strong>at</strong>egory modA.An interesting result is th<strong>at</strong> these three c<strong>at</strong>egories C, C/Hand modA are equivalent as triangul<strong>at</strong>ed c<strong>at</strong>egories.Contributed Talks Group 3Discrete M<strong>at</strong>hem<strong>at</strong>icsNumerical verific<strong>at</strong>ion method for well conditionedspherical t-designsCongpei AnJinan University, Chinaandbach@163.comA set X N of N points on the unit sphere is a sphericalt-design if the average value of any polynomial of degree<strong>at</strong> most t over X N is equal to the average value of thepolynomial over the sphere. In this talk, we focus on thecomput<strong>at</strong>ional construction of spherical t-designs on theunit sphere S 2 ⊂ R 3 when N ≥ (t + 1) 2 , the dimension ofthe space P t of spherical polynomials of degree <strong>at</strong> mostt. We show how to construct well conditioned sphericaldesigns with N ≥ (t+1) 2 points by maximizing the determinantof a m<strong>at</strong>rix while s<strong>at</strong>isfying a system of nonlinearconstraints for 1 ≤ t ≤ 100. Interval methods are thenused to prove the existence of a true spherical t-designvery close to the calcul<strong>at</strong>ed points and to provide a guaranteedinterval containing the determinant. The resultingspherical designs have good geometrical properties (separ<strong>at</strong>ionand mesh norm). We discuss some open problemson the distribution of point set over the sphere.This is a joint work with X.Chen, I. H. Sloan and R. S.Womersley.Edge colouring graphs with bounded colourclassesDavid CariolaroXi’an Jiaotong-Liverpool University, Chinadavid.cariolaro@xjtlu.edu.cnAn edge colouring of a graph G is a function which assignsa colour to each edge of G in such a way th<strong>at</strong> adjacentedges receive distinct colours. The minimum number ofcolours used by an edge colouring of G is a well knownand studied graph parameter called chrom<strong>at</strong>ic index anddenoted by χ ′ (G). It was proved by Holyer in 1981 th<strong>at</strong>computing χ ′ (G) is in general NP-hard. We consider avari<strong>at</strong>ion of the edge colouring problem, which may beof interest for applic<strong>at</strong>ions. Specifically, we consider edgecolourings of G such th<strong>at</strong> no colour is assigned to morethan B edges, where B is a positive integer fixed in advance(clearly such edge colourings always exist). We callany such colouring a B-bounded edge colouring of G. Theminimum number of colours in a B-bounded edge colouringof G is a graph parameter which we denote by χ ′ B (G)and call B-bounded chrom<strong>at</strong>ic index. A B-bounded edgecolouring which uses exactly χ ′ B (G) colours is called anoptimal B-bounded edge colouring of G.It is not difficult to see th<strong>at</strong>, for every graph G,χ ′ B (G) = max{χ′ (G), ⌈ |E(G)|B ⌉.This prompts the question of whether the parameter χ ′ Band an optimal B-bounded edge colouring can be computedin polynomial time for a fixed value of B. Ourgoal in this talk will be to answer this question in theaffirm<strong>at</strong>ive. This is joint work with Romeo Rizzi [1].[1] R. Rizzi and D. Cariolaro, Polynomial time complexityof Edge Colouring Graphs with Bounded Colour Classes,Algorithmica (2013), in press, doi: 10.1007/s00453-013-9746-7.Realizing joint degree m<strong>at</strong>ricesAaron DutleUniversity of South Carolina, USAdutle@m<strong>at</strong>h.sc.eduThe Joint Degree M<strong>at</strong>rix of a graph is a m<strong>at</strong>rix whose(i, j) entry is the number of edges connecting vertices ofdegree i to vertices of degree j. A given m<strong>at</strong>rix is calledrealizable if it is the joint degree m<strong>at</strong>rix of a simple graph.As in the case of degree sequences, there is a simple set ofconditions for when a m<strong>at</strong>rix is realizable, as well as anoper<strong>at</strong>ion th<strong>at</strong> can be used to transform any realiz<strong>at</strong>ioninto any other realiz<strong>at</strong>ion. We discuss these problems,as well as the extremal question of when a joint degreem<strong>at</strong>rix is uniquely realizable.Generaliz<strong>at</strong>ion of Legendre polynomials theoryLemin GuTongji University, Chinagulemin@tongji.edu.cnIn all of n-order polynomials th<strong>at</strong> highest coefficientis 1čňLegendre polynomials are in the interval [−1, 1]with the least square error of zero polynomials, th<strong>at</strong> forP∫n(x) = x n + a(n − 1)x n−1 + ... + a1x + a0, making[P n(x)] 2 dx = min. Promotes the Legendre multinomialbasicprinciple: In all of n-order polynomials th<strong>at</strong> highestcoefficient is not 1, namely an ≠ 1,there must be a newpolynomials Gn(x) = x n + a(n − 1)x n−1 + ... + a1x + a0,making ∫ [Gn(x)] 2 dx = min. Through discussion of thesquare error minimiz<strong>at</strong>ion, leads to the new polynomialsestablishment necessity. For convenient on elabor<strong>at</strong>ionin this abstract,called it "Gn(x) polynomial" (Generaliz<strong>at</strong>ionof Legendre polynomial). First the existenceof Gn(x) polynomials issues are studied: By establishingGn(x) equ<strong>at</strong>ion the ordinary solution expressions in the
