Ramanujan Coverings of Graphs

Seminar: 
Combinatorics Seminar
Event time: 
Thursday, December 10, 2015 - 11:00am to 12:00pm
Location: 
215 LOM
Speaker: 
Doron Puder
Speaker affiliation: 
IAS
Event description: 

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 (a.k.a. $d$-lift) 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.