3. Postdoctoral Program - MSRI

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04/29/2010 Research Workshop: Homology Theories of Knots and Links March 15 - 19, 2010 at <strong>MSRI</strong>, Berkeley, CA Officially Registered Participant Information Participants 138 Gender 138 Male 70.29% 97 Female 25.36% 35 Declined to state 4.35% 6 Ethnicity* 142 White 76.76% 109 Asian 11.27% 16 Hispanic 2.82% 4 Pacific Islander 0.00% 0 Black 1.41% 2 Native American 0.00% 0 Declined to state 7.75% 11 * ethnicity specifications are not exclusive
Report on the “Hot Topic” Workshop “Black Holes in Relativity” The workshop focused on the emergent area of mathematical research dedicated to the study of black holes and related dynamical phenomena arising in General Relativity. The subject has undergone an incredible transformation in the last 5 years accompanied by the a new evolving understanding of the mathematical properties of black holes. Nothing is more emblematic of this revolutionary progress than the recent work of Demetrios Christodoulou on formation of black holes. This result was chosen as a central theme of the workshop. The mathematical study of the dynamics of the Einstein equations forms a central part of both partial differential equations and geometry, and is intimately related to our current physical understanding of gravitational collapse. The celebrated singularity theorems of Penrose, proven in the 1960s, showed that geodesic incompleteness is inevitable provided that initial data contain what is known as a closed trapped surface. Trapped surfaces are also related to the presence of black holes. A breakthrough into the understanding of trapped surface formation has recently been achieved by Christodoulou in his 600 page monograph: ”The formation of black holes in General Relativity”, Publications of the EMS, January 2009, where it is shown that trapped surfaces form in evolution for the Einstein vacuum equations from completely dispersed initial configurations, a phenomenon caused purely by the focussing of gravitational waves. The proof brings together ideas from geometric analysis and non-linear hyperbolic equations and at the same time introduces new techniques adapted to large data problems. The methods will undoubtedly have many future applications in both general relativity and other equations of mathematical physics. In particular, the work provides the first global ”large data” result in general relativity (without symmetry assumptions) and opens the possibility for many new developments on dynamical problems relating to black holes. The workshop brought together experts in General Relativity, Hyperbolic Equations and Geometric Analysis. It was particularly successful in attracting a large number of graduate students and postdocs (Baskin, Bieri, Chen, Ghanem, Holzegel, Huang, Jang, Luk, Nguyen, Oh, Rubinstein, Smulevici, Speck, Tohaneanu, Yang) who had an opportunity to be exposed to the cutting edge research in these areas and to interact with the senior participants (Bartnik, Christodoulou, Dafermos, Eskin, Friedlander, Galloway, Isenberg, Kapitanski, Lindblad, LeFloch, Mazzeo, Rendall, Rodnianski, Sideris, Schoen, Vasy, Wang, Weinstein). This type of mixture of very junior and very senior participants is unique for meetings in these subjects. A typical workshop is either a high intensity scientific meeting with a large number of talks focused narrowly on the very latest advances and thus allowing very little room for junior participants, or has a summer school format concentrating on the educational component but providing very little interaction between junior and (very few) senior participants. In the current workshop the interaction proved to be extremely useful and beneficial for both sides. The junior participants in particular have been unanimous in their satisfaction with the chosen topic and the format of the workshop. The 5-day workshop begun on Monday, September 14 and ended on Friday, September 18. Its format, with the exception of Wednesday, was an hour lecture in the morning, followed by lunch, and two one hour lectures in the afternoon. Such scheduling left an ample time for interaction between the participants and additional discussions, an arrangement highly appreciated by all the partcipants. The scientific part of the workshop was focused on the breakthrough work of Demetrios Christodoulou on formation of black holes. A major coup was achieved in securing an agreement from Christodoulou to come to the workshop and explain the content of his work. Christodoulou gave 5 highly detailed and 1
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Final Report, 2005-2010 and Annual
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6. Appendix - Final Reports .......
