Generalized Kahler geometry

Course information

Code: MAT1312F
Instructor: Marco Gualtieri
Class schedule: W12-1 F10-12 BA6180
Evaluation: There will be some assignments and a project assigned by the instructor. Students in year > 2 of the PhD who wish to audit the course, please contact the instructor.

This will be an introductory graduate course in generalized geometry, with a special emphasis on generalized K\"ahler geometry. The main references for this class are the published papers on generalized complex and K\"ahler geometry, but we will also draw from more recent developments in the physics literature.

A basic familiarity with manifolds will be assumed; here is a list of topics which will be covered in the lecture course:

Gerbes, B-fields, and exact Courant algebroids;

Relation to sigma models in physics;

Linear algebra of a split-signature real bilinear form; pure spinors;

Generalized Riemannian structures and the generalized Hodge star;

Integrability, Dirac structures, Lie algebroids and bialgebroids;

Generalized complex structures; examples of such;

Generalized holomorphic bundles

Generalized K\"ahler geometry;

Hodge decomposition theorem for Generalized K\"ahler structures;

Equivalence theorem Generalized K\"ahler=Bihermitian

The generalized K\"ahler potential

Generalized K\"ahler reduction

The generalized K\"ahler–Ricci flow of Streets and Tian