ABSTRACTS

Anatole Katok: Measure rigidity and Diophantine approximation.

                (Abstract TBA)

Akshay Venkatesh: Arithmetic aspects of the geodesic flow on the modular surface.

The (mainly expository) talk will be an account of a theorem of W. Duke from the 1980s. This result describes the distribution of
certain closed geodesics on the "modular surface", and is closely tied to both classical questions and modern results in analytic number theory.   As time permits,  we shall discuss a proof using dynamical ideas,  and discuss a few generalizations of the result.
 

Manfred Einsiedler: The distribution of ideal classes in SL(3,Z)\SL(3,R).
 

We will discuss how ideal classes in totally real number fields give rise to compact orbits of the diagonal subgoup acting on
SL(3,Z)\SL(3,R). Conjecturably this connection should imply that one can improve (the constant in) Minkowski's theorem on representing ideal classes by ideals of bounded norm. We show how the partial measure classification by A.Katok, E.Lindenstraus, and myself can be used to prove special cases of this conjecture by establishing a link between the discriminant and regulator of the field and the entropy of a limit measure. This is joint work with E.Lindenstrauss, Ph.Michel, and A.Venkatesh.