December  9, 2023
Thematic Program on O-minimal Structures and Real Analytic Geometry
January-June 2009

Distinguished Lecture Series
Jean-Christophe Yoccoz, Collège de France

May 25-27, 2009
Uniformly hyperbolic SL(2,R) cocycles

Let N be an integer greater than 1. We will study the set of N-tuples (A1, A2,.., AN) of matrices in SL(2,R) such that the norm of words in A1, A2,.. AN (with no inverses allowed) grow exponentially with the length. This open set is well-understood when N=2; for instance, in this case, the set of connected components is naturally in 1-to-1 correspondence with rational numbers in (0,1). When N is at least 3, new phenomena occur , leading to several open questions. This is jointwork with Artur Avila and Jairo Bochi.

Jean-Christophe Yoccoz received the Agrégation de Mathématiques in 1977 in joint first position. He was a student of M. Herman and submitted his doctoral thesis in 1985. As a student of Herman, a leading word expert on dynamical systems, it was not surprising that Yoccoz would himself work on dynamical systems. In his thesis, Yoccoz improved theorems of his supervisor Herman by giving simpler proofs but also obtaining the same results under weaker hypotheses.

He was appointed as professor at the University of Paris-Sud (Orsay). He became a member of the Institut Universitaire de France and a member of the Unité Recherche Associé "Topology and Dynamics" of the Centre National de la Recherche Scientifique at Orsay.

At the International Congress of Mathematicians in Zurich in 1994, Yoccoz received his greatest honour for this work on dynamical systems when he was awarded a Fields Medal.

Speakers in the Distinguished Lecture Series (DLS) have made outstanding contributions to their field of mathematics. The DLS consists of a series of three one-hour lectures.

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