In this talk we review a recent result by Marcus, Spielman and Srivastava (http://arxiv.org/abs/1304.4132) which establishes the existence of infinite families of bipartite Ramanujan graphs for all degrees. We cover all the necessary background from Linear Algebra, Graph Theory and Theory of Stable polynomials.

Mirko Visontai is currently a postdoctoral researcher at the Royal Institute of Technology (KTH), and was previously at the University of Pennsylvania, where he completed his Ph.D. in 2012. His research interests include algebraic and enumerative combinatorics, and the study of polynomials with only real roots.