Speaker: Nicolai Reshetikhin (UC Berkeley and BIMSA)

Abstract: This system is a "relativistic" generalization of the infinite Toda chain. In is a $GL(\infty)$ version of the Toda-Coxeter system for $SL(N)$ with the standard Poisson Lie structure. The phase space of this system is an example of an infinite cluster variety. Assuming an analog of rapidly decaying boundary conditions we construct soliton solutions for both, factorization discrete time dynamics and for continuous time integrable dynamics. We also construct action-angle variables from scattering data. This is a joint work with Cory Lansford.