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The Fukaya category of the punctured torus

4:00 pm Thursday, January 20, 2011
Tim Perutz (UT Austin)

The Fukaya category of a symplectic manifold has long had a fearsome reputation: hard to define, impractical to compute. Work of Seidel gave both a precise definition and a means of computation. The area is now developing rapidly, with applications to concrete problems in symplectic topology. I'll describe as simply as I can what the Fukaya category is and what it is good for. As an example, I will outline joint work with Yanki Lekili which describes the Fukaya category of the punctured 2-torus, making connections both to 3-manifold topology (Heegaard Floer homology) and algebraic geometry (Weierstrass cubic curves). No knowledge of symplectic topology will be assumed.

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