Fan Qin

Mathematics Seminar

The skein algebra of a marked surface admits 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 a joint work with Travis Mandel, we show that the two bases coincide except for the once-punctured torus. Long-standing conjectures on strong positivity and atomicity follow as corollaries.

Contact: Karin M. Jacobsen
Revised: 25.05.2023