Andrei Marshakov (HSE University) – Decorated Newton polygons and reductions of cluster integrable systems

I start with the definition of cluster integrable systems a la Goncharov and Kenyon, defined by convex Newton polygons, up to the action of $SA(2,\mathbb{Z})$. There are several arguments requiring that to complete the picture, this class should be extended by their Hamiltonian reductions, which can be performed preserving the structure of cluster variety.