Title: Nonstandard analysis and new standard proof of the containers theorem
Speaker: Henry Towsner (University of Pennsylvania)
Abstract: The hypergraph containers theorem, introduced by Balogh-Morris-Samotij and Saxton-Thomason, is a breakthrough in extremal combinatorics which gives a tool for controlling the number of independent sets in finite hypergraphs. (We do not assume any familiarity with the containers method!) The original proof depends on giving a program which constructs 'containers' for independent sets and analyzing its behavior to ensure the construction has the right properties. Inspired by the idea of pseudofinite dimension in ultraproducts (with which familiarity is also not assumed), we give a new, elementary and nonalgorithmic, proof of the containers theorem which gives an direct characterization of the 'containers'.
Joint work with Bernshteyn, Delcourt, and Tserunyan.
