Abstract:

Beginning with Riemann, geometers have studied the question of finding all possible complex structures on a given differentiable manifold. After Deligne, the Betti cohomology of a compact Kahler manifold comes equipped with a (pure) Hodge structure. Hence, one is naturally led to the study of variation of these Hodge structures as the complex structure is changed.

In the lecture I will try to expound on the above ideas.