Title: Intersection of Matroids
| Speaker: | He Guo |
| Affiliation: | Umeå University |
| Location: | Please contact Sabrina Lato for Zoom link. |
Abstract: We study simplicial complexes (hypergraphs closed under taking subsets) that are the intersection of a given number k of matroids. We prove bounds on their chromatic numbers (the minimum number of edges required to cover the ground set) and their list chromatic numbers. Settling a conjecture of Kiraly and Berczi--Schwarcz--Yamaguchi, we prove that the list chromatic number is at most k times the chromatic number. The tools used are in part topological. If time permits, I will also discuss a result proving that the list chromatic number of the intersection of two matroids is at most the sum of the chromatic numbers of each matroid, improving a result by Aharoni and Berger from 2006. The talk is based on works joint with Ron Aharoni, Eli Berger, and Daniel Kotlar. In this talk, there is no assumption about background knowledge of matroid theory or algebraic topology.