The topology of algebraic varieties

Abstract

I will discuss how complex geometry interacts with topology  in the context of algebraic geometry (the study of varieties defined by algebraic equations). This is a subject which goes back to  Abel and Riemann, but has been developed  since the 1970's on the basis of the work of Hodge and Kodaira. Following Griffiths and Deligne, Hodge theory, or the theory of Hodge structures, appeared as the right tool  to make a general theory of higher dimensional "periods", allowing to study the topology of complex algebraic manifolds and their deformations.