Abstract
Algebraic geometry involves very different mathematical fields, such as topology, analytic geometry and differential geometry. Claire Voisin's lesson covers several notions of complex geometry (holomorphic functions, algebraic varieties, local maps) and topology (singular homology, bundle theory), as well as her area of specialization: Hodge theory. A decisive tool for studying the topology of algebraic varieties, this theory is the framework for one of the seven mathematical challenges of the millennium posed by the Clay Mathematical Institute in 2000.
