Leonid Petrov: Overview talk: Probabilistic methods (part 2)

Speaker
Leonid Petrov, University of Virginia

Abstract
We offer a probabilistic point of view on solvable lattice models and algebraic combinatorics. The goal is to present the Yang-Baxter equation as a source of Markov operators that transport probability measures attached to vertex models, via local moves. We derive the classical Robinson-Schensted-Knuth correspondence directly from the Yang-Baxter equation for a vertex model connected to the symmetric Schur polynomials, and discuss generalizations related to other cases of Macdonald polynomials.