Cluster reductions, mutations and q-Painleve equations

par Prof. Andrei Marshakov (Krichever Center, Skoltech; IHES)

vendredi 14 févr. 2025, 16:30 → 18:00 Europe/Paris

Salle Pierre Grisvard (IHP - Bâtiment Borel)

I plan to explain how q-difference Painleve equations arise in the context of deautonomization of integrable systems on the Poisson cluster varieties. These include the Goncharov-Kenyon systems, originating from dimer configurations on bipartite graphs on a torus, as well as their Hamiltonian reductions. Equivalent cluster integrable systems are related by mutations in some dual cluster structure, while the q-Painleve examples correspond exactly to the self-dual cases in this picture. The talk is based on joint works with M.Bershtein, P.Gavrylenko & M.Semenyakin.

2025_02_14_A_Marshakov.pdf