52 PRIMA 2013 Abstractsinterval |x| < 1 are given, have proven th<strong>at</strong> when n is positiveinteger and the interval is in |x| ≤ 1, two linear independencespecial solutions of them are Gn(x) polynomials,and provide the general term expression; Second, thegeometric meaning of Gn(x) polynomials are discussed,have proven th<strong>at</strong> Gn(x)polynomials are the polynomialsth<strong>at</strong> in [−1, 1] with the error squares value are the least;Third, the main properties of Gn(x) polynomials are introducedčňwhichincluding Gn(x)polynomials recurrenceformula, the orthogonality, the odevity, the squares valuearea, the former n=9 polynomials, the corresponding geometry,and so on. Last, some special applic<strong>at</strong>ions ofGn(x) polynomials under different boundary conditionsare given: Combined with the best Chebyshev approxim<strong>at</strong>iontheory they can constitute maximum error minimizingleast square approxim<strong>at</strong>ion; Combined with theLeast Absolute Devi<strong>at</strong>ion approxim<strong>at</strong>ion theory can constitutezero error type least square approxim<strong>at</strong>ion; Underthe conditions of an=1 form the Legendre polynomial,andso on.The subsets counting problems and their applic<strong>at</strong>ionsJiyou LiShanghai Jiao Tong University, Chinalijiyou@sjtu.edu.cnLet G be an abelian group and D be a finite subset of G.∑Denote N(b) to be the number of subsets S in D such th<strong>at</strong>x∈S x = b and N k(b) to be the number of k-subsets Sin D such th<strong>at</strong> ∑ x∈S x = b. When G is the set of integers,the decision version of the subset sum problem, i.e.,determining if N(b) > 0, is a well-known NP-completeproblem. And its counting version, the explicit enumer<strong>at</strong>ionof N(b) or N k (b), is a #P-complete problem. Inthis talk, we will investig<strong>at</strong>e these problems from a m<strong>at</strong>hem<strong>at</strong>icalpoint of view, and introduce their rel<strong>at</strong>ions toadditive combin<strong>at</strong>orics, coding theory and computer sciences.P<strong>at</strong>hs and cycles of interval graphsPeng LiShanghai Jiao Tong University, Chinalidetiansjtu@sjtu.edu.cnWe recently find a linear time algorithm for solving the 1-Fixed-Endpoint P<strong>at</strong>h Cover Problem on interval graphs.The design and the analysis of this algorithm motiv<strong>at</strong>eus to develop many properties on the p<strong>at</strong>hs and cycles ofinterval graphs and graphs. In this short present<strong>at</strong>ion, wereport a series of equivalent characteriz<strong>at</strong>ions of Hamiltonianconnectedness and other p<strong>at</strong>h/cycle properties ofinterval graphs.This is joint work with Yaokun Wu.The spectrum of 3-way k-homogeneous L<strong>at</strong>intradesTrent G. MarbachThe University of Queensland, Australi<strong>at</strong>rent.marbach@uqconnect.edu.auThe theory of L<strong>at</strong>in trades has a deep and interestingstructure, with connections to permut<strong>at</strong>ion groups, geometryand topology. The study of µ-way k-homogeneousL<strong>at</strong>in trades has received <strong>at</strong>tention recently. The effortsof five public<strong>at</strong>ions completed the spectrum of the ordersof 2-way k-homogeneous L<strong>at</strong>in trades. This was followedby a recent paper (Bagheri Gh., et al. 2012), whichfocused particularly on the 3-way k-homogeneous L<strong>at</strong>intrades with k ≤ 15. In this talk, I will give a brief reporton the existence of µ-way k-homogeneous L<strong>at</strong>in trades,including three new constructions th<strong>at</strong> complete the 3-way k-homogeneous L<strong>at</strong>in trade spectrum for all but ahandful of values. We will also provide the directions forfurther research motiv<strong>at</strong>ed by this work.On the fractional metric dimension of treegraphsSuhadi Wido SaputroInstitut Teknologi Bandung, Indonesiasuhadi@m<strong>at</strong>h.itb.ac.idLet G be a finite, simple, and connected graph. The distancebetween any two vertices u, v ∈ V (G), denoted byd G (u, v), is the length of a shortest (u − v) p<strong>at</strong>h in G.A vertex x ∈ V (G) is called resolve a pair {u, v} of verticesof G if d G (u, x) ≠ d G (v, x). For u, v ∈ V (G), theset of all vertices which resolve the pair {u, v} is denotedby R G {u, v}. A real value function g : V (G) → [0, 1]is called a resolving function of G if g(R G {u, v}) ≥ 1for any two distinct vertices u, v ∈ V (G). The fractionalmetric dimension, denoted by dim f (G), is givenby dim f (G) = min{|g| : g is a resolving function of G},where |g| = g(V (G)). In this paper, we determine thefractional metric dimension for tree graph T n of ordern ≥ 3.Unimodality of genus distribution of laddersLiangxia WanBeijing Jiaotong University, Chinalxwan@bjtu.edu.cnGiven a graph,its genus distribution is unimodal? Asthough many results about genus distribution of graphshave obtained, there are only several those about unimodalityof genus distribution of graphs. In this talk,unimodality of genus distri- bution of some graphs areverified.The lit-only σ-gameZiqing XiangShanghai Jiao Tong University, ChinaZiqingXiang@gmail.comLet G be a finite graph with vertex set V which may notnecessarily be loopless. For each v ∈ V , let α v ∈ F V 2 bethe map which takes value 1 on w ∈ V if and only if thereis an edge between v and w in G; let T v be the linear mapon F V 2 th<strong>at</strong> sends x ∈ FV 2 to itself if x(v) = 0 and sendsx ∈ F V 2 to x + αv if x(v) = 1. Note th<strong>at</strong> Tv is a transvectionwhen v is not a loop in G while T v is an idempotentwhen v is a loop in G. We consider the digraph Γ withvertex set F V 2 and arc set {(x, Tv(x) : x ∈ FV 2 , v ∈ V },which is the phase space of the lit-only σ-game on G.We determine the reachability rel<strong>at</strong>ion for the digraph Γ.A surprising corollary of this work is th<strong>at</strong>, for α, β ∈ F V 2 ,basically, α can reach β in Γ if and only if α − β lies inthe binary linear subspace spanned by {α v : v ∈ V }.An important step of our work is to define the line graphof a multigraph and to provide a forbidden subgraph characteriz<strong>at</strong>ion.If the graph G is loopless, as an applic<strong>at</strong>ionof our knowledge of the corresponding digraph Γ, we areable to determine the multiplic<strong>at</strong>ive group gener<strong>at</strong>ed by{T v : v ∈ V }. We also indic<strong>at</strong>e possible approaches onextending the work here to the general case of G being adigraph.This is joint work with Yaokun Wu.
