Seminar in Real and Complex Geometry

Thursday, March 31, 2022, 16:15-17:45, online (via zoom)

Vivek Shende
(Centre for Quantum Mathematics at Syddansk Universitet & University of California, Berkeley)

Skein valued curve counting and quantum mirror symmetry for the conifold


I'll explain how to define counts of all-genus curves with Lagrangian boundary conditions in Calabi-Yau 3-folds. Then I'll do an example: the conifold with a single Aganagic-Vafa brane. Here I'll show a priori (i.e. without first computing the invariants), that the partition function satisfies an operator equation, given by a skein-valued quantization of the mirror curve. Said equation gives a recursion which can be solved explicitly. [This talk presents joint work with Tobias Ekholm.]