On 5th June 2024 Dr. Theodoros Kouloukas gave a talk on the Integrability of Deformed Cluster Maps at the conference at Heriot-Watt University on algebraic aspects of the Yang-Baxter equation.

Abstract: We present deformations of cluster mutations with covariant log-canonical presymplectic forms defined by the corresponding exchange matrix. By considering periodic sequences of cluster mutations, we define deformed cluster maps and investigate their Liouville integrability. We study examples of parametric deformations of A4 cluster map and of affine Dynkin quivers associated with periodic reductions of integrable lattice equations and Yang-Baxter maps.