53 PRIMA 2013 AbstractsPancyclicity of 4-connected {K 1,3, Z 8}-freegraphsHong-Jian Lai, Mingquan Zhan, Taoye Zhang, and JuZhouKutztown University of Pennsylvania, USAzhou@kutztown.eduA graph G is said to be pancyclic if G contains cycles oflengths from 3 to |V (G)|. In this paper, we show th<strong>at</strong>every 4-connected claw-free Z 8 -free graph is either pancyclicor is the line graph of the Petersen graph. Thisimplies th<strong>at</strong> every 4-connected claw-free Z 6 -free graph ispancyclic, and every 5-connected claw-free Z 8 -free graphis pancyclic.The number of subtrees of a treeXiao-Dong ZhangShanghai Jiao Tong University, P.R. Chinaxiaodong@sjtu.edu.cnIn this talk, we consider how to determine the maximumand minimum number of subtrees a tree with a givendegree tree sequence. It is proven th<strong>at</strong> the greedy treeamong all trees with the same degree sequence has themaximum number subtrees, while it is tough to determinewhich tree has minimum number of subtrees. This work isjoined with Daniel Gray, Hua Wang, and Xiu-Mei Zhang.Contributed Talks Group 4Comput<strong>at</strong>ional M<strong>at</strong>hem<strong>at</strong>ics & Optimiz<strong>at</strong>ionA semidefinite approxim<strong>at</strong>ion for symmetrictravelling salesman polytopesJulián Ariel Romero BarbosaUniversity of los Andes, Colombiaja.romero913@uniandes.edu.coIn this talk we will present a positive semidefinite approxim<strong>at</strong>ionof compact convex sets introduced by A. Barvinokand E. Veomett [1]. In particular we will discussthe behaviour of this relax<strong>at</strong>ion when the convex sets tobe approxim<strong>at</strong>ed are the Traveling Salesman PolytopesT n and T n,n associ<strong>at</strong>ed to the complete graphs K n andK n,n respectively. E. Veomett has shown th<strong>at</strong> the scalingof the k−th approxim<strong>at</strong>ion by n/k + O(1/n) containsthe polytope T n for k ≤ ⌊n/2⌉ . Here, we will showth<strong>at</strong>√these metric bounds can be improved by a factor of1 k−13 n2−1 + 2 for the case when n is even. Finally, we3will show new metric bounds for the approxim<strong>at</strong>ion ofthe polytope T n,n.This results are joint work with M. Velasco and are partof my master’s dissert<strong>at</strong>ion <strong>at</strong> the University of los Andes.[1] Veomett, Ellen. A positive semidefinite approxim<strong>at</strong>ionof the symmetric traveling salesman polytope. DiscreteComput. Geom. 38 (2007), no. 1, 15-28.An analysis of HDG methods for theHelmholtz equ<strong>at</strong>ionJintao CuiUniversity of Arkansas <strong>at</strong> Little Rock, USAjxcui1@ualr.eduIn this talk we discuss the hybridizable discontinuousGalerkin (HDG) methods for the Helmholtz equ<strong>at</strong>ionwith first order absorbing boundary condition in two andthree dimensions. We prove th<strong>at</strong> the proposed HDGmethods are stable (hence well-posed) without any meshconstraint. The stability constant is independent of thepolynomial degree. By using a projection-based erroranalysis, we also derive the error estim<strong>at</strong>es in L 2 norm forpiecewise polynomial spaces with arbitrary degree. Thisis joint work with Wujun Zhang from University of Maryland.An Uzawa method for solving steady Navier-Stokes equ<strong>at</strong>ions discretized by mixed elementmethodsJianguo HuangShanghai Jiao Tong University, Chinajghuang@sjtu.edu.cnNumerical solutions of Navier-Stokes equ<strong>at</strong>ions play fundamentalroles in scientific computing and fluid dynamics.The need to do this frequently occurs in many appliedsciences. Mixed element methods are widely usedfor discretizing steady Navier-Stokes equ<strong>at</strong>ions in applic<strong>at</strong>ions.However, it is challenging to devise fast solvers forthe resulting nonlinear system. A typical solver involvesnumerical solution of the discretized Oseen equ<strong>at</strong>ions <strong>at</strong>each iter<strong>at</strong>ion step; or equivalently, a non-symmetric saddlepoint system must be solved <strong>at</strong> each iter<strong>at</strong>ion step.However, it is by no means trivial to solve such a subproblemefficiently.In this talk, we are going to design an Uzawa-type iter<strong>at</strong>ivemethod for the previous nonlinear system, for whichwe require to solve no saddle point system <strong>at</strong> each iter<strong>at</strong>ionstep. Under some reasonable conditions, we prove itsconvergence r<strong>at</strong>e is independent of the finite element meshsize h, even for the shape regular triangul<strong>at</strong>ion. Finally,we provide a series of numerical experiments to show theaccuracy and performance of the method proposed. Thisis a joint work with Puyin Chen and Huashan Sheng.Semi-classical limit for the Schrödinger equ<strong>at</strong>ionwith l<strong>at</strong>tice potential, and band-crossingQin LiUniversity of Wisconsin-Madison, USAqinli@m<strong>at</strong>h.wisc.eduIn this talk, I am going to present the deriv<strong>at</strong>ion of thesemi-classical limit of the Schrödinger equ<strong>at</strong>ion with l<strong>at</strong>ticepotential, where the l<strong>at</strong>tice constant and the Planckconstant are <strong>at</strong> the same order. Bloch theory is used todecompose the solution into eigenfunctions. Here we encountertwo problems: 1. eigenvalues degener<strong>at</strong>e, whenthis happens one cannot distinguish the associ<strong>at</strong>ed eigenfunctions,and the so called transition r<strong>at</strong>e between energybands should be introduced; 2. the evolution of theprojection coefficients follow a coupled integro-differentialequ<strong>at</strong>ion, which can be hard to compute. By carryingout the Wigner transform<strong>at</strong>ion of all the Bloch bands,we find a complete basis on the phase space. The coefficientsfor them are controlled by a simple hyperbolicequ<strong>at</strong>ion, and the transition r<strong>at</strong>es <strong>at</strong> the point of thedegeneracy are characterized explicitly. A domain decompositionmethod based on the distances between energybands is designed associ<strong>at</strong>ed to this newly developedmodel. This is a joint work with Lihui Chai and Shi Jin.Legendre pseudospectral method for solvingthree-dimensional non-linear hyperbolic partialdifferential equ<strong>at</strong>ionsAbdur RashidGomal University, Pakistanprof.rashid@yahoo.com
