**Seminario Teoría de Números UAM-ICMAT**

**THE ZERO SET OF THE INDEPENDENCE POLYNOMIAL OF A GRAPH **

**SPEAKER: Martín Sombra (ICREA & UB) **

**DATE: Tuesday, 29th January 2019 - 11:30 **

**VENUE: Aula 520, Módulo 17, Departamento de Matemáticas, UAM **

**ORGANISER: UAM - ICMAT **

**ABSTRACT: In statistical mechanics, the independence polynomial of a **

**graph G arises as the partition function of the hard-core lattice gas model **

**on G. The distribution of the zeros of these polynomials when G → ∞ is **

**relevant for the study of this model and, in particular, for the **

**determination of its phase transitions. **

**In this talk, I will review the known results on the location of these zeros, **

**with emphasis on the case of rooted regular trees of fixed degree and **

**varying depth k ≥ 0. Our main result states that for these graphs, the zero **

**sets of their independence polynomials converge as k → ∞ to the **

**bifurcation measure of a certain family of dynamical systems on the **

**Riemann sphere. **

**This is ongoing work with Juan Rivera-Letelier (Rochester).**