ECTS Credits: 6
CRISTINA TONINELLI, BEATRICE TAUPINART DE TILIERE
The aim of statistical mechanics is to understand the macroscopic
behavior of a physical system by using a probabilistic model
containing the information for the microscopic interactions. The
goal of this course is to give an introduction to this broad
subject, which lies at the intersection of many areas of
mathematics: probability, graph theory, combinatorics, algebraic
geometry, ...
In the first part of the course we will introduce the key notions of
equilibrium statistical mechanics. In particular we will study the
phase diagram of the following models: Ising model (ferromagnetism),
dimer models (crystal surfaces) and percolation (flow of liquids in
porous materials). In the second part we will introduce interacting
particle systems, a large class of Markov processes used to model
dynamical phenomena arising in physics (e.g. the kinetically
constrained models for glasses) as well as in other disciplines such
as biology (e.g. the contact model for the spread of infections) and
social sciences (e.g. the voter model for the dynamics of opinions).
For more informations, see here