54 PRIMA 2013 AbstractsIn this talk, numerical solutions of three-space non-linearhyperbolic partial differential equ<strong>at</strong>ions will be presentedby using Legendre pseudospectral method. The discretiz<strong>at</strong>ionof the sp<strong>at</strong>ial deriv<strong>at</strong>ives of the problem havebeen solved by using Legendre pseudospectral method. Asystem of non-linear ordinary differential equ<strong>at</strong>ions is gener<strong>at</strong>ed.The values of unknown function u can be foundby using kronecker product. The represent<strong>at</strong>ion of thiskind of product can easily be extended to higher dimensions.The numerical results are obtained and comparewith exact solutions to valid<strong>at</strong>e the high precision of theLegendre pseudospectral method [1-6].Efficient duality method to a class of globaloptimiz<strong>at</strong>ions problems with nonconvex objectivefunctionNing RuanUniversity of Ballar<strong>at</strong>, Australian.ruan@ballar<strong>at</strong>.edu.auIn this talk, the speaker presents a comprehensive reviewand some important developments on the canonicalduality theory for solving a broad classes of minimiz<strong>at</strong>ionproblem with nonconvex objective function. Theseproblems arise in many real-world applic<strong>at</strong>ions. By usingthe canonical dual transform<strong>at</strong>ion, the nonconvex primalproblem can be converted into a canonical dual problem(i.e., either a concave maximiz<strong>at</strong>ion or a convex minimiz<strong>at</strong>ionproblem) with zero duality gap. The idea and themethod presented in this talk can be generalized to solvemany other difficult problems in nonconvex mechanics,network communic<strong>at</strong>ion, and scientific comput<strong>at</strong>ions.M<strong>at</strong>h and gamingXingzhong ShiWenzhou-Kean University, Chinafshi_xz@yahoo.comM<strong>at</strong>h is indispensable and fundamental in computer videogames. Rel<strong>at</strong>ionship between M<strong>at</strong>h and game developmentis briefed. Computer video game classific<strong>at</strong>ion,computer programming languages for cre<strong>at</strong>ing computervideo games and some game API’s (Applic<strong>at</strong>ion ProgrammingInterfaces) and engines or libraries are introduced.Gaming elements rel<strong>at</strong>ed to M<strong>at</strong>h are identified. TheCartesian coordin<strong>at</strong>es in M<strong>at</strong>h and the Screen Coordin<strong>at</strong>eSystem in gaming are compared. The "Dark GDK"Library is used to demonstr<strong>at</strong>e how to draw basic shapesand cre<strong>at</strong>e interactive video games. Sample C++ programsand their results are shown for developing videogames using "DarkGDK", from basic 2-D shapes to interactivevideo games.Full Eulerian finite element methods for fluidstructureinteraction problem in fictitious domainand phase field approachesPengtao SunUniversity of Nevada Las Vegas, USApengtao.sun@unlv.eduIn this talk we will present a full Eulerian model for a dynamicfluid-structure interaction (FSI) problem by meansof Lagrange multiplier/fictitious domain approach andphase field formul<strong>at</strong>ion, and design its full Eulerian finiteelement discretiz<strong>at</strong>ion and effective iter<strong>at</strong>ive method. Inthe fictitious domain approach, the fluid domain and comput<strong>at</strong>ionalmesh are fixed by extending the fluid to thestructural domain, and the FSI interfacial conditions arereinforced by Lagrange multiplier. Thus an interpol<strong>at</strong>iontechnique is needed to interpol<strong>at</strong>e the fluid variables intothe structural domain. We also demonstr<strong>at</strong>e a method todeal with the incompressible fluid-compressible structureinteraction problem with fictitious domain approach.In the second approach-phase field formul<strong>at</strong>ion, the derivedfull Eulerian FSI model effectively demonstr<strong>at</strong>es theinteraction between fluid flow and solid structure in termsof an uniform system of governing equ<strong>at</strong>ions defined in asingle domain, thus the comput<strong>at</strong>ional grid is fixed, andthe re-meshing and interpol<strong>at</strong>ion techniques which are alwaysrequired by other FSI modeling approaches are nolonger needed here. A stabilized solution skill is developedto effectively solve the Euler equ<strong>at</strong>ion which is essentiallythe Eulerian description of solid motion for theincompressible hyperelastic m<strong>at</strong>erial. Numerical experimentis carried out for a cross spinning around its centralaxis due to the passing flow field, and the numerical resultsdram<strong>at</strong>ically show the spinning motion of the crossdue to the interaction with the fluid, showing th<strong>at</strong> ourmodel and numerical methods are effective to simul<strong>at</strong>ethe dynamic fluid-structure interaction phenomena.Linear numerical schemes for epitaxial thinfilm growth modelCheng WangUniversity of Massachusetts Dartmouth, USAcwang1@umassd.eduA few linear schemes for nonlinear PDE model of thinfilm growth model without slope selection are presentedin the talk. In the first order linear scheme, the idea ofconvex-concave decomposition of the energy functional isapplied, and the particular decomposition places the nonlinearterm in the concave part of the energy, in contrastto a standard convexity splitting scheme. As a result,the numerical scheme is fully linear <strong>at</strong> each time stepand unconditionally solvable, and an unconditional energystability is guaranteed by the convexity splitting n<strong>at</strong>ureof the numerical scheme. To improve the numericalaccuracy, a second order temporal approxim<strong>at</strong>ion for thenonlinear term is recently reported, which preserves anenergy stability. To solve this highly non-trivial nonlinearsystem, a linear iter<strong>at</strong>ion algorithm is proposed, withan introduction of a second order artificial diffusion term.Moreover, a contraction mapping property is proved forsuch a linear iter<strong>at</strong>ion. As a result, the highly nonlinearsystem can be decomposed as an iter<strong>at</strong>ion of purely linearsolvers. Some numerical simul<strong>at</strong>ion results are alsopresented in the talk.Applic<strong>at</strong>ion of MILP to solve complexscheduling problemsWei WengWaseda University, Japanwengwei@toki.waseda.jpThis talk describes the role of mixed integer linear programming(MILP) in solving scheduling problems in complexproduction processes such as reentrant flexible jobshops (RFJS). We modeled such scheduling problems byusing several different MILP models. The first model wasbased on the traditional way of MILP modeling, which denotesthe machines, workst<strong>at</strong>ions, jobs, oper<strong>at</strong>ions, andthe time slots th<strong>at</strong> arrange the oper<strong>at</strong>ions on each machine.The second model improved the efficiency of thetraditional design by reducing the variable for machinesthrough the rel<strong>at</strong>ionship between machines and oper<strong>at</strong>ions.The third model further and significantly reducedthe comput<strong>at</strong>ional complexity of the second model byutilizing the rel<strong>at</strong>ionship between jobs on the same machineto replace the role of time slots, which were commonlyused in previous studies. Accordingly, the improvedmodel can obtain the solution for RFJS problemswith dozens of jobs whereas the traditional model, in mostcases, is unable to obtain even a feasible solution for thesame problems.
