## Main lectures (July 06-10)

### Aspects of homological mirror symmetry (Paul Seidel). 5 lectures.

**LECTURE 1. Lefschetz fibrations and mirror symmetry.**
Directed Fukaya categories. Exceptional collections. Provisional definition of
homological mirror symmetry. The action of the braid group. Derived categories. Better
definition of homological mirror symmetry.

**LECTURE 2. Examples.**
The projective line and plane. Orbifold versions. Additional examples as
time permits, e.g. the Hannay-Vegh quiver description.

** LECTURE 3. Additional algebraic structures.**
Modules and bimodules over A-infinity algebras. The Serre functor. Fukaya categories
reconsidered. The mirror symmetry interpretation.

**LECTURE 4. Holomorphic curves in Lefschetz fibrations.**
Floer cohomology of Lefschetz thimbles. The Fukaya category of the Lefschetz fibration.
Geometric meaning of the Serre functor.

**LECTURE 5. Wrapped Floer cohomology**
Definition. Wrapped Floer cohomology for Lefschetz thimbles. Mirror-symmetric
interpretation. Maydanskiy's examples of Stein manifolds, and others.

### Wrapped Floer homology (Mohammed Abouzaid). 3 lectures.

### Lagrangian torus fibrations and mirror symmetry (Denis Auroux). 3 lectures.

### Homological mirror symmetry for the four-torus (Ivan Smith). 3 lectures.

### Involutions, obstructions, and mirror symmetry (Jake Solomon). 3 lectures.

## Precourse: July 4-5

**1. Lefschetz fibrations, vanishing cycles, directed Fukaya categories (Mark McLean)
**

2. Derived categories of coherent sheaves (Marc Nieper-Wisskirchen)

**
3. A-infinity structures (Janko Latschev)
**