Homogeneous Flows, Moduli Spaces and Arithmetic

11 June 2007 - 6 July 2007

This event is part of an intensive research period:
Dynamical Systems and Number Theory.

Aims

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, 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. Furthermore, understanding the dynamics of such concrete system 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 foundational courses and one week of mini-courses focusing on more advanced topics. Foundational Courses The following 3 week lecture series will be held:

"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

Shorter courses will be given by Svetlana Katok and Shahar Mozes. Advanced minicourse will be given by Nalini Anantharaman, Artur Avila, Hee Oh, Akshay Venkatesh and others.