Georgia Institute of Technology College of Sciences

We will outline the proof that shows the existence of bipartite Ramanujan Graphs of any degree as well as some of mixed degrees. Our approach uses the idea of Bilu and Linial to show that there exists a 2-lift of a given Ramanujan graph which maintains the Ramanujan property. This will include introducing a new technique for establishing the existence of certain combinatorial objects that we call the "Method of Interlacing Polynomials." This talk is intended to be accessible by a general computer science audience, and represents joint work with Dan Spielman and Nikhil Srivastava.- See more at: http://www.arc.gatech.edu/events/arc-colloquium-adam-marcus-crisplycom-and-yale-university#sthash.qdZRaV1k.dpuf