EVENT DETAILS AND ABSTRACT

Title: Bracelets bases are theta bases
Speaker: Travis Mandel
Speaker Info: University of Oklahoma
Brief Description:
Special Note: Note special day
Abstract:

Cluster algebras from marked surfaces can be interpreted as skein algebras, as functions on decorated Teichmüller space, or as functions on certain moduli of SL2-local systems. These algebras and their quantizations have well-known collections of special elements called "bracelets" (due to Fock-Goncharov and Musiker-Schiffler-Williams, and due to D. Thurston in the quantum setting). On the other hand, Gross-Hacking-Keel-Kontsevich used ideas from mirror symmetry to construct canonical bases of ``theta functions'' for cluster algebras, and this was extended to the quantum setting in my work with Ben Davison. I will review these constructions and describe upcoming work with Fan Qin in which we prove that the (quantum) bracelets basis coincides with the corresponding (quantum) theta basis.