Talking About Combinatorial Objects Student Seminar: Tropical Grassmannian and Dressian for a Matroid

Seminar | December 8 | 1-2 p.m. | 748 Evans Hall

 Madeline Brandt, UC Berkeley

 Department of Mathematics

The Grassmannian $Gr_M$ of a realizable matroid $M$ is an algebraic variety which provides an example of a realization space for the matroid $M$. In this talk, we give a brief introduction to tropical geometry, and then we study the properties of two tropical objects related to $Gr_M$, namely its tropicalization and a tropical prevariety called the Dressian, whose points give all regular matroid subdivisions of the matroid polytope of $M$. We will compute examples and study them in detail. No prior knowledge of tropical geometry is assumed.