Invariant subsets of homogeneous spaces

Yves Benoist

Université Paris-Sud 11

Brandeis University

Thursday, October 16, 2008

Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall

Abstract: Let G be a Lie group, X be a G-homogeneous space of finite volume, and H be a closed subgroup of G. What are the H-invariant probabilities on X? What are the H-invariant closed subsets in X?

I will first survey Ratner's results addressing the case when H is generated by unipotent elements. I will then focus on a joint work with J.F. Quint addressing the case when G is simple and H is Zariski dense. In this case, the Haar probability on X is the only atom-free H-invariant probability on X. Moreover every H-invariant subset of X is either finite or dense. The proof uses random walks on X.

Home Web page: Alexandru I. Suciu Posted: September 19, 2008
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