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比利时vs摩洛哥足彩 ,
university of california san diego

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special colloquium

steven sivek

princeton university

the augmentation category of a legendrian knot

abstract:

a well-known principle in symplectic geometry says that information about the smooth structure on a manifold should be captured by the symplectic geometry of its cotangent bundle. one prominent example of this is nadler and zaslow's microlocalization correspondence, an equivalence between a category of constructible sheaves on a manifold and a symplectic invariant of its cotangent bundle called the fukaya category. the goal of this talk is to describe a model for a relative version of this story in the simplest case, corresponding to legendrian knots in the standard contact 3-space. this construction, called the augmentation category, is a powerful invariant which is defined in terms of holomorphic curves but can also be described combinatorially. i will describe some interesting properties of this category and relate it to a category of sheaves on the plane. this is joint work with lenny ng, dan rutherford, vivek shende, and eric zaslow.

host: kiran kedlaya

january 12, 2016

3:00 pm

ap&m 6402

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