Non-commutative surfaces, cluster exchange groupoid, and positivity
数学专题报告
报告题目(Title)： Non-commutative surfaces, cluster exchange groupoid, and positivity
报告人(Speaker)：黄敏（中山大学珠海校区）
地点(Place)：腾讯会议883330117 密码123456
时间(Time)：2025年10月15日 （周三）16:30-17:30
邀请人(Inviter)：肖杰、覃帆、周宇
报告摘要
The aim of the talk is to introduce noncommutative cluster algebras $A$ from marked surfaces possibly with orbifold points of various orders, which includes noncommutative clusters, i.e., embeddings of a given group $G$ into the multiplicative monoid $A^\times$ and an action of a certain braid-like group $Br_A$ by automorphisms of each cluster group in a compatible way. We will explain how the group $Br_A$ is related to the point group of the cluster exchange groupoid defined by King and Qiu in the unpunctured case. For punctured surfaces, we construct noncommutative tagged clusters and establish a noncommutative Laurent Phenomenon. This is a joint work with Berenstein and Retakh.
