Tropical Geometry in the Tropics

In 2015, IMPA will organize a Special Thematic Program on Algebraic Geometry. The activities will take place on IMPA's premises in Rio de Janeiro, Brazil, from April to June, 2015. 

We expect a very relaxed atmosphere where visitors will take part in weekly seminars, in a series of workshops and in other activities they deem interesting including their fellow visitors and local mathematicians. 

Please feel very welcome to plan a visit during the period. The Organizing Committee has already obtained funds to support visitors and is committed to finding even more resources, though unfortunately these are always limited. So that we are able to have as many visitors as possible, we encourage you to apply elsewhere for funds for traveling and local expenses to support your visit. 

If you want to come, please let us know, by registering! If you have a certain period in mind, a particular week or the whole three months, please let us know! The sooner we know, the better for planing the trimester, allocating the available funds, searching for more resources, and making your visit possible!


Alicia Dickenstein (UBA)
Ethan Cotterill (UFF)
Nicolas Puignau(UFRJ)
Oliver Lorscheid (IMPA)

Playlist no Youtube:



Minicourse I
Ilia Itenberg (Institut de Mathematiques de Jussieu)

Enumerative aspects of tropical geometry

The main purpose of this mini-course is to present several applications of tropical geometry in real and complex enumerative problems. In particular, we will discuss various combinatorial and recursive formulas designed for a calculation of GromovWitten type invariants (complex case) and Welschinger invariants (real case). We will also discuss so-called refined (or quantum) enumeration of tropical curves and its applications.

Download Videos

Class 1 -
11.05.2015 - download
Class 2 - 12.05.2015 - download
Class 3 - 13.05.2015 - download

Minicourse II
Matt Baker (Georgia Institute of Technology)

Specialization of divisors from algebraic to tropical curves

This minicourse will consist of three lectures, each aimed at a general algebraic geometry audience. In the first lecture we will discuss tropical curves, formulate a Riemann-Roch theorem for them, and give a sketch of the proof. In the second lecture, we will provide a gentle introduction to Berkovich's theory of non-Archimedean analytic spaces, with an emphasis on the cases of curves. We will then formulate and prove the Specialization Lemma, which relates the rank of a divisor on a Berkovich curve X to the rank of its retraction to the skeleton of X. In the final lecture, we will give an overview of some applications of this framework to algebraic geometry, including Brill-Noether theory and the theory of limit linear series.

Download Videos

Class 1 - 11.05.2015 - download
Class 2 - 12.05.2015 - download
Class 3 - 13.05.2015 - download

Download Videos


Jeff Giansiracusa (University of Swansea) 
Bend relations, valuations, and universal tropicalization

Lothar Göettsche (ICTP) 
Refined curve counting and tropical geometry

Eric Katz (University of Waterloo) 
Hodge theory in combinatorics

Diane Maclagan (University of Warwick) 
Tropical ideals, varieties, and schemes

Lucia Lopez de Medrano (UNAM Mexico) 
Decomposition of Tropical Skeletons

Margarida Melo (Universidade de Coimbra) 
Regular matroids: Torelli theorem and moduli space

Sam Payne (Yale University) 
Algebraic curves, tropical geometry, and moduli

Jean-Jacques Risler (Université de Paris VI) 
Curvature of Real Algebraic Sets

Louis Rowen (Bar-Ilan University) 
Towards Supertropical Representation Theory

Kristin Shaw (Freie Universität Berlin) 
Tropical Surfaces

Josephine Yu (Georgia Institute of Technology) 
Product-Mix Auction and Tropical Geometry