55 PRIMA 2013 AbstractsEfficient numerical method for boundary conditionsof kinetic equ<strong>at</strong>ionsChang YangUniversité Claude Bernard Lyon 1, Franceyang@m<strong>at</strong>h.univ-lyon1.frIn this talk we present a new algorithm based on Cartesianmesh for the numerical approxim<strong>at</strong>ion of the kineticmodels on complex geometry boundary. Due to the highdimensional property, numerical algorithms based on unstructuredmeshes for a complex geometry are not appropri<strong>at</strong>e.Here we propose to adapt the inverse Lax-Wendroff procedure, which was recently introduced forconserv<strong>at</strong>ion laws [1], to the kinetic equ<strong>at</strong>ions. We firstapply this algorithm for Boltzmann type oper<strong>at</strong>ors (BGK,ES-BGK models) in 1D × 3D and 2D × 3D [2]. Then weextend a similar method to bacterial chemotaxis models[3], which is a coupling problem of kinetic equ<strong>at</strong>ionand parabolic equ<strong>at</strong>ion. Numerical results illustr<strong>at</strong>e theaccuracy properties of these algorithms.[1] S. Tan and C.-W. Shu, Inverse Lax-Wendroff procedurefor numerical boundary conditions of conserv<strong>at</strong>ionlaws, Journal of Comput<strong>at</strong>ional Physics, 229 (2010),8144-8166.[2] F. Filbet and C. Yang, Inverse Lax-Wendroff methodfor boundary conditions of Boltzmann equ<strong>at</strong>ions, Journalof Comput<strong>at</strong>ional Physics, accepted.[3] F. Filbet and C. Yang, Numerical Simul<strong>at</strong>ions of KineticModels for chemotaxis, submitted.MD simul<strong>at</strong>ions for motions of evapor<strong>at</strong>ivedroplets driven by thermal gradientsCongmin WuXiamen University, Chinacmwu@xmu.edu.cnThe driving mechanism of fluid transport <strong>at</strong> nanoscaleis one of the key problems on the design of micro- andnanofluidic devices. We performed molecular dynamicssimul<strong>at</strong>ions to study the motions of evapor<strong>at</strong>ive dropletsdriven by thermal gradients along nanochannels. The effectof droplet size and the effect of the co-existent fluidtemper<strong>at</strong>ure on the motions of droplets are investig<strong>at</strong>ed.Our simul<strong>at</strong>ion results are in semi-quantit<strong>at</strong>ive agreementwith the prediction of the continuum model (Xu and Qian2012 Phys. Rev. E 85 061603). It is found th<strong>at</strong> thedroplet mobility is inversely proportional to a dimensionlesscoefficient associ<strong>at</strong>ed with the total r<strong>at</strong>e of dissip<strong>at</strong>iondue to droplet movement. Our results show th<strong>at</strong> this coefficientis of order unity and increases with the dropletsize for the small droplets (∼ 10nm). Through a theoreticalanalysis on the size of the thermal singularity, itcan be shown th<strong>at</strong> the droplet mobility decreases with decreasingcoexistence temper<strong>at</strong>ure. This is also observedin our MD simul<strong>at</strong>ions.This is a joint work with Xinpeng Xu and Tiezheng Qianfrom HKUST.Calcul<strong>at</strong>ing areas and volumes with rot<strong>at</strong>edaxisPablo Zafra, Christopher FloresKean University, USApzafra@kean.edufloresc1@kean.eduFinding areas under a curve and volumes of solid of revolutionsare standard applic<strong>at</strong>ions of definite integrals ina Calculus class. Conventional examples in calculus textbooksuse the regular Cartesian coordin<strong>at</strong>e system withvertical and horizontal axes. We explore in this researchthe problem of calcul<strong>at</strong>ing areas and volumes when theaxis is rot<strong>at</strong>ed, and use basic tools from geometry andlinear algebra to formul<strong>at</strong>e the corresponding definite integrals.We present some insights as well as difficultiesencountered in setting-up the integrals, and in evalu<strong>at</strong>ingthem analytically or numerically using graphing calcul<strong>at</strong>orsor online m<strong>at</strong>h tools.Inversion of geothermal he<strong>at</strong> flux in a thermomechanicallycoupled Stokes ice sheet modelHongyu Zhu, Noemi Petra, Georg Stadler, Toby Isaac,Omar Gh<strong>at</strong>tas, Thomas J.R. HughesUniversity of Texas <strong>at</strong> Austin, USAzhuhongyu@ices.utexas.eduModeling the dynamics of polar ice sheets is critical forprojection of future sea level rise. Yet, there remainlarge uncertainties in the basal boundary conditions (e.g.,geothermal he<strong>at</strong> flux) of the ice sheet. Here we targetthe inversion of the basal geothermal he<strong>at</strong> flux using surfacevelocity measurements. The flow of ice sheets andglaciers is modeled as a sheer thinning, viscous incompressiblefluid with temper<strong>at</strong>ure-dependent viscosity viaa thermomechanically coupled Stokes model. The inverseproblem is formul<strong>at</strong>ed as a nonlinear least-squares optimiz<strong>at</strong>ionproblem with a cost functional th<strong>at</strong> contains themisfit between surface velocity observ<strong>at</strong>ions and modelpredictions and a Tikhonov regulariz<strong>at</strong>ion term to renderthe problem well-posed. We use an adjoint-basedinexact Newton method for the solution of this leastsquares optimiz<strong>at</strong>ion problem. Results for 2-D and 3-Dmodel problems demonstr<strong>at</strong>e the ability of inverting for asmoothly varying geothermal he<strong>at</strong> flux in cold ice regions.This capability will be incorpor<strong>at</strong>ed into a st<strong>at</strong>e-of-the-artcontinental-scale ice sheet dynamics model.Modelling of temper<strong>at</strong>ure and pricingwe<strong>at</strong>her deriv<strong>at</strong>ives: a comparison formainland ChinaManuela Ender, Lu ZongXi’an Jiaotong-Liverpool University, Chinamanuela.ender@xjtlu.edu.cnTemper<strong>at</strong>ure-based we<strong>at</strong>her deriv<strong>at</strong>ives are a promisingfinancial instrument to hedge we<strong>at</strong>her risk. In most m<strong>at</strong>urefinancial markets of the world, we<strong>at</strong>her deriv<strong>at</strong>ivesare traded for several years now. However in MainlandChina, such a market does not exist yet. To make thelaunch of such instruments possible, multi-regional researchis needed to find the most suitable temper<strong>at</strong>uremodel for Mainland China. The contribution of this paperis to compare the performance of several up-to-d<strong>at</strong>etemper<strong>at</strong>ure models to d<strong>at</strong>a from twelve cities from allclim<strong>at</strong>ic zones in China. The models are compared interms of fitting the daily average temper<strong>at</strong>ure, normalityof residuals, simul<strong>at</strong>ion errors and model risk whenused for pricing futures and options. The comparison includesa model with monthly contant vol<strong>at</strong>ility (Al<strong>at</strong>onet al, 2002), with daily vol<strong>at</strong>ility (Benth et al, 2007), amodel with stochastic vol<strong>at</strong>ility like proposed by Benthand Benth (2011) and a model using a Spline approachfor surface modelling similar to Schiller et al (2012). Thisis the first paper on multi-regional temper<strong>at</strong>ure modellingand we<strong>at</strong>her deriv<strong>at</strong>ives pricing using such a large numberof cities in a comparison of different models in MainlandChina.Contributed Talks Group 5Differential Equ<strong>at</strong>ionsNonlinear impulsive differential equ<strong>at</strong>ionsarising from chemotherapeutic tre<strong>at</strong>ment
