3. Postdoctoral Program - MSRI

With a view on the many graduate students and young mathematicians attending, the focus
of this introductory event were two short-courses (two 1h lectures each, interconnected with
exercises and informal discussion sessions):
• Federico Ardila: Linearity in the tropics
• Hannah Markwig: Counting tropical plane curves.
The short-courses were complemented by five research lectures
• Josephine Yu: Tropical varieties, elimination, and mixed fiber polytopes
• Lucia Lopez de Medrano: Tropical inflection points of tropical planar curves
• Annette Werner: Buildings and tropical geometry
• Marianne Akian: Tropical linear independence and symmetrization of the tropical semiring
• Lauren Williams: The tropical Grassmannian and its positive part
There were also three short communications (by Thomas Markwig, Kirsten Schmitz, and Anne
Shiu), and a panel discussion on career issues for female mathematicians.
Introductory Workshop: Tropical Geometry, Aug 24–28, 2009, organized by Eva-Maria
Feichtner, Ilia Itenberg, Grisha Mikhalkin and Bernd Sturmfels.
Paying tribute to the introductory character of the event, the main emphasis of this workshop
was on five mini-courses that were designed to present the various approaches and viewpoints on
tropical geometry and lay out the scene for the research work of the upcoming semester. Each
minicourse consisted of three 1h-lectures.
• Denis Auroux: Some tropical aspects of mirror symmetry
• Ilia Itenberg: Real aspects of tropical geometry
• Diane Maclagan: Introduction to tropical algebraic geometry
• Mikael Passare: Amoebas and co-amoebas
• Evgeni Tevelev: Tropical elimination theory.
The mini-courses were complemented by five research lectures:
• Grigory Mikhalkin: Basic tropical notions: varieties and maps
• Jean-Jacques Risler: Real algebraic geometry, tropical geometry and total curvature
• Alicia Dickenstein: A naive approach to the implicitization of rational varieties using
tropical tools
• Mohammed Abouzaid: Symplectic perspectives on tropical geometry
• Mark Gross: Towards canonical theta functions for Calabi-Yaus.
Two topical workshops followed later during the program:
Tropical Geometry in Combinatorics and Algebra, Oct 12–16, 2009, organized by Federico
Ardila, David Speyer, Jenia Tevelev and Lauren Williams.
The focus of the workshop was on tropical methods in combinatorics and algebra, e.g., in
combinatorial linear algebra, combinatorial representation theory, and algebraic statistics. Here
is the list of research lectures in chronological order:
• Sam Payne: Topology of compactified tropicalizations
• Alex Esterov: Newton polyhedra and Minkowski integrals
• Eric Katz: Realization spaces for tropical Varieties
• Arkady Berenstein: Geometric crystals and tropical combinatorics
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