Statistical Mechanics, Integrability and Combinatorics - Fendley, Paul; Pronko, Andrei; Reshetikhin, Nicolai; Wiegmann, Paul; Zinn- Justin, Paul (Colle di Galileo, 2016)
In Spring 2015, the Galileo Galilei Institute for Theoretical Physics hosted an eight-week Workshop on "Statistical Mechanics, Integrability and Combinatorics". The Workshop addressed a series of questions in the realm of exactly solvable models of statistical mechanics, featuring numerous ties and overlaps with various problems in modern combinatorics, probability theory, and representation theory. Much recent progress in these areas exploits the underlying notion of quantum integrability. We report here on the scientific motivations and background for this activity and on its main outputs. Keywords. Statistical mechanics, lattice models, quantum integrability, exact results, combinatorics, tilings, dimers, growth processes, limit shape phenomena, random matrices, random surfaces, determinantal processes, discrete holomorphicity.