56 PRIMA 2013 AbstractsBaili ChenGustavus Adolphus College, USAbchen@gustavus.eduWe prove the existence of periodic solutions of systemsof nonlinear impulsive differential equ<strong>at</strong>ions arising fromchemotherapeutic tre<strong>at</strong>ment for cancer. Our analysis isbased on Mawhin’s continu<strong>at</strong>ion theorem of coincidencedegree theorem.Analysis of some nonlinear PDEs from multiscalegeophysical applic<strong>at</strong>ionsBin ChengUniversity of Surrey, UKb.cheng@surrey.ac.ukThis talk is regarding PDE systems from geophysical applic<strong>at</strong>ionswith multiple time scales, in which linear skewself-adjointoper<strong>at</strong>ors of size 1/epsilon gives rise to highlyoscill<strong>at</strong>ory solutions. Analysis is performed in justifyingthe limiting dynamics as epsilon goes to zero; furthermore,the analysis yields estim<strong>at</strong>es on the difference betweenthe multiscale solution and the limiting solution.We will introduce a simple yet effective time-averagingtechnique which is especially useful in general domainswhere Fourier analysis is not applicable.Some piston problems in fluid dynamicsMin DingShanghai Jiao Tong University, Chinaminding@sjtu.edu.cnThe piston problem is analyzed from the m<strong>at</strong>hem<strong>at</strong>icalpoint of view. Some fe<strong>at</strong>ures and phenomena caused bythe motion of the piston are revealed. We discuss somepiston problems for both classical Euler equ<strong>at</strong>ions andrel<strong>at</strong>ivistic Euler equ<strong>at</strong>ions of compressible fluids. In particular,we focus on strong shock front solutions.Over-compressive shock profile associ<strong>at</strong>edwith a simplified system from MHDLinglong DuN<strong>at</strong>ional University of Singapore, Singaporeg0901229@nus.edu.sgIn this talk, we present the wave propag<strong>at</strong>ion around anover-compressive shock profile with large amplitude for asimplified system from MHD, which is a rot<strong>at</strong>ionally invariantsystem of viscous conserv<strong>at</strong>ion laws. We showth<strong>at</strong> the solution converges pointwise to another overcompressiveprofile exponentially, when the perturb<strong>at</strong>ionsof the initial d<strong>at</strong>a to a given profile are sufficiently small.We also give the explicit structure of the solution forthe linearized system. The approach begins with an extractionof non-decaying component stacked <strong>at</strong> the shockfront, followed by an iter<strong>at</strong>ed approxim<strong>at</strong>ion process forthe remainder. This sharp estim<strong>at</strong>e is strong enough tostudy the nonlinear problem and conclude the stability ofprofile.This is a joint work with Professor Shih-Hsien Yu.Global stability of E-H type regular refractionof shocks on the interface between two mediaBeixiang FangShanghai Jiao Tong University, Chinabxfang@sjtu.edu.cnIn this talk I will discuss the refraction of shocks on theinterface for 2-d steady compressible flow. Particularly,the class of E-H type regular refraction is defined and itsglobal stability of the wave structure is verified. The 2-dsteady potential flow equ<strong>at</strong>ions is employed to describethe motion of the fluid. The stability problem of the E-Htype regular refraction can be reduced to a free boundaryproblem of nonlinear mixed type equ<strong>at</strong>ions in an unboundeddomain. The corresponding linearized problemhas similarities to a generalized Tricomi problem of thelinear Lavrentiev-Bitsadze mixed type equ<strong>at</strong>ion, and itcan be reduced to a nonlocal boundary value problemof an elliptic system. The l<strong>at</strong>ter is finally solved by establishingthe bijection of the corresponding nonlocal oper<strong>at</strong>orin a weighted Hölder space via careful harmonicanalysis.This is a joint work with CHEN Shuxing and HU Dian.Multiplicity of positive solutions for a p-q-Laplacian equ<strong>at</strong>ion with critical nonlinearitiesTsing-San HsuChang Gung University, Taiwan R.O.C.tshsu@mail.cgu.edu.twIn this talk, we study the effect of the coefficient f(x)of the critical nonlinearity on the number of positive solutionsfor a p-q-Laplacian equ<strong>at</strong>ion. Under suitable assumptionsfor f(x) and g(x), we should prove th<strong>at</strong> forsufficiently small λ > 0, there exist <strong>at</strong> least k positivesolutions of the following p-q-Laplacian equ<strong>at</strong>ion−∆ pu−∆ qu=f(x)|u| p∗ −2 u+λg(x)|u| r−2 u in Ω,u = 0 on ∂Ω,where Ω ⊂ R N is a bounded smooth domain, N > p,1 < q < N(p−1) < p ≤ max{p, p N−1 ∗ − qp−1 } < r < p∗ ,p ∗ =Np is the critical Sobolev exponent and ∆su =N−pdiv(|∇u| s−2 ∇u) is the s-Laplacian of u.The linear hyperbolic initial boundary valueproblems in a domain with cornersAimin HuangIndiana University, USAaimhuang@indiana.eduIn this article, we consider linear hyperbolic InitialBoundary Value Problems (IBVP) in a rectangle in boththe constant and variable coefficients cases. We use semigroupmethod instead of Fourier analysis to achieve thewell-posedness of the linear hyperbolic system, and wefind by diagonaliz<strong>at</strong>ion th<strong>at</strong> there are only two simplemodes in the system which we call hyperbolic and ellipticmodes. The hyperbolic system in consider<strong>at</strong>ion is eithersymmetric or Friedrichs-symmetrizable.On quasilinear elliptic equ<strong>at</strong>ions with variableexponentsYun-Ho KimSangmyung University, Koreakyh1213@smu.ac.krWe study the following elliptic equ<strong>at</strong>ions with variableexponents−div(φ(x, |∇u|)∇u) = λf(x, u)in Ωwhich is subject to Dirichlet boundary condition. Undersuitable conditions on φ and f, employing the vari<strong>at</strong>ionalmethods, in particular, mountain pass theorem
57 PRIMA 2013 Abstractsand fountain theorem, we establish the existence of nontrivalsolutions for a class of quasilinear elliptic problemswith variable exponents. Also we show the existence ofpositivity of the infimum of all eigenvalues for the aboveproblem.Overdetermined boundary value problemswith strongly nonlinear elliptic PDEFengquan Li (with Boqiang Lv, Weilin Zou)Dalian University of Techology, Chinafqli@dlut.edu.cnWe consider the strongly nonlinear elliptic Dirichlet problemin a connected bounded domain, overdetermined withthe constant Neumann condition F (∇u) = c on theboundary. Here F is convex and positively homogeneousof degree 1, and its polar F ∗ represents the anisotropicnorm on R n . We prove th<strong>at</strong>, if this overdeterminedboundary value problem admits a solution in a suitableweak sense, then Ω must be of Wulff shape.Stability of boundary layers for the nonisentropiccompressible circularly symmetric2D flowCheng-Jie LiuShanghai Jiao Tong University, Chinacjliusjtu@gmail.comIn this paper, we study the asymptotic behavior of the circularlysymmetric solution to the initial boundary valueproblem of the compressible non-isentropic Navier-Stokesequ<strong>at</strong>ions in a two-dimensional exterior domain with impermeableboundary condition when the viscosities andthe he<strong>at</strong> conduction coefficient tend to zero. By multiscaleanalysis, we obtain th<strong>at</strong> away from the boundarythe compressible non-isentropic viscous flow can be approxim<strong>at</strong>edby the corresponding inviscid flow, and nearthe boundary there are boundary layers for the angularvelocity, density and temper<strong>at</strong>ure in the leading orderexpansions of solutions, while the radial velocity andpressure do not have boundary layers in the leading order.The boundary layers of velocity and temper<strong>at</strong>ure aredescribed by a nonlinear parabolic coupled system. Weprove the stability of boundary layers and rigorously justifythe asymptotic behavior of solutions in the L ∞ −normfor the small viscosities and he<strong>at</strong>-conduction limit in theLagrangian coordin<strong>at</strong>es, as long as the strength of theboundary layers is suitably small. Finally, we show th<strong>at</strong>the similar asymptotic behavior of the small viscositiesand he<strong>at</strong> conduction limit holds in the Eulerian coordin<strong>at</strong>esfor the compressible non-isentropic viscous flow.Dynamics in immune reactions during woundhealing processesJianzhong Su a) , Larrissa Owens a) and Akif Ibraguimov b)a) University of Texas <strong>at</strong> Arlington, USAb) Texas Tech Universitysu@uta.eduWe propose a partial differential equ<strong>at</strong>ion model adaptedfrom the principles of wound healing studies and analyzeit to gain insights regarding the dynamics