Szego Seminar: "A topological proof of Kneser's Conjecture"

Speaker: Shibashis Mukhopadhyay, Washington University in Saint Louis

Abstract: Suppose we have a finite set, and we want to partition all its subsets of a fixed cardinality into disjoint classes such that two subsets belong to the same class only if they have non-empty intersection. Martin Kneser in 1956 predicted the minimum number of such classes required but couldn't prove it. In 1978, Lovasz ( the 2021 joint Abel Prize winner) gave a topological proof for Kneser's guess. This turned out to be more than just a proof- it kicked off the exciting area of mathematics that came to be known as topological combinatorics. This involves the application of algebro-topological (simple, in the problem I'll be speaking about!) methods to solving problems in combinatorics. I will be giving a simplified version of Lovasz's proof to Kneser's Conjecture and also try to talk about some other problems in topological combinatorics. The talk will be self-contained as long as you are willing to believe without proof the statements I make on some rare occasions!

Host: Jeremy Cummings