Tropical Schemes

Abstract: The tropicalization of a subscheme of P^n is given by a homogeneous ideal in the semiring of tropical polynomials that satisfies some matroidal conditions. This can be thought of as a "tower of valuated matroids". In this talk I will highlight what we currently know about the connection between these matroids and the geometry of the subscheme, including recent progress on the Nullstellensatz with Felipe Rincon, and some connections still to be understood.

algebraic geometrycombinatorics

Audience: researchers in the topic

Combinatorics and Geometry BLT Seminar