On 27 June 2023 Dr. Theodoros Kouloukas gave a talk on Integrable maps associated with deformations of cluster mutations at the ISLAND 6 workshop, Dualities and Symmetries in Integrable Systems, Sabhal Mor Ostaig, Isle of Skye  26-30 June 2023.

Abstract: We consider deformations of sequences of cluster mutations in finite type cluster algebras, which destroy the Laurent property but preserve the presymplectic structure defined by the exchange matrix. In the case of non-degenerate exchange matrices parametric symplectic maps are derived, while the degenerate cases are reduced to symplectic maps in lower dimensional spaces (U-systems). We investigate the Liouville integrability of such maps by imposing suitable constraints on the parameters. Cluster mutations of affine Dynkin quivers  involving fractional linear transformations are also presented which correspond to plane wave reductions of integrable lattice equations.