Bracelet bases are theta bases

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 recent work with Fan Qin in which we prove that the (quantum) bracelets bases coincide with the corresponding (quantum) theta bases.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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