Bramham Barney "Poincaré's last geometric theorem: a 21st century proof"

Résumé
Poincare's last legacy to mathematics, his ``last geometric theorem'' is now one of the more beautiful elementary statements in dynamical systems. Simple to state but tricky to prove, Poincare himself did not quite live long enough to see the problems' first solution in 1913 by the young American mathematician George Birkhoff. There are now many proofs of this problem and some fascinating generalizations.
In this talk I will explain the statement of the theorem and as a curiousity outline yet another proof. The argument I will describe relies on modern tools that were completely unavailable in Poincar\'e's day. But if we take the existence of these tools for granted, a simple picture emerges, which hopefully captures some of the geometric spirit of Poincar\'e's own methods.
Note(s) Biographique(s)
Barney Bramham obtient en 2008 son doctorat en mathématique à New York.
Il est actuellement membre de l'École de mathématiques à l'Institute for Advanced Study à Princeton.
Son domaine de recherche est la géométrie symplectique et de contact. En particulier sur les courbes pseudoholomorphic.
Barney Bramham s'intéresse également à la combinaison des outils symplectiques avec ceux des systèmes dynamiques pour explorerles questions où la dynamique hamiltonienne et la théorie ergodique lisse se chevauchent.
Réalisation : Quentin Lazzarotto
Date : 20/11/2012
Lieu : Institut Henri Poincaré