Title: Bounded degree high dimensional expanders
Speaker: Shai Evra (Institute of Advanced Study)
Abstract: In the past decade, a new theory has emerged which generalizes the notion of expander graphs to higher dimensions. The following major open problem in this field was raised by Gromov: Are there bounded degree high dimensional expanders? There are several competing definitions for high dimensional expanders, but here we focus on the two notions which appear in Gromov's work, namely coboundary expanders and topological expanders. Recently, in a combined effort of many researchers in this field, the above question was answered affirmatively for topological expanders. In this talk I will present a quick overview of the theory of high dimensional expanders, and describe an outline of the proof of this result, focusing on a new local-to-global criterion for high-dimensional expansion.
This is joint work with Tali Kaufman.
