BIRS Workshop Lecture Videos
Fukaya categories and gentle algebras I Lekili, Yanki
I will review the combinatorial description of partially wrapped Fukaya categories of punctured surfaces due to Haiden-Katzarkov-Kontsevich and show how it provides a geometric model for the derived category of any graded gentle algebra. As an application, I will discuss my joint work with A. Polishchuk, which uses the action of the mapping class group to give sufficient numerical criteria for two gentle algebras to be derived equivalent. Time permitting, I will also discuss homological mirror symmetry for punctured surfaces which links this story to another geometric model of gentle algebras related to the derived categories associated to nodal stacky curves.
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