Cluster Integrable Systems

Mykola Semenyakin (Perimeter Institute)

Thursday 1st February 16:00-17:00 Maths 311B

Abstract

Cluster integrable systems are a wide class of integrable systems of trigonometric type with the structure of X-cluster variety on the phase space. On top of integrable flows, defined by Poisson-commuting Hamiltonians, there is also a group of discrete automorphisms of the integrable system inherited from the cluster mapping class group of X-cluster variety. These systems have been discovered independently as integrable systems on Poisson-Lie groups and in the context of dimer models, and are under active studies nowadays.

 

In my talk, I will explain how to construct these integrable systems and how to see the structure of (and what is) X-cluster variety on their phase spaces. If time permits I will tell a bit more about recent studies on those systems.

 

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