The topology of algebraic varieties
Claire Voisin (Collège de France)
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.