Zeros of Multivariate Polynomials in Combinatorics

Abstract.
Zeros of univariate polynomials in combinatorics, and related notions such as unimodality and log-concavity have been studied for a long time. In particular, several important polynomials in combinatorics are known to have only real zeros. Recently a theory around a generalization of real-rooted polynomials to several variables has been developed and used to solve problems in combinatorics and other areas of mathematics. We will survey this method, with particular focus on combinatorial aspects.