**UM Math Graduate Student Seminar**

August Hozie*University of Miami ***will present**

**A Gentle Intro to Fukaya Categories**

Friday, September 14th, 2018, 5:00pm

Ungar Building Room 402**Abstract:**

The Fukaya Category is a fundamental piece of Homological

Mirror Symmetry, a program which seeks to relate the symplectic geometry

of a manifold to the category of coherent sheaves on its conjectured

"mirror". It's construction, in general, is complicated and requires

intimate use of the symplectic geometry of the manifold. However in

real-dimension 2 much of this data can be packaged in the so-called

Topological Fukaya Category of Abouzaid, which has considerably simpler

structure. We will review this construction, and how it serves as a nice

example of the general notion of an A-infinity (pre-)Category.