Lectures on generalized complex geometry for physicists

Lectures on complex geometry, Calabi–Yau manifolds and toric geometry

These are introductory lecture notes on complex geometry, Calabi–Yau manifolds and toric geometry. We first define basic concepts of complex and Kähler geometry. We then proceed with an analysis of various definitions of Calabi–Yau manifolds. The last section provides a short introduction to toric geometry, aimed at constructing Calabi–Yau manifolds in two different ways; as hypersurfaces in to...

Lectures on Symplectic Geometry

Lectures on Geometry

Lectures on Noncommutative Geometry

These Lectures are based on a course on noncommutative geometry given by the author in 2003. The lectures contain some standard material, such as Poisson and Gerstenhaber algebras, deformations, Hochschild cohomology, Serre functors, etc. We also discuss many less known as well as some new results such as noncommutative Chern-Weil theory, noncommutative symplectic geometry, noncommutative diffe...

Lectures on Kähler Geometry