数论与表示论讨论班

Number Theory and Representation Theory Seminar

Time: June 14, Wednesday, 16:00-17:00

Venue: 数学高等研究院Lecture Hall

Speaker: 覃帆Fan Qin (Shanghai Jiao Tong University)

Title: Bracelets are theta functions for surface cluster algebras

Abstract: The skein algebra of a marked surface possesses the basis of bracelet elements constructed by Fock-Goncharov and Musiker-Schiffler-Williams. As a cluster algebra, it also admits the theta basis from the cluster scattering diagram by Gross-Hacking-Keel-Kontsevich.

In this talk, we show that the two bases coincide except for the once-punctured torus. It is based on a joint work with Travis Mandel. Long-standing conjectures on strong positivity and atomicity follow as corollaries. We also connect our results to Bridgeland's stability scattering diagrams.

简介

覃帆，上海交通大学长聘副教授，研究方向是代数和表示论，主要研究丛代数和相关领域的课题。论文独立发表于《Duke Mathematical Journal》《Journal of the European Mathematical Society》等国际一流数学杂志。

2020年获得代数表示论领域的重要国际奖项ICRA奖。