## Combinatorics Seminar

When: Sunday, December 7, 10am
Where: Schreiber 309
Speaker: Tali Kaufman, Bar-Ilan University
Title: High dimensional expanders
## Abstract:

Expander graphs have been intensively studied in the last four
decades. In recent years a high dimensional theory of expanders
has emerged. In this talk I will introduce the notion of high
dimensional expanders and some of the motivations for studying them.
As opposed to (1-dimensional) expanders, where a random bounded
degree graph is an expander, a probabilistic construction of
a bounded degree high dimensional expander is not known. A major
open problem, formulated by Gromov, is whether *bounded degree* high
dimensional expanders could exist for dimension d>= 2. I will discuss
a recent construction of explicit bounded degree 2-dimensional
expanders, that answer Gromov's question in the affirmative.
Joint work with David Kazhdan and Alexander Lubotzky.