PIRSA:24100141

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

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

Semenyakin, Mykola. Cluster Reductions, Mutations, and q-Painlev'e Equations. Perimeter Institute, Oct. 31, 2024, https://pirsa.org/24100141 

          @misc{ pirsa_PIRSA:24100141,
            doi = {10.48660/24100141},
            url = {https://pirsa.org/24100141},
            author = {Semenyakin, Mykola},
            keywords = {Mathematical physics},
            language = {en},
            title = {Cluster Reductions, Mutations, and q-Painlev{\textquoteright}e Equations},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {oct},
            note = {PIRSA:24100141 see, \url{https://pirsa.org}}
          }

Mykola Semenyakin

Perimeter Institute for Theoretical Physics

Talk number
PIRSA:24100141
Collection
Talk Type
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.