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• Spring 2008: Representation The
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place the highest value on the oppo
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which establishes the relation betw
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Public Understanding of Mathematics
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1.3 Scientific Programs and their A
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The first week of May 2010 coincide
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The goal of this program was, throu
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"An illustration of the tropical Ab
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• lead to new breakthroughs in th
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Other mathematical breakthroughs th
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• Advice on preparing for intervi
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An off-site workshop partially fund
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1.7 Other Scientific Workshops Hot
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experienced circle leaders. Togethe
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2. Program and Workshop Data 2.1 Pr
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Jöricke Burglind Institut des Haut
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Smith Ivan Centre for Mathematical
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Home Institution Classified by Stat
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2.4 Workshop Participant List (See
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2.7 Program Publication List Last N
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Ghiggini Paolo Sutures and contact
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Lekili Yanki Geometric composition
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Draisma Jan The tropical projective
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Krasner Daniel Patterns in sl(2)-li
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Sarkar Sucharit Murasugi sums Matt
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Falk Michael Feichtner Eva Tropical
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Manolescu Ciprian Manolescu Ciprian
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Steingrimsson Einar Steingrimsson E
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Here are additional details on the
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Kutluhan, Cagatay Lekili, Yanki Cag
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Savelyev, Yakov Vertesi, Vera Yakov
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Katz, Eric Lopez de Medrano, Lucia
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Grigsby, Elisenda Kutluhan, Cagatay
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Sazdanovic, Radmila Wehrli, Stephan
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Angeltveit, Vigleik Crofts, Scott H
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3.2 Postdoctoral Fellow Placement L
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3.4 Postdoctoral Fellow Demographic
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Home Institution Classified by Coun
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SGS 1: IAS/PCMI Summer Workshop: Th
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Jafarov, Elchin University of Alask
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Xie, Yu Purdue University Graduate
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4.3 Program Associates Program Asso
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P r o g r a m A s s o c i a t e s D
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Home Institution Classified by Coun
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5. Undergraduate Program (MSRI-UP)
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This project seeks to use elliptic
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6. Appendix - Final Reports 97
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2 2. Participants The response to o
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4 • Gleb Koshevoy: Bases of tropi
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6 While at MSRI, Gathmann extended
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8 In conclusion, my postdoc at MSRI
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10 -with Christian Haase, who staye
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12 “I was working on the relation
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14 Josephine Yu PhD: UC Berkeley, 2
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16 6. Alex Fink was an invited spea
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Tropical Geometry Postdoctoral Fell
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Tropical Geometry Demographic Summa
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Ozsváth-Szabó Heegaard homology t
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field. Nevertheless, some of it is
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developments which occurred in this
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the audience would know a little ab
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on the group of Hamiltonian diffeom
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German Research Foundation Mentor:
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Mark spend his time at MSRI working
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PhD: University of Texas, 2007 Posi
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example Gadbled, Mandini, Ma’u, H
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Symplectic and Contact Geometry and
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Symplectic and Contact Geometry and
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2 REPORT ON THE MSRI WORKSHOP “HO
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Homology Theory of Knots and Links
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Complementary Program August 17, 20
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Complementary Program 2009-10 Postd
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Complementary Program Demographic S
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MID YEAR REPORT - DECEMBER 2009 VIG
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California. We talked about several
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EXTERNAL POSTDOCTORAL FELLOW REPORT
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on. While his research area is some
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POSTDOCTORAL FELLOW REPORT December
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[1] (with Garcia-Puente, Martin del
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REPORT FROM MENTOR June 2010 Year e
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I have also begun working on relate
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2 Professional Travel Sep. 6 - 26,
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REPORT FROM MENTOR June 2010 Karl h
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POSTDOCTORAL FELLOW REPORT June 201
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REPORT FROM MENTOR June 2010 ------
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Postdoctoral Program supported by t
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RO(S 1 )-graded homotopy groups of
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MSRI POSTDOCTORAL FELLOWSHIP REPORT
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2 TRISTRAM BOGART and its facets ar
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To Whom It May Concern: During the
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MSRI FELLOWSHIP FINAL REPORT SCOTT
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As his mentor at UCSC, I had freque
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- UC Davis Combinatorics Seminar -
