Tropical h-vectors of polytopes

Series: 
Research Horizons Seminar
Wednesday, February 13, 2019 - 12:05pm
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
Georgia Tech
Organizer: 
For a polytope P, the h-vector is a vector of integers which can be calculated easily from the number of faces of P of each dimension. For simplicial polytopes, it is well known that the h-vector is symmetric (palindromic) and unimodal. However in general the h-numbers may even be negative. In this talk I will introduce the tropical h-vector of a polytope, which coincides with the usual h-vector of the dual polytope, if the polytope is simple. We will discuss how they are related to toric varieties, tropical geometry, and polytope algebra. I will also discuss some open problems.