Speaker: Martin Ulirsch.
Affiliation: Goethe University Frankfurt am Main.
Venue: Ramanujan Hall,
Time: 5 March, 4pm.
Title: What is the combinatorial shadow of a matrix?
Abstract: Tropicalization is a process that associates to an
algebro-geometric object a piecewise linear polyhedral shadow that
captures its essential combinatorial structure. In this talk, I will give
an overview of the numerous ways of how to extract tropical information
from a matrix. Our focus will be on naturally occurring logarithmically
concave sequences associated to a matrix (or more generally a matroid
respectively a bimatroid), an area of study, which in recent years has
tremendous progress due to the introduction of methods originating from
Hodge theory. A particular emphasis will be made to make this story
accessible; a background in algebraic geometry is not necessary to follow
this talk.
This talk draws from joint work with Felix Röhrle as well as with Jeff
Giansiracusa, Felipe Rincon, and Victoria Schleis.