Abstract
I will talk about real stable polynomials as a "natural" generalization of (univariate) real rooted polynomials, and their corresponding probability distributions known as strongly Rayleigh distributions.
I will then talk about stability preserver operators which are natural tools to prove a given polynomial is real stable.
We will see many applications of these polynomials and preserver operators in computer science. In particular, I will talk about a deterministic algorithm to approximate permanent of matrices with nonnegative entries, approximation algorithms for traveling salesman problems, and repulsive point processes, a.k.a., DPPs.