Combinatorics Seminar

When: Sunday, November 24, 10am
Where: Schreiber 309
Speaker: Roy Meshulam, Technion
Title: Random Latin Squares and 2-dimensional Expanders


In view of the ubiquity of expander graphs in discrete mathematics, there is in recent years a growing interest in high-dimensional expanders. While there are several "competing" definitions for k-dimensional expansion, we shall focus on the notion of cohomological expansion of simplicial complexes. This k-dimensional version of the graphical Cheeger constant came up independently in work on homological connectivity of random complexes and in Gromov's remarkable work on the topological overlap property. After reviewing some background, we'll discuss a result concerning the existence of 2-dimensional expanders with bounded edge degrees. The proof involves a new model of random complexes and depends on two ingredients: A spectral bound on the expansion of small 2-cochains and a large deviation result for random Latin squares.

Joint work with Alex Lubotzky.