8680-2018

Combinatorics of Integrability

Topics include:

- Laurent phenomenon: SOMOS and Gale-Robinson sequences, cluster recurrences, LP sequences.

- singularity confinement: discrete Painleve equations, R-systems.

- algebraic entropy: cluster recurrences, monomial maps, R-systems.

- pentagram map: cluster nature, singularity confinement, Devron property, generalizations.

- T systems: periodicity, linearizability, and algebraic entropy.

- Q-nets: multidimensional consistency, Devron property.

- cube recurrence.

- Arnold-Liouville integrability: in cluster structures, pentagram map and beyond.

- solitons: continuous, and discrete, and ultradiscrete.

- Toda lattice: classical and discrete.

- Ising model.