DMS Combinatorics Seminar

Speaker: Alexander (Sasha) Polyanskii (Emory University)

Title: The KKM lemma implies the colorful Carathéodory theorem: A short direct proof

Abstract: The goal of my talk is to share a new elementary proof of the colorful Carathéodory theorem using the KKM lemma. Although these results have a geometric and topological flavor, they are very combinatorics-friendly and have purely combinatorial consequences, which I will also cover in my talk.

This proof arose as a byproduct of joint work with Mikhail Bludov.