20150526-20150708Introuduction to Complex Geometry
Complex geometry has been a very active area in recent years. It has deep interactions with other areas, e.g. algebraic geometry, Riemannian geometry and math physics. Despite the recent enormous progress, there are still many interesting directions to explore. This course will serve as an introduction to complex geometry. We will cover the following topics: holomorphic functions of several variables on domains of $C^n$, complex manifolds, holomorphic vector bundles and Chern classes, Kahler metrics, sheafs and their cohomology,Hodge theory, the Riemann-Roch theorem (proof for Riemann surfaces), the L^2 estimates and applications.