Lectures and Precourse

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)