Introduction to Interlacing Polynomials, Barrier Functions, and Kadison-Singer
Daniel Spielman (Yale University)
MSRI: Simons Auditorium
I will introduce the method of interlacing polynomials and analysis by barrier functions through a proof of the Restricted Inevitability Principle. I will state Weaver's discrepancy-theoretic version of the Kadison-Singer Conjecture, and sketch the role that hyperbolic polynomials play in its proof. If time permits, I will connect these with Ramanujan graphs and the matchings polynomials of graphs.