【Seminar】 Intersections of Dual SL3-Webs

Speaker: Prof. Zhe Sun, University of Science and Technology of China

Title:  Intersections of Dual SL3-Webs

Abstract:  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.

Zoom Link

https://oist.zoom.us/j/96072307299?pwd=TzE1QUdnbHdLWWxaTEJFTi8rbEN2UT09

Meeting ID: 960 7230 7299

Passcode: 426952