Dynamical Systems and Number Theory

16 April 2007 - 13 July 2007

Aims

The primary goal of this trimester is to provide a state of the art description of the subject of interaction between dynamics and number theory accessible both to young mathematicians wishing to do research in this area and to professional mathematicians from both disciplines interested in learning some of the most recent developments in the field.

Workshops

Renormalization small divisors continued fractions and geodesic flows. April 16-27, 2007 Continued fractions modular symbols periods of automorphic forms and theta functions. April 30 - May 11, 2007 Teichmueller dynamics. May 14 - June 1, 2007 Rigidity in dynamics and number theory. June 2-6, 2007

In the framework of the research programme, it will take place the Clay Research Summer School at the Centro di Ricerca Matematica "Ennio De Giorgi" (Pisa, Italy) June 11th to July 6th 2007

The Clay Mathematics Institute will conduct its annual summer school for 2007 at the De Giorgi Mathematics Research Center in Pisa, Italy, from June 11th to July 6th 2007. The topic is "Homogeneous flows, moduli spaces, and arithmetic." Designed for graduate students and mathematicians within five years of their Ph.D., the program is an introduction to the theory of flows on homogeneous spaces and moduli spaces. These flows define concrete dynamical systems whose complex and subtle behavior leads to a rich theory, many interesting problems and conjectures, and a wealth of applications to number theory and geometry, e.g., equidistribution, diophantine approximation, rational billiards, and automorphic forms.

The school will consist of three weeks of foundational courses and one week of mini-courses focusing on more advanced topics. During the first three weeks there will be three long courses, of 14 lectures each, by Alex Eskin and Dmitry Kleinbock, Jean-Christophe Yoccoz, Manfred Einsiedler and Elon Lindenstrauss.

Organizing Committee: Manfred Einsiedler (Ohio State University), David Ellwood (Clay Mathematics Institute), Alex Eskin (University of Chicago), Dmitry Kleinboc (Brandeis University), Elon Lindenstrauss (Princeton University), Gregory Margulis (Yale University), Stefano Marmi (Scuola Normale Superiore Pisa), Peter Sarnak (Princeton University), Jean-Christophe Yoccoz: (Collège de France), Don Zagier (Max Planck Institut, Bonn and Collège de France).