of immunecells/proteins following the insertion of a foreign body.Specifically we look <strong>at</strong> the multiple roles of macrophagesand the conditions for stabilizing/destabilizing the equilibriumst<strong>at</strong>e. Furthermore, we investig<strong>at</strong>e the impact ofdiffusion and chemotaxis on the stability and the transientbehavior of the system.On the radi<strong>at</strong>ion field for wave equ<strong>at</strong>ionsFang WangPrinceton University, USAfangwang@m<strong>at</strong>h.princeton.eduDefinitions for the radi<strong>at</strong>ion field by Lax-Phillips andFriedlander are introduced for standard wave equ<strong>at</strong>ionon Minkowski space-time, which can be generalized tocurved space-time (such as Schiwarzschild space-time)and nonlinear wave equ<strong>at</strong>ions (such as Einstein vacuumequ<strong>at</strong>ions). Regularities of the radi<strong>at</strong>ion field are studied.Mapping property for Moller wave oper<strong>at</strong>or, whichmaps initial d<strong>at</strong>a to the radi<strong>at</strong>ion field, are investig<strong>at</strong>ed.In the case th<strong>at</strong> the Molloer wave oper<strong>at</strong>or is an (or alocal) isomorphism, the characteristic initial problem isconsidered.Rel<strong>at</strong>ionship between ω-limit Sets and MinimalSetsLarry WangSouthern Polytechnic St<strong>at</strong>e University, USAlwang@spsu.eduIn this paper, we study the rel<strong>at</strong>ion between ω-limit setsand minimal sets. It is known th<strong>at</strong> every minimal set is aω-limit set. However, not every ω-limit set is a minimalset, although it contains a minimal set. We would like toknow under wh<strong>at</strong> condition an ω-limit set turns out tobe a minimal set. We establish a necessary and sufficientcondition under which every ω-limit set is minimal.The regularity of semi-hyperbolic p<strong>at</strong>ches <strong>at</strong>sonic lines for the pressure gradient equ<strong>at</strong>ionin gas dynamicsQin WangShanghai Jiao Tong University, Chinam<strong>at</strong>hwq@sjtu.edu.cnWe study the uniform regularity of semi-hyperbolicp<strong>at</strong>ches of self-similar solutions near sonic lines to a generalRiemann problem for the pressure gradient equ<strong>at</strong>ion.This type of solutions, in which one family of characteristicsstarts on a sonic line and ends on a transonicshock wave, is common for the Riemann problems for theEuler system in two space dimensions. The global existenceof smooth solutions was established in Song andZheng(2009), but the smoothness near the sonic lines isnot clear. We establish th<strong>at</strong> the smooth solutions are uniformlysmooth up to their sonic boundaries and the soniclines are C 1 continuous.Constructing global Lyapunov function forcomplex systemsXinAn WangShanghai Jiao Tong University, Chinawangxinan@sjtu.edu.cnLyapunov function, as one of the most significant conceptsin dynamical systems, has been widely applied inmany disciplines. However, the classical Lyapunov functionin the theory of ordinary differential equ<strong>at</strong>ions areusually restricted to the analysis of the stability near theequilibriums of the system, and no general constructivemethod has been found. Thus, it cannot be applied tomore complex dynamical behaviors, such as multi-stablest<strong>at</strong>es, periodic <strong>at</strong>tractor like limit cycle, and chaos. Recently,a series of works based on the construction of potentialfunction in physics for stochastic dynamical processdemonstr<strong>at</strong>e potential function plays a critical rolein the quantit<strong>at</strong>ive analysis of dynamical systems. In deterministiccases, the potential function is the Lyapunov
58 PRIMA 2013 Abstractsfunction globally constructed for the systems. In this talk,we first present a novel numerical constructive methodon the Lyapunov function for a wide series of dynamicalsystems. Then, we apply this method in some famousexamples, such as the Van Der Pol oscill<strong>at</strong>or and Lorenzsystem. On the other hand, we analytically construct theLyapunov function in a chaotic system and the competitiveLotka-Volterra systems. The structure of the <strong>at</strong>tractors,such as fractal, are demonstr<strong>at</strong>ed clearly by theLyapunov function.The half line versus finite domain problems ofthe Modified Buckley-Leverett equ<strong>at</strong>ionYing WangUniversity of Minnesota, USAwang@umn.eduBuckley-Leverett (MBL) equ<strong>at</strong>ion describes two-phaseflow in porous media. The MBL equ<strong>at</strong>ion differs fromthe classical Buckley-Leverett (BL) equ<strong>at</strong>ion by includinga balanced diffusive-dispersive combin<strong>at</strong>ion. The dispersiveterm is a third order mixed deriv<strong>at</strong>ives term, whichmodels the dynamic effects in the pressure difference betweenthe two phases. The classical BL equ<strong>at</strong>ion gives amonotone w<strong>at</strong>er s<strong>at</strong>ur<strong>at</strong>ion profile for any Riemann problem;on the contrast, when the dispersive parameter islarge enough, the MBL equ<strong>at</strong>ion delivers non-monotonew<strong>at</strong>er s<strong>at</strong>ur<strong>at</strong>ion profile for certain Riemann problemsas suggested by the experimental observ<strong>at</strong>ions. In thistalk, we show th<strong>at</strong> the solution of the finite interval [0, L]boundary value problem converges to th<strong>at</strong> of the half-line[0, +∞) boundary value problem expoentially fast for theMBL equ<strong>at</strong>ion as L → +∞. (This is a joint work withChiu-Yen Kao.)Blowup of classical solutions to the compressibleNavier-Stokes equ<strong>at</strong>ionsWei YanInstitute of Applied Physics and Comput<strong>at</strong>ional M<strong>at</strong>hem<strong>at</strong>ics,Chinawyanm<strong>at</strong>h@gmail.comIn this talk, we present our recent results on the finitetime blow up of smooth solutions to the CompressibleNavier-Stokes system. We prove th<strong>at</strong> any classical solutionsof viscous compressible fluids without he<strong>at</strong> conductionwill blow up in finite time, as long as the initial d<strong>at</strong>ahas an isol<strong>at</strong>ed mass group (see definition in the paper).The results hold regardless of either the size of the initiald<strong>at</strong>a or the far fields being vacuum or not. This improvesthe blowup results of Xin (1998, CPAM) by removing thecrucial assumptions th<strong>at</strong> the initial density has compactsupport and the smooth solution has finite total energy.Furthermore, the analysis here also yields th<strong>at</strong> any classicalsolutions of viscous compressible fluids without he<strong>at</strong>conduction in bounded domains or periodic domains willblow up in finite time, if the initial d<strong>at</strong>a have an isol<strong>at</strong>edmass group s<strong>at</strong>isfying some suitable conditions.Stability of supersonic contact discontinuitiesfor three dimensional compressible steady EulerflowsFang YuShanghai Jiao Tong University, Chinayufang0820@sjtu.edu.cnIn this talk, we discuss the nonlinear structural stabilityof supersonic contact discontinuities in three dimensionalcompressible isentropic steady Euler equ<strong>at</strong>ions. Weobtain a necessary and sufficient condition for the linearstability of supersonic planar contact discontinuitiesand a priori estim<strong>at</strong>es of solutions to the linearized problem.The weak stability of this contact discontinuityalso