High dimensional expanders

Seminar
Combinatorics
Speaker
Tali Kaufman (Bar-Ilan University)
Date
14/12/2014 - 15:30 - 14:00Add to Calendar 2014-12-14 14:00:00 2014-12-14 15:30:00 High dimensional expanders 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. אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
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.

Last Updated Date : 07/12/2014