Anton Kapustin

A-branes and noncommutative geometry.


We describe how noncommutative geometry arises in the study of topological D-branes. In particular, we show that in certain cases the category of A-branes on a Calabi-Yau manifold X can be related to the category of B-branes on a noncommutative deformation of X. This duality is distinct from mirror symmetry and can be regarded as a categorical generalization of the Seiberg-Witten transform which relates gauge theories on commutative and noncommutative tori. We sketch an application of this duality to the geometric Langlands correpondence.