Paris, 05-07 October 2015

The tropicalization of an algebraic variety X over a field k included in a n-dimensional torus is a piecewise linear variety which (roughly speaking) is associated with the geometry of the exponents appearing in the defining equations of X and the relative sizes of the coefficients, as measured with a valuation of k. Tropical geometry provides us with tools that detect the geometry of X from its tropicalization. But when one changes the embeddings (or the variables) the geometry of the equation changes and hence its tropicalization does too. To deal with this, one can construct a universal object which contains all the tropicalizations (with all choices of variables, embeddings), or can search for a special embedding in order to have a tropical variety which reflects the best the geometry of X.
One goal of our meeting is to compare these two approaches.

On the other hand, Tropicalization can be thought as the inverse manipulation to the construction of toric varieties, in which we construct algebraic varieties from combinatorial objects. T-varieties are generalizations of toric varieties.
Our second goal is to meet these relatively new objects, whose construction is not completely combinatorial, and maybe to figure out what the inverse manipulation is.

Speakers  :

Kevin Langlois (Bonn)
Hannah Markwig (Saarbrücken)
Bernard Teissier (Paris)

Organizers :

Hussein Mourtada, Matteo Ruggiero, Bernard Teissier.