Integrable Difference Equations and Orthogonal Polynomials with respect to a Discrete Measure

Explore a comprehensive lecture on integrable difference equations and orthogonal polynomials delivered by Jérémie Bouttier at the International Centre for Theoretical Sciences. Delve into discrete integrable systems as part of a two-week program focusing on difference equations, cluster algebras, and probabilistic models. Learn about exactly solvable systems and their conserved quantities, examining both continuous and discrete integrable systems derived from theoretical physics and mathematics. Discover the interconnections between statistical physics, string theory, combinatorics, representation theory, geometry, and probability through the lens of discrete systems' algebraic structures. Gain insights into three major research areas: integrable difference equations and their soliton solutions, cluster algebra structures in discrete integrable systems, and integrable probability including interacting particle systems and stochastic growth models. Participate in mini-courses, problem sessions, and workshop activities designed for both junior and senior researchers interested in discrete integrable systems and related fields.