MAT 620 Tuesday, Thursday 10:00am-11:30am, Physics P123

MAT 620:Topics in Topology: The Fukaya Category

Course Instructor: Mark McLean

Tuesday, Thursday 10:00am-11:30am, Physics P123

Introduction to the Course

The aim of this course is to introduce an invariant of a symplectic manifold 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 the first part of the course we will define Lagrangian Floer cohomology and give some dynamical applications of this invariant. After that we will define the Fukaya category in the simplest setting and state some additional properties. At the end of the course we will explain a couple of applications and also sketch some of the basic ideas behind homological mirror symmetry. This is an advanced course.

Prerequisites

You need to know some symplectic geometry and some complex geometry.

Office Hours:

Tuesday 2:30pm-3:30pm (Math 4-101B)
Wednesday 12pm-1pm (Math 4-101B)

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