Alex Lubotzky (Hebrew University of Jerusalem and Yale University):"Ramanujan complexes and topological expanders"
Abstract: Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 4 decades and more recently also in pure math. In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1.
This question was answered recently (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by T. Kaufman and S. Evra for general d) by showing that the d-skelton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders.
4:15 PM - 5:15 PM EST
- Exley 121
- Venue Address
- 45 Wyllys Avenue, Middletown, CT United States