Péter Csikvári: An introduction to the theory of independence polynomial

In this talk I give some basic facts about the so-called independence polynomial. This polynomial originally arises from statistical physics as the partition function of the hard-core model, and  is related to combinatorics through the Lovász local lemma. As an easy application of the theory I will  give a proof of Mantel's theorem. This proof is based on a fact about the smallest root of the independence polynomial. There will be no new result in this talk.