Colored Vertex Models, Orthogonal Functions and Probability - Lecture 1

Explore fundamental concepts of discrete integrable systems in this lecture from a two-week program at the International Centre for Theoretical Sciences. Delve into colored vertex models, orthogonal functions, and probability theory as part of a comprehensive series focusing on difference equations, cluster algebras, and probabilistic models. Learn from expert Michael Wheeler in this 78-minute session that bridges theoretical physics and mathematics. Gain insights into exactly solvable systems, their conserved quantities, and applications across statistical physics, string theory, combinatorics, representation theory, geometry, and probability. Examine the interconnections between integrable difference equations, cluster algebra structures, and integrable probability while understanding their relationships to quantum groups, tropical geometry, and stochastic processes. Participate in a program designed for both junior and senior researchers, featuring mini-courses, problem sessions, and workshop components that explore the rich landscape of discrete integrable systems.