Mathematics Seminar Series: Algebra, Geometry, and Combinatorics

Speaker: Ariana Chin (UCLA)

Title: Zamolodchikov Periodic Cluster Algebras 

Abstract: Zamolodchikov periodicity is a property of certain discrete dynamical systems and was one of the primary motivations for the creation of cluster algebras. It was first observed by Zamolodchikov in his study of thermodynamic Bethe ansatz for simply-laced Dynkin diagrams, and was proved by Keller to hold for tensor products of two Dynkin diagrams. In this talk, we discuss the classification of all Zamolodchikov periodic cluster algebras, with connections to W-graphs, root systems, and maximal green sequences.