活动地点：

活动类型：学术报告

主讲人：

活动时间：2023-09-05 14:00:00--2023-09-05 15:00:00

活动内容：

孙哲教授专题学术报告

 

报告人：孙哲（中国科学技术大学）

时间：9月5号（周二）下午2点

腾讯会议：224352266

题目：Asymmetric intersection number and Fock-Goncharov duality

摘要：Fock and Goncharov introduced a pair of mirror moduli spaces associated to G and G^L which generalized the Teichmüller space and the decorated Teichmüller space, and they proposed a duality: the canonical basis of the regular function ring of one space X is parameterized by the tropical integral points of its mirror X^V. In this talk, I will explain my joint work with Linhui Shen and Daping Weng for SL3, where we introduce the topological asymmetric intersection numbers between webs on the surfaces to provide the duality pairings and the map from webs to tropical points. We prove that the map is the same as the previous one obtained by Douglas and myself. We relate the cluster algebra and skein algebra by this intersection number and prove the mutation equivariance, where the flip equivariance is a consequence.