Categorical dynamical systems arising from sign-stable mutation loops

Abstract 

A cluster modular group is a symmetry group of the theory of cluster algebras. An element is called a ''mutation loop''. I and T. Ishibashi introduced the notion of sign stability of the mutation loops as a generalization of the pseudo-Anosovness of the mapping classes. In this talk, I will define the autoequivalences of the derived category of the Ginzburg dg algebra of a quiver with potential associated with a sign-stable mutation loop, and show the calculation of their categorical entropies. If time permits, I'll explain the pseudo-Anosovness of these autoequivalences.

About the speaker 

Shunsuke Kano Tohoku University

I am an Assistant Professor of Research Alliance Center for Mathematical Sciences, Tohoku University.

Research Interests: cluster algebras, triangulated categories

https://sites.google.com/view/shunsuke-kano