Introduction to Fukaya categories 1

Abstract: This minicourse will provide an introduction to Fukaya categories. I will assume that participants are also attending Keller's course on $\mathrm{A}_{\infty}$ categories.

Lecture 1: Basics of symplectic geometry for Fukaya categories. Symplectic manifolds; Lagrangian submanifolds; exactness conditions; almost complex structures; holomorphic maps; Maslov indices and gradings.

Lecture 2: Floer cohomology and the Fukaya category. Lagrangian intersection theory; Floer differential; $\mathrm{A}_{\infty}$ operations; Gromov compactification and $\mathrm{A}_{\infty}$ equations.

Lecture 3: Examples of Fukaya categories. The case of surfaces; other cases as time permits.

rings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the discipline

Winter School "Connections between representation theory and geometry"

Series comments: Please register at least two hours before the first talk of the day in order to get the access data in time.