## Combinatorics Seminar

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

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.