Title:

On a conjecture of Sokal concerning roots of the independence polynomial

Abstract:

In this talk I will introduce the independence polynomial of a graph, also known as the partition of the hard-core model in statistical physics. Then I will explain how zero-free regions for the independence polynomial are closely related to the existence of efficient approximation algorithms for computing evaluations of the independence polynomial and relate this to Sokal’s conjecture and its solution. After that I will explain a connection between the location of zeros of the independence polynomial and complex dynamical systems and give some ideas of our proof of the conjecture.

Based on joint work with Han Peters