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Christopher J. Hillar University of
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G. Isely, C. Hillar, and F. Sommer,
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Postdoc Report for: Dr. Christopher
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2 NSF REPORT FOR ERIC KATZ linear s
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Year-End Report 2010-11 NSF Math In
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Jan. 25 - 28, 2011 Recruitment Visi
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MSRI POSTDOCTORAL FELLOWSHIP REPORT
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Final report: mentoring Sikimeti Ma
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eginning of the Fall semester, and
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MSRI FINAL REPORT JARED SPECK 1. Ba
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External Postdoctoral Fellows 2009-
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External Postdoctoral Fellows 2009-
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2 connections to geometry, topology
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Connections for Women: Tropical Geo
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Participant List MSRI Workshop: Con
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Connections for Women: Tropical Geo
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2 Combinatorics, Several Complex Va
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Introductory Workshop: Tropical Geo
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Currently Available Videos � Sam
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Name Institution Hering, Milena Uni
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Introductory Workshop: Tropical Geo
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analysis. The clarity of Payne’s
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Tropical Geometry in Combinatorics
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Name Institution Kharlamov, Viatche
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Tropical Geometry in Combinatorics
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Above satisfactory 35 73% Somewhat
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Tropical structures in geometry and
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Research Workshop: Tropical Structu
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Research Workshop: Tropical Structu
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Algebraic Structures in the Theory
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2 WORKSHOP REPORT toric fibrations,
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Algebraic Structures in the Theory
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Wednesday November 18, 2009 09:00AM
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Participant List MSRI Workshop: Alg
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Name Institution Smith, Ivan Centre
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Research Workshop: Symplectic and C
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Detailed review: We will now discus
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Symplectic and Contact Topology and
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Research Workshop: Symplectic and C
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Final Report MSRI Connections for W
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Connections : Symplectic and Contac
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Currently Available Videos � Siki
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Milin, Isidora University of Illino
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Final Report Introductory Workshop
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at a variety of levels. Since a hig
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Introductory Workshop: Symplectic a
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Participant List MSRI Workshop: Int
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Park, Jongil Seoul National Univers
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Yes.. I would like to talk to 4 - 6
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No, but I have continued to make my
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5. Are you planning to work with co
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(1) change the order of my curricul
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I will show my 6th grade teacher co
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to teaching and planning. Perhaps b
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III - Develop a lesson on similarit
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4. What are you going to implement/
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matics? * How are people teaching t
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Evaluation #23 (I guess this is Cla
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Evaluation #24 1. What were the ben
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2010 Mathematical Sciences Research
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During the 2007-2009 summers, 46 st
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MSRI-UP peers promoted mathematical
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The outcome of all the students’
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school in mathematics.” They prov
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16. Evidence Already Pointing to Lo
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II. Research Projects 1. Your resea
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5. Is there a workshop, discussion
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V. Non-Academic Aspects of MSRI-UP
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MSRI-UP 2010 Calendar, Weeks 1 and
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MSRI-UP 2010 Calendar, Weeks 5 and
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In 1945 Stanislaw Ulam posed a ques
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2.2 Circle Theorem 2. Let r ∈ Q w
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parabola is (a) The parabola and tw
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Proof. For each 1 ≤ i < j ≤ 4 w
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2.5 Non-Concyclic Points on a Parab
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⎛ ⎜ 1 ⎜ 0 ⎜ 0 ⎜ 0 ⎜ 0
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following rational points: n23 = Y1
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Toric Varieties Cox, David Invited
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Toric varieties Held: June 15-26, 2
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the graduate participants to hear a
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This lecture series addressed topic
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Participant List MSRI Workshop: Sym
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Example of a Summer Graduate Worksh
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Random Matrix theory July 6, 2009 t
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Random Matrix Theory Held: July 6 -
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Participant List MSRI Workshop: Ran
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Below is the list of topics conside
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stability estimates for the inverse
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Participant List MSRI Workshop: Inv
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The Arithmetic of L-Functions IAS/P
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ackground material on group represe
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Computational Theory of Real Reduct
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3. Postdoctoral Program - MSRI

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