Fock Goncharov duality, intersection number and skein algebra
报告题目(Title)：Fock Goncharov duality, intersection number and skein algebra
报告人(Speaker)：孙哲（中国科学技术大学）
地点(Place)：后主楼1223
时间(Time)：2024年5月31日 10:00-11:30, 14:00-15:30
邀请人(Inviter)：田垠
报告摘要
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 the first part of my talk, I will explain how Fock and Goncharov relate both sides by multicurves for SL_2, and its relation with the skein algebra. In the second talk, I will explain for SL3, how we relate webs to both sides using the topological asymmetric intersection numbers between webs on the surfaces, and its relation with the skein algebra. This is based on my joint work with Daniel Douglas and joint work with Linhui Shen and Daping Weng.
