GCOE lecture series

Seminar information archive ~07/13Next seminarFuture seminars 07/14~


2010/02/18

10:30-17:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yves Benoist (Pars Sud) 10:30-11:30
Discrete groups acting on homogeneous spaces III
[ Abstract ]
In this course I will focus on recent advances
on our understanding of discrete subgroups of Lie groups.

I will first survey how ideas from semisimple algebraic groups,
ergodic theory and representation theory help us to understand properties of these discrete subgroups.

I will then focus on a joint work with Jean-Francois Quint
studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:

We fix two integral matrices A and B of size d, of determinant 1,
and such that no finite union of vector subspaces is invariant by A and B.
We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
Yves Benoist (Paris Sud) 15:00-16:00
Discrete groups acting on homogeneous spaces IV