Solitons in Infinite Relativistic Toda System

Explore a lecture on solitons in the infinite relativistic Toda system, delivered by Nicolai Reshetikhin from UC Berkeley and BIMSA at the M-Seminar, Kansas State University. Delve into this "relativistic" generalization of the infinite Toda chain, examining its connection to the $GL(\infty)$ version of the Toda-Coxeter system for $SL(N)$ with standard Poisson Lie structure. Investigate the phase space as an example of an infinite cluster variety, and learn about the construction of soliton solutions for both factorization discrete time dynamics and continuous time integrable dynamics. Discover the process of constructing action-angle variables from scattering data in this joint work with Cory Lansford. Cover topics such as Hamiltonian integrable systems, cluster varieties, Poisson brackets, spectral problems, and special solutions while exploring the mathematical intricacies of this complex system.

Introduction
Title
Plan
Hamiltonian
integrable systems
integrability
integrable system
simpletic meaningful
goal of this talk
why do we keep Epsilon
H Omega K
Two linear operators
Integral systems
Cluster variables
Double prior cells
Cluster varieties
Coordinate charts
Coordinate Atlas
Poisson Bracket
integrable
algebra
simpletic leaves
time evolution
Geo Infinity
Infinite Cycles
Variables
Hamiltonians
Spectral problem
Special solutions