# Justin Sawon : Fourier-Mukai transforms and deformations in generalized complex geometry

Homological Mirror Symmetry proposes an equivalence between the derived category of coherent sheaves on a complex manifold and the (derived) Fukaya category of the mirror symplectic manifold. It is natural to consider the behaviour of these categories and equivalences under deformations of the underlying spaces.

In this talk I will describe Toda's results on deformations of the category Coh(X) of coherent sheaves on a complex manifold X. They come from deformations of X as a complex manifold, non-commutative deformations, and gerby deformations. These can all be interpreted as deformations of X as a generalized complex manifold; in some instances it is possible to deform X to a symplectic manifold. Toda also described how to deform Fourier-Mukai equivalences, and I will present some examples coming from mirror SYZ fibrations.

**Category**: Geometry and Topology**Duration**: 01:34:52**Date**: February 2, 2010 at 4:25 PM**Views**: 117-
**Tags:**seminar, Geometry/topology Seminar

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