Introduction

This is a continuation of my BIMSA lectures given in 2022-23, where I was discussing the 2D Ising model, as well as thе independent percolation.

This year I will start with the random surfaces, as they appear in the statistical mechanics. They are the interfaces separating phases in the models undergoing phase transitions, with several phases below the critical temperature. Then I will proceed to the models with continuous symmetry.

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

Audience

Graduate

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.