Cluster Reductions, Mutations, and q-Painlev'e EquationsConfirmed

by Mykola Semenyakin (Perimeter Institute for Theoretical Physics)

Thursday Oct 31, 2024, 11:00 a.m. → 12:30 p.m. America/Toronto

PI/4-400 - Space Room (Perimeter Institute for Theoretical Physics)

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.