On 19th June 2023 Dr. Theodoros Kouloukas gave a talk on Deformations and integrability of cluster maps at the 14th International Conference on Symmetries and Integrability of Difference Equations (SIDE14.2), University of Warsaw, Warsaw, Poland, June 19-23, 2023.

Abstract:
Cluster algebras constitute a class of commutative algebras whose generators are defined by a recursive process called mutation. Cluster maps  are generated by considering particular sequences of cluster mutations.  Cluster maps associated with An quivers arise in the framework of Coxeter’s frieze patterns, or as a simple example of Zamolodchikov periodicity in integrable quantum field theories. We introduce parametric deformations of these  maps and study the integrability of the corresponding discrete systems using the properties of the underlying cluster algebra structure. We also study examples of more general types of deformed mutations associated with affine Dynkin quivers which correspond to periodic reductions of the discrete sine-Gordon equation.