Algebra and Combinatorics Seminar
Date: October 9, 2020
Time: 3:00PM - 4:00PM
Location: Zoom
Speaker: Cvetelina Hill, Georgia Tech
Title: Tropical convex hulls of polyhedral sets
Abstract: This talk is based on joint work with Sala Lamboglia and Faye Pasley Simon. During the first part of the talk we will focus on the tropical convex hull of convex sets and polyhedral complexes. We will introduce results on the tropical convex hull of a line segment and a ray, show that for sets in two dimensions tropical convex hull and ordinary convex hull commute, and give a characterization of tropically convex polyhedra. In the second part of the talk we will use these results to show that the dimension of a tropically convex fan depends on the coordinates of its rays and give a lower bound on the degree of a fan tropical curve using only tropical techniques. The talk will be based on the work in this paper: https://arxiv.org/abs/1912.01253v2.