Ramanujan coverings of graphs

Computer Science/Discrete Mathematics Seminar II
Topic:Ramanujan coverings of graphs
Speaker:Doron Puder
Affiliation:Member, School of Mathematics
Date:Tuesday, December 8
Time/Room:10:30am - 12:30pm/West Bldg. Lect. Hall

Ramanujan graphs are optimal expander graphs, and their existence and construction have been the focus of much research during the last three decades. We prove that every bipartite Ramanujan graph has a $d$-covering which is also Ramanujan. This generalizes the $d = 2$ case, a recent major breakthrough in the subject due to Marcus, Spielman and Srivastava. The main tools we use are the Peter-Weyl theory in group representations, as well as the theory of interlacing polynomials. All notions will be explained. Joint work with Chris Hall and Will Sawin.