Algebraic and categorical entropies of sign-stable mutation loops
数学专题报告
报告题目(Title)：Algebraic and categorical entropies of sign-stable mutation loops
报告人(Speaker)：Shunsuke Kano (Tohoku University)
地点(Place)：后主楼1124
时间(Time)：2月26日(周三) 14:30-16:30
邀请人(Inviter)：肖杰、覃帆、周宇、兰亦心
报告摘要
Mutation is a fundamental way to deform quivers. A sequence of mutations is called a mutation loop if the initial and terminal quivers coincide. A mutation loop induces a discrete dynamical system on certain schemes, known as cluster varieties, as well as on certain triangulated categories. Moreover, if a quiver arises from an ideal triangulation of a punctured surface, the corresponding mutation loop can be regarded as a mapping class of the surface, making it a natural generalization of a mapping class. In the theory of mapping classes, pseudo-Anosovness is one of their most significant properties. In this talk, we introduce a generalization of pseudo-Anosovness for mutation loops, called sign stability, and explore its implications for the associated discrete dynamical systems, drawing analogies with known properties of pseudo-Anosov mapping classes. This talk is based on joint work with Tsukasa Ishibashi.
