Mohan Ravichandran: Root bounds for Real Stable polynomials and applications

Abstract

Real stable polynomials have seen a large number of applications in recent years and key to these have been Borcea and Branden's characterization of stability preserving operators. A parallel story to this was written in 2013 by Marcus, Spielman and Srivastava who developed techniques to describe zero free regions of real stable polynomials and used these to resolve the Kadison-Singer problem. There have been several extensions of these results, notably Branden's hyperbolic version of these. I'll talk about a couple of contributions I have made to this area and pose some curious and basic open problems.