Department of Mathematics - Master Calendar

In many situations of interest, integrable systems are defined on symplectic leaves of a Poisson manifold. Furthermore, if the Poisson manifold is a cluster Poisson variety and the symplectic leaves are cluster charts, we have a natural way to transition between seemingly different integrable systems (namely, cluster transformations). Even more, we have a canonical quantization in which cluster transformations act as unitary operators. These are called cluster integrable systems. Starting from a bipartite graph on a torus, I will discuss how to construct a large class of these systems, which were first introduced by Goncahrov and Kenyon.