3. Postdoctoral Program - MSRI

"An illustration of the tropical Abel-Jacobi map" from G. Milkhalkin, I. Zharkov: "Tropical
curves, their Jacobians and Theta functions," arXiv: math/0612267.
Workshop 3: Tropical Geometry in Combinatorics and Algebra
October 12, 2009 to October 16, 2009
Organized by Federico Ardila* (San Francisco State University), David Speyer (Massachusetts
Institute of Technology), Jenia Tevelev (University of Massachusetts, Amherst), and Lauren
Williams (University of California, Berkeley)
This workshop concentrated on tropical methods in Combinatorics and Algebra. Some of the
topics explored were
• tropical ideas in combinatorial linear algebra, such as tropical convexity, tropical linear
spaces and oriented matroids, tropical matrix algebra and its applications;
• tropical methods in combinatorial representation theory, including both discovery of new
formulas and improved understanding of old ones;
• computational issues, including both how to compute tropical objects and how to use
tropical tools in other computational settings; and
• applications of tropical methods in algebraic statistics.
Workshop 4: Tropical Structures in Geometry and Physics
November 30, 2009 to December 04, 2009
Organized by Mark Gross (University of California, San Diego), Kentaro Hori (University of
Toronto), Viatcheslav Kharlamov (Université de Strasbourg), and Richard Kenyon* (Brown
University)
One of the successes of tropical geometry is its applications to a number of different areas of
currently developing mathematics. Among these are enumerative geometry, symplectic field
theory, mirror symmetry, dimer models/random surfaces, amoebas and algae, instantons, cluster
varieties, and tropical compactifications. While these fields appear quite diverse, the common
meeting ground of tropical geometry provided a basis for fruitful interactions between
participants.
T G P r o g r a m H i g h l i g h t s
The Tropical Geometry program at MSRI was the first major research program at a mathematics
institute devoted entirely to the subject. The program was the culmination of a bout of activity in
this newly emerging field and will likely be recognized as a milestone on the way to TG
becoming a recognized discipline that straddles Algebra, Analysis, Combinatorics, and
Geometry. The response to the program from the emerging tropical community was
enthusiastic.
Six of eight research professors were in residence for the full duration of the program as were all
of the four organizers. Together with 23 research members, most of them staying for several
months, they shaped an exciting program and helped provide mentoring for the unusually high
numbers of postdocs (16) and program associates (9). Special care was taken in assigning senior
mentors to the postdocs, aiming to avoid the obvious matchings and to assign mentors who could
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