Marco Gualtieri, University of Toronto
"From generalized Kahler geometry to noncommutative algebra"
The celebrated Kodaira embedding theorem explains how and when compact Kahler manifolds, transcendental objects of study in complex and Riemannian geometry, give rise to projective algebraic varieties, which may be characterized purely algebraically. Ever since Hitchin's introduction of generalized Kahler geometry 15 years ago, it has been believed that a similar relationship should exist between generalized Kahler manifolds, which are deformations of Kahler manifolds in a certain sense, and noncommutative algebraic varieties. I will explain a sequence of ideas, heavily relying on notions from geometric quantization and from symplectic groupoids, which allow us to realize this belief, at least in some interesting cases.