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PIRSA:24100141

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

APA

Semenyakin, M. (2024). Cluster Reductions, Mutations, and q-Painlev'e Equations. Perimeter Institute for Theoretical Physics. https://pirsa.org/24100141

Mykola Semenyakin Perimeter Institute for Theoretical Physics

Talk numberPIRSA:24100141
Source RepositoryPIRSA

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.