From Analysis situs to the theory of periods
Channel: Institut Henri Poincaré
Date: 2013-05-28

By Claire Voisin
Abstract: The talk will focus on the pairing between singular homology and de Rham cohomology: Combinatorics of cells of a triangulation on one side, differential forms on the other side. The two aspects of the subject were already present in Poincaré's work, but the fact that this pairing is perfect has been proved much later by de Rham. De Rham's comparison theorem is not the end but the beginning of the story. Indeed, the two sides compute cohomology with different coefficients: In particular, in the context of algebraic geometry, the de Rham side is sensitive to the definition field of the variety, while the singular or Betti side sees the cohomolgy with integral coefficients. This leads to the modern theory of periods, and rises arithmetic questions related to the Hodge conjecture.Note(s) Biographique(s)
Directrice de recherche à l'Institut de Mathématiques de Jussieu, Claire Voisin est diplômée de l'ENS où elle passera sa thèse en 1986, la même année où elle intègrera le CNRS.
Elle obtiendra d'ailleurs en 1988 la médaille de bronze du CNRS, et par la suite divers prix incluant le "Clay research award" en 2008.
Depuis 2010 elle est membre de l'Académie des Sciences.
Réalisation : Quentin Lazzarotto
Date : 23/11/2012
Lieu : Institut Henri Poincaré