Extensions of Discrete Toda Lattices and their Applications - Lecture 3

Explore advanced mathematical concepts in this third lecture focusing on extensions of Discrete Toda Lattices and their applications, delivered by Satoshi Tsujimoto at the International Centre for Theoretical Sciences. Part of a comprehensive program on discrete integrable systems, this lecture delves into difference equations, cluster algebras, and probabilistic models. Learn about integrable systems' exact solvability properties, conserved quantities, and their significance in understanding non-integrable models. Examine the intersection of theoretical physics and mathematics, covering topics like statistical physics, string theory, combinatorics, representation theory, geometry, and probability. Discover the relationships between integrable difference equations, soliton solutions, singularity structures, and their connections to quantum groups, tropical geometry, and stochastic processes. Investigate cluster algebra structures in discrete integrable systems, their geometric applications, and their relevance to mathematical physics concepts like Y-systems and the Toda lattice.