Title: Cluster varieties and integrable systems
I am going to construct a class of integrable systems on the Poisson submanifolds of the (generally - affine) Poisson-Lie groups, enumerated by cyclically irreducible elements the co-extended affine Weyl groups. Their phase spaces admit cluster coordinates and the integrals of motion are cluster functions. This class of integrable systems coincides with the constructed by Goncharov and Kenyon out of dimer models on a two-dimensional torus and are classified by equivalence class of the Newton polygons.
Particular examples of such systems include the well-known relativistic Toda chains, the system of "pentagram map" and their natural generalizations.
Location: KdVI meeting room, Science Park 105-107, room F3.20