##### Department of Mathematics,

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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