Clay Mathematics Institute

Dedicated to increasing and disseminating mathematical knowledge

Homogeneous Flows, Moduli Spaces and Arithmetic

June 11 - July 6, 2007

Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy

Organizers: David Ellwood, Manfred Einsiedler, Alex Eskin, Dmitry Kleinbock, Elon Lindenstrauss, Gregory Margulis, Stefano Marmi, Peter Sarnak, Jean-Christophe Yoccoz, Don Zagier

Designed for graduate students and mathematicians within five years of their PhD, the program is an introduction to the theory of flows on homogeneous spaces, moduli spaces, and their many applications.

These flows give concrete examples of dynamical systems with highly interesting behavior and a rich and powerful theory.  They are also a source of many interesting problems and conjectures.  Futhermore, understanding the dynamics of such concrete systems lends to numerous applications in number theory and geometry regarding equidistributions, diophantine approximations, rational billiards and automorphic forms.

The school will consist of three weeks of foundtional courses and one week of mini-courses focusing on more advanced topics.

Foundational Courses

Unipotent Flows and Applications
Alex Eskin, Dmitry Kleinbock

Diagonalizable Actions and Arithmetic Applications
Manfred Einsiedler, Elon Lindenstrauss

Interval Exchange Maps and Translation Surfaces
Jean-Christophe Yoccoz