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Geometry-Topology Seminar

Thursday, December 7, 2017 - 4:30pm

Yanki Lekili

King's College London


University of Pennsylvania


A symplectic manifold gives rise to a triangulated A-infinity category, the derived Fukaya category. Its construction was originally motivated in order to study the topology of Lagrangian submanifolds (and there is still much research in this direction).  More recently, Fukaya categories have become popular among algebraic geometers, algebraic topologists, representation theorists, physicists.... Much of this is motivated by homological mirror symmetry conjecture, but in a somewhat different direction there also is a deep connection to classical topology through the theory of microlocal sheaves (roughly, Morse theory on singular spaces) and Legendrian surgery. I will try to give a quick description of various flavors of Fukaya categories of interest, and give sample computations in order to demonstrate these connections.