Garrett Hinkley (UMass). Intro to Fukaya Categories of Surfaces.

Fukaya categories have gained recent interest due to their role in Kontsevich's homological mirror symmetry conjecture. They're hard to define in general, but in the case of surfaces, they can be defined purely combinatorially. We introduce Fukaya categories and Floer homology for symplectic surfaces and give some basic examples. If time permits, we will also discuss deformations of Lagrangian submanifolds and applications to algebraic geometry. This talk is intended to be elementary and accessible.