February 15-17, 2005 -- Marco Gualtieri (Fields):
'Generalized geometric structures'
Generalized complex geometry is a unification of complex and symplectic geometry, and provides a geometrical context for understanding parts of mirror symmetry. In these lectures I will provide an introduction to generalized complex, Kahler, and related geometries, and describe some of their appearances in physics.
Course start times
Feb. 15, 11am
Feb. 16 11am
Feb. 17 11am

February 15 -17, 2005 -- Yi Li (Caltech):
'Twisted Generalized Calabi-Yau Manifolds and Topological Sigma Models with Flux'
In these lectures, we examine how twisted generalized Calabi-Yau (GCY) manifolds arise in the construction of a general class of topological sigma models with non-trivial three-form flux. The topological sigma model defined on a twisted GCY can be regarded as a simultaneous generalization of the more familiar A-model and B-model. Emphasis will be given to the relation between topological observables of the sigma model and a Lie algebroid cohomology intrinsically associated with the twisted GCY. If time permits, we shall also discuss topological D-branes in this more general setting, and explain how the viewpoint from the Lie algebroid helps to elucidate certain subtleties even for the conventional A-branes and B-branes. The lectures will be physically motivated, although I will try to make the presentation self-contained for both mathematicians and physicists.
Course start times
Feb. 15, 2 pm
Feb. 16 3:30pm
Feb. 17 2pm

March 1-3, 2005 -- 11 a.m. Rm 405, Perimeter Institute
Mariana Grana (Ecole Polytechnique & Ecole Normale Superieure)
'Supergravity Backgrounds from Generalized Calabi-Yau Manifolds'
We will see how generalized Calabi-Yau manifolds as defined by Hitchin emerge from supersymmetry equations in type II theories. In the first lecture, we will review the formalism of G-structures, which is central in the context of compactification with fluxes. In the second lecture we will see how (twisted) generalized Calabi-Yau manifolds emerge from supersymmetry equations using SU(3) structure. In the last lecture, we will discuss special features about compactifications on Generalized Calabi-Yau's.