Tuesday, February 19, 2008
4:15 PM -
5:15 PM
Thomas Wolff Memorial Lecture in Mathematics
Renormalization and Quasiperiodicity in Some Low-Dimensional Dynamical Systems
Andre Avila,
Laboratoire de Probabilites et Modeles Aleatoires,
Speaker's Bio:
Artur Avila was born in 1979 in Rio de Janeiro and got his PhD in 2001 at IMPA, as a student of Welington de Melo. He was a post-doc at the Collège de France for two years before becoming a CNRS researcher at the Laboratoire de Probabilités et Modèles Aléatoires in Paris. He holds a Clay Research Fellowship from July 2006 to June 2009 and is currently at IMPA. Avila gave a Cours Peccot" at the Collège de France in 2005 and has been awarded the Bronze Medal of the CNRS and the Salem Prize for his work on Lyapounov exponents and quasiperiodic behaviour in unimodal maps, Schrödinger-like cocycles, interval exchange maps and Teichmüller flows". Avila's work typically combines dynamical intuition with techniques from probability, combinatorics and complex analysis. His sequence of results on quasiperiodic cocycles with Raphaël Krikorian, Svetlana Jitomirskaya and David Damanik has led to the complete solution of three outstanding problems on the almost Mathieu operator in Barry Simon's list. Among his other main contributions, one finds results with Moreira and Lyubich concerning the statistical properties of unimodal maps and the Hausdorff dimension of Julia sets, and works with Forni and Viana on the mixing properties of interval exchange transformations and the Lyapunov exponents of the the Teichmüller flow which aswered conjectures of Veech and Kontsevich-Zorich.
Artur Avila was born in 1979 in Rio de Janeiro and got his PhD in 2001 at IMPA, as a student of Welington de Melo. He was a post-doc at the Collège de France for two years before becoming a CNRS researcher at the Laboratoire de Probabilités et Modèles Aléatoires in Paris. He holds a Clay Research Fellowship from July 2006 to June 2009 and is currently at IMPA. Avila gave a Cours Peccot" at the Collège de France in 2005 and has been awarded the Bronze Medal of the CNRS and the Salem Prize for his work on Lyapounov exponents and quasiperiodic behaviour in unimodal maps, Schrödinger-like cocycles, interval exchange maps and Teichmüller flows". Avila's work typically combines dynamical intuition with techniques from probability, combinatorics and complex analysis. His sequence of results on quasiperiodic cocycles with Raphaël Krikorian, Svetlana Jitomirskaya and David Damanik has led to the complete solution of three outstanding problems on the almost Mathieu operator in Barry Simon's list. Among his other main contributions, one finds results with Moreira and Lyubich concerning the statistical properties of unimodal maps and the Hausdorff dimension of Julia sets, and works with Forni and Viana on the mixing properties of interval exchange transformations and the Lyapunov exponents of the the Teichmüller flow which aswered conjectures of Veech and Kontsevich-Zorich.
"Renormalization and Quasiperiodicity in Some Low-Dimensional Dynamical Systems," Andre Avila, Laboratoire de Probabilites et Modeles Aleatoires.
Event Sponsors:
For more information, please contact stacey croomes by phone at 626-395-4335 or by email at [email protected] or visit http://math.caltech.edu/events/wolff08.html.