Video URL
https://pirsa.org/24100141Cluster Reductions, Mutations, and q-Painlev'e Equations
Mykola Semenyakin Perimeter Institute for Theoretical Physics
Source RepositoryPIRSA
Collection
Talk Type
Scientific Series
Subject
Abstract
In my talk I will explain how to extend the Goncharov-Kenyon class of cluster integrable systems by their Hamiltonian reductions. In particular, this extension allows to fill in the gap in cluster construction of the q-difference Painlev'e equations. Isomorphisms of reduced Goncharov-Kenyon integrable systems are given by mutations in another, dual in non-obvious sense, cluster structure. These dual mutations cause certain polynomial mutations of dimer partition functions and polygon mutations of the corresponding decorated Newton polygons.