Aarhus Universitets segl

Bracelets are theta functions for surface cluster algebras

Fan Qin
Onsdag 22. februar 2023 14:15–15:15 Koll. G (1532-214)
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.

Kontakt: Karin M. Jacobsen Revideret: 25.05.2023