Record: Yes

Level: Graduate

Language: English

Prerequisite:

Undergraduate Probability: Independent events, Laws of large numbers. Basic measure theory and functional analysis.

Introduction:

I will discuss the simplest model of Statistical Mechanics: the 2D Ising model, a drosophila of mathematical physics. Yet there are open problems left and many papers are still written on it. I will also treat related models: thе independent percolation, the models with continuous symmetry, the models on other lattices, like the trees and the Lobachevsky plane.

Keywords: phase transition, criticality, correlation decay, Gibbs state, Markov random field, conformal invariance,… All will be explained in full details.

Lecturer Intro:

Senya Shlosman obtained his PhD in 1978, from the St.-Petersburg branch of Steklov institute. His adviser was Roland Dobrushin. He obtained his second PhD (habilitation) in 1989, from the Ukrainian Institute of Mathematics. From 1991 he was Professor of the Dept. of Math., UC Irvine. He moved to France in 1996, getting the position of Directeur de Recherche in CPT, CNRS, Luminy, Marseille. Currently he is a leading scientific researcher in the Institute for Information Transmission Problems of the Academy of Science, Moscow, and Professor of the Center for Advance Studies in Skolkovo Inst. of Technology, Moscow.