Andrei Caldararu (Spring 2017):

This course will be a gentle introduction to the ideas of homological mirror symmetry and curve counting invariants using homological algebra methods. Some of the topics that will be covered are

- A-infinity algebras
- Hochschild homology and cohomology
- operads
- Gerstenhaber and Batalin-Vilkovisky algebras
- Fukaya categories
- Kontsevich's Homological Mirror Symmetry conjecture
- Costello's constructions of Topological Field Theories from A-infinity algebras

The course should be reasonably self-contained, but a good knowledge of basic homological algebra will be very useful. Basic algebraic geometry will also be used, but is not absolutely necessary.

semester:

Spring

prereqs:

Math 750 or Math 763 are highly recommended