250044 SE Low Dimensional Topology (2021S)

The aim of this reading course is to get acquainted with an invariant of symplectic manifolds called the Fukaya category and to describe a few applications of this invariant. This is a "category" whose objects are built from Lagrangian submanifolds and whose morphisms come from intersection points of these Lagrangians along with additional data.

In this reading seminar, we will try to understand the basics of Fukaya and we will study:
-A-infinity categories
-symplectic manifolds
-Floer homology
-Fukaya category
-and various applications of the Fukaya category in an understanding of knot invariants