3. Postdoctoral Program - MSRI

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Introductory Workshop: Tropical Geometry Held: August 24-28, 2009 The Mathematical Sciences Research Institute Officially Registered Participant Information 140 participants Male Gender (n = 140participants) 66.13% 82 Female 32.26% 40 Declined to state 1.61% 2 White Ethnicity (n =83 participants) 59.04% 49 Asian 16.87% 14 Hispanic 3.61% 3 Pacific Islander 0.00% 0 Black 2.41% 2 Native American 2.41% 2 Declined to state 15.66% 13
Report on the MSRI Workshop: Tropical Geometry in Combinatorics and Algebra Federico Ardila (San Francisco State University) David E Speyer (MIT) Jenia Tevelev (UMass Amherst) Lauren Williams (Harvard) 1 Introduction The oldest use of tropical methods, and the origins of the term “tropical” itself, come from combinatorial optimization theory. For example, let M be the square matrix expressing distances in a graph. Then M ⊙M, where the product is taken tropically, gives the shortest two-step path between any two points. Similarly, the sum 1 ⊕ M ⊕ M ⊙ M ⊕ · · · gives the shortest route between any two points. This sort of algebraic manipulation of tropical objects, in the solution of combinatorial problems, played an important role in the early history of tropical mathematics. The recent growth in tropical work comes from a very different direction. Grigory Mikhalkin, following an idea of Kapranov, has shown how to use tropical methods to compute Gromov-Witten invariants. This development of tropical methods has come from the community of geometers and mathematical physicists, and the resulting mathematics has a more visual and geometric style. Our workshop focused on researchers who are bringing these new methods into algebraic geometry and number theory, and back into combinatorics. This has involved finding foundations which are more algebraic, such as substituting non-Archimedean analysis for degeneration of complex structure; and finding methods which are more computational, such as using Gröbner bases in place of the space of all valuations. A frequent theme of conversations, in the lecture hall and at tea, was how to take sophisticated tools and make them computationally effective. All lectures were recorded, both by video camera and by a designated notetaker, and are available to the public on the MSRI website; so that they may cointinue to serve as a valuable reference. 2 Summary of lectures Our first lecture, delivered by Sam Payne, described how to set up the formalism of tropical geometry to connect cleanly with tools from non-Archimedean 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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Page 214 and 215: Final report: mentoring Sikimeti Ma
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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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Symplectic and Poisson Geometry in
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Symplectic and Poisson Geometry in
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Symplectic Geometry, Noncommutative
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09:00AM - 10:00AM Registration 10:0
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REPORT ON THE MSRI WORKSHOP “HOMO
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of the theory via webs and foams mo
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Schedule Connections for Women: Hom
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Connections for Women: Homology The
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04/29/2010 Connections for Women: H
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REPORT ON THE MSRI WORKSHOP “INTR
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INTRODUCTORY WORKSHOP, FINAL REPORT
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Introductory Workshop: Homology The
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Connections for Women: Homology The
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Research Workshop: Homology Theorie
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Schedule Research Workshop: Homolog
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Currently Available Videos Research
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Research Workshop: Homology Theorie
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04/29/2010 Research Workshop: Homol
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comprehensive lectures explaining t
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Hot Topics: Black Holes in Relativi
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Currently Available Videos � Miha
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Shao, Shuanglin Institute for Advan
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MATHEMATICAL SCIENCES RESEARCH INST
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MPDI Summer Institute 2009: Final R
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school teachers (in the case of sim
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in length)? The audience would be e
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Evaluation #1 1. What were the bene
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6. Do you have to report to an admi
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your class because your way of teac
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employee with a summary of what you
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what have you learned in this insti
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Evaluation #9 (signed Kelly L.) 1.
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therefore should not be given the j
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would you like them organized? Plea
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Evaluation #11 1. What were the ben
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Evaluation #12 (signed Jake Disston
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ideas are insignificant in light of
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manipulative and pictorial level. F
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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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