Tali Kaufman-Halman (Bar-Ilan University)
Wednesday, 31.12.2014, 12:30
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.