Algebraic Graph Theory seminar

Matching Polynomials, Real Stable Polynomials and Ramanujan Graphs

Abstract:

In important recent work Marcus, Spielman and Srivastava have proved that for if k > 2, there is a family of bipartite Ramanujan graphs of valency k. Their proof makes use of properties of matching polynomials and real stable polynomials. This will be the first in a shortish series of seminars where we work through this paper.