Venue： Lecture Hall

Speaker：Fan Qin (Shanghai Jiao Tong University)

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.

Welcome!