results in a loss of regularity with respect to thesource terms in the interior domain and on the boundaryin the a priori estim<strong>at</strong>es of solutions to the linearizedproblem. Contact discontinuities with tangential velocityfields on two sides of the discontinuous front parallelor non-parallel are both considered. Moreover, using thecalculus of paradifferential oper<strong>at</strong>ors and taking advantageof the control of non-characteristic components ofunknowns by the equ<strong>at</strong>ions and the problems s<strong>at</strong>isfied byvorticities of velocity fields, we get estim<strong>at</strong>es of high orderderiv<strong>at</strong>ives of solutions to the linearized problem of a nonplanarcontact discontinuity. As there is a loss of regularityin the estim<strong>at</strong>es of solutions to the linearized problem,we adapt the Nash-Moser-Hörmander iter<strong>at</strong>ion scheme toobtain the nonlinear stability of supersonic contact discontinuitiesin three dimensional compressible isentropicsteady Euler equ<strong>at</strong>ions. This is a joint work with Ya-Guang Wang.Global structure of admissible BV solutionsto strictly hyperbolic conserv<strong>at</strong>ion laws in onespace dimensionLei YuScuola Internazionale Superiore di Studi Avanz<strong>at</strong>i, Italyyulei@sissa.itIn [1], we describe the qualit<strong>at</strong>ive structure of an admissibleBV solution to a strictly hyperbolic system of conserv<strong>at</strong>ionlaws whose characteristic families are piecewisegenuinely nonlinear. More precisely, we prove th<strong>at</strong> thereare a countable set of points Θ and a countable family ofLipschitz curves T such th<strong>at</strong> outside T ∪Θ the solutionis continuous, and for all points in T \Θ the solution hasleft and right limit. This extends the corresponding structuralresult in [2] for genuinely nonlinear systems. Theproof is based on the introduction of subdiscontinuities ofa shock, whose behavior is qualit<strong>at</strong>ively analogous to thediscontinuities of the solution to genuinely nonlinear systems.An applic<strong>at</strong>ion of this result is the stability of thewave structure of solution w.r.t. L 1 loc-convergence. Alsoa remark on the generaliz<strong>at</strong>ion of the results of generalstrictly hyperbolic conserv<strong>at</strong>ion laws will be given.[1] S. Bianchini and L. Yu, Global structure of admissibleBV solutions to piece- wise genuinely nonlinear,strictly hyperbolic conserv<strong>at</strong>ion laws in on space di- mension.To appear on Comm. Partial Differential Equ<strong>at</strong>ions(arXiv:1211.3526), 2012.[2] A. Bressan and P. G. LeFloch, Structural stabilityand regularity of entropy solutions to hyperbolic systemsof conserv<strong>at</strong>ion laws, Indiana Univ. M<strong>at</strong>h. J., 48 (1999),pp. 43–84.Contributed Talks Group 6Probability and St<strong>at</strong>isticsEstim<strong>at</strong>es of Itô integral and applic<strong>at</strong>ions torandom dynamical systemsXiaoming FanSouthwest Jiaotong University and Beijing Normal University,Chinafanxm@swjtu.cnThis paper obtains two estim<strong>at</strong>es of Itô integral and theirstochastic Gronwall’s inequalities, which present an ultim<strong>at</strong>eway to deal with almost sure estim<strong>at</strong>es for stochastic(partial) differential equ<strong>at</strong>ions with white noises ofany type. As examples, they are applied to present a
59 PRIMA 2013 Abstractsformula estim<strong>at</strong>ing the Hausdorff dimensions of the temperedcompact random invariant sets and investig<strong>at</strong>e theexistence and the Hausdorff dimensions of random <strong>at</strong>tractorsfor a stochastic wave equ<strong>at</strong>ion with noisy damping.D<strong>at</strong>a fusion based on evidence theoryYanyan HeFlorida St<strong>at</strong>e University, USAyhe2@m<strong>at</strong>h.fsu.eduD<strong>at</strong>a fusion techniques integr<strong>at</strong>e d<strong>at</strong>a from multiplesources (such as sensors, institutions, and etc.), and thecombined inform<strong>at</strong>ion can help to reach more accur<strong>at</strong>eand more specific inference. In this present<strong>at</strong>ion, evidencetheory based combin<strong>at</strong>ion approaches are introduced tocombine distinct sources of uncertain inform<strong>at</strong>ion. Theuncertainty in each source of inform<strong>at</strong>ion is representedby a belief function individually, which are then combinedto produce a single belief function representing inform<strong>at</strong>ionfrom all the sources. The approaches are illustr<strong>at</strong>edwith examples.The generalized Itô-Wentzell formula for Itô’sprocess and the stochastic first integralElena KarachanskayaPaciŕc N<strong>at</strong>ional University, Russiachalykh@mail.khstu.ruWe present the Generalized Itô-Wentzell formula, whichis the generaliz<strong>at</strong>ion of Itô-Wentzell formula for a multidementionalItô’s process with the Wiener and the Poissonperturb<strong>at</strong>ions.This result allowed to set equ<strong>at</strong>ions for the stochastic firstintegrals of a stochastic differential equ<strong>at</strong>ions system.An explicit cross entropy scheme for mixturesXiang ZhouCity University of Hong Kong, Hong Kong, Chinaxiang.zhou@cityu.edu.hkThe key issue in importance sampling is the choice of thealtern<strong>at</strong>ive sampling distribution, which is often chosenfrom the exponential tilt family of the underlying distribution.However, when the problem exhibits certain kindof nonconvexity, it is very likely th<strong>at</strong> a single exponentialchange of measure will never <strong>at</strong>tain asymptotic optimalityand may lead to erroneous estim<strong>at</strong>es. In this paper weintroduce an explicit iter<strong>at</strong>ive scheme which combines thetraditional cross-entropy method and the EM algorithmto find an efficient altern<strong>at</strong>ive sampling distribution inthe form of mixtures. We also study the applic<strong>at</strong>ions ofthis scheme to option price estim<strong>at</strong>ion.Asymptotic analysis for tipping points problemsJielin ZhuUniversity of British Columbia, Canadajielinzhu@m<strong>at</strong>h.ubc.caA tipping point, observed as a rapid change in clim<strong>at</strong>eor ecology, can be induced by a slowly varying controlparameter of a saddle-node bifurc<strong>at</strong>ion. The position ofthe tipping point can be significantly changed by smallnoise or periodic terms. A local multiple scaling methodis used to describe the behaviour of the system based onthe rel<strong>at</strong>ion of the drifting r<strong>at</strong>e, noise and frequency of theperiodic terms. A one-dimensional canonical slowly varyingsystem with a saddle-node bifurc<strong>at</strong>ion is analysed, tofind out the effect of the noise or the frequency of the periodicterms separ<strong>at</strong>ely. We also show results for a globalenergy balance model in clim<strong>at</strong>e dynamics.
1925221232461511 号 门华 山 路 1954 号进 口 、 出 口Entrance1954 Hua Shan RoadEntrance/Exit3教 师 活 动 中 心午 休Faculty ClubLunch Break55 号 门广 元 西 路 55 号进 口 、 出 口Main Entrance55 Guang Yuan Xi RoadEntrance/Exit6校 医 院医 疗 救 护School HosptialHealth Service19工 程 馆分 会 场Engineering Hall23 Sessions/Contributed Talks/Registr<strong>at</strong>ion12新 上 院停 靠 点Xin Shang YuanParking lot22ATM 取 款 机银 行 服 务ATMATM22 25餐 厅午 餐CanteenLunch24文 治 堂主 会 场Wen Zhi HallPublic & Plenary Lectures/Opening
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