# Hypergraphs

Friday, November 14, 2014 - 10:30am - 11:00am

Andrew Suk (University of Illinois, Chicago)

A k-ary semi-algebraic relation E on R^d is a subset of R^{kd}, the set of k-tuples of points in R^d, which is determined by a finite number of polynomial equations and inequalities in kd real variables. Given point sets P_1,...,P_k subset R^d and a k-ary semi-algebraic relation E on R^d, let H = (P_1,...,P_k,E) be the underlying k-partite k-uniform hypergraph with parts P_1,..,P_k.

Tuesday, September 9, 2014 - 10:15am - 11:05am

Andrew Thomason (University of Cambridge)

Unlike the ordinary chromatic number, the list chromatic number necessarily

grows with the average degree. Indeed, Alon (2000) proved it grows with the

logarithm of the average degree. Recently, the same has been shown to be

true for uniform hypergraphs, by means of the container method: we sketch

how this works. The question then arises as to the precise value of the

minimum list chromatic number. Here the answer turns out to be not what was

expected. We attempt to sketch the latest progress, and its implications

grows with the average degree. Indeed, Alon (2000) proved it grows with the

logarithm of the average degree. Recently, the same has been shown to be

true for uniform hypergraphs, by means of the container method: we sketch

how this works. The question then arises as to the precise value of the

minimum list chromatic number. Here the answer turns out to be not what was

expected. We attempt to sketch the latest progress, and its implications