Aditya Potukuchi, Rutgers University

Abstract

The chromatic number of the Kneser graph (conjectured in 1955) was a seemingly difficult open problem until it was solved by Lovasz in 1978 by using quite non-trivial ideas from topology. Using a bit of geometry, Barany (1978) turned this into an extremely short (yet non-trivial!) proof. The main idea of behind talk is to try and understand at least some of the power that is to be gained by using topological ideas to solve problems that seemingly stem (purely!) from combinatorics. In particular, the paper that will be used for this attempt is a paper by Alon-Frankl-Lovasz, who generalize Lovasz's earlier proof to hypergraphs.