Math CS Colloquium, Alex Lubotzky (Hebrew University of Jerusalem and Yale University):"Ramanujan complexes and topological expanders"

Thursday, February 11, 2016
4:15 PM - 5:15 PM (ET)
Exley 121
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Han Li
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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. 

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