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.

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.

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.

TBA

Four dimensional N=4 super Yang-Mills theory contains a bigger superalgebra than AdS or superconformal algebra, su(2,2/4). It corresponds to a noncentral extension of the latter. The talk is for both physicsts and mathematicans interested in a novel way of obtaining noncentral extensions of Lie algebras.

Compact Calabi-Yau manifolds are a key ingredient for dimensional reduction in string theory. For this, one requires the Ricci-flat metric on these manifolds. Whilst Yau proved this metric exists, no explicit smooth examples are known, essentially as it is very difficult (impossible?) to find them analytically as they have no continuous isometries. Taking a new approach, I will discuss numerical methods to solve the Einstein equation on these manifolds. I will pedagogically describe the construction, and give results, for a particular one parameter family of metrics on K3 (the unique 4-dimensional Calabi-Yau manifold). I will discuss possible applications of these methods, and generalizations to geometries with matter such as those relevant for flux compactifications. There will be some nice pictures.