Trainer: Mikhail Bershtein
Title: Cluster integrable systems
Abstract: Cluster integrable systems form a relatively new, interesting, and important class of integrable systems. One of their basic features is that they are multiplicative (in more physical words relativistic). Another important feature is the natural constructions of discrete flows and quantization. Perhaps the most important application is the (conjectural) structure of cluster integrable system on the Coulomb branches of 4d supersymmetric theories.
A preliminary plan of the course (aka list of keywords): open Toda system, the definition of cluster varieties, cells in Poisson-Lie group, closed Toda system, spectral curves, dimer models, quantization of cluster varieties, quantum Toda systems. The course will be based on the works of Fock, Goncharov, Marshakov, Kenyon, Schrader, Shapiro.