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Group Actions and Automorphic Forms

Fall 2008

Day changes!

Nov 4, Tue

  Fine 110
Yves Benoist
Université Paris-Sud
Invariant subsets of homogeneous spaces.
I will explain a joint work with J.F. Quint. Let G be a simple Lie group, X be a G-homogeneous space with finite G-invariant measure, and H be a Zariski dense subgroup of G. Then every H-invariant subset of X is either finite or dense. Moreover, the Haar probability on X is the only atom-free H-invariant probability on X. The proof uses random walks on X.
Nov 24, Mon

   Fine 601
Nimish Shah
Yale University
Limits of translates of curves on homogeneous spaces and Dirichlet's theorem on Diophantine approximation
By proving an equidistribution theorem for certain sequences of expanding translates of smooth measures on curves on homogeneous spaces of SL(n,R), we show that the Dirichlet's theorem on simultaneous diophantine approximation cannot be improved for related quantities in the sense of Davenport and Schmidt.
Dec 2, Tue

   Fine 801
Hee Oh
Brown University
On counting Apollonian circles of bounded curvature
I will talk about an asymptotic formula for the number of circles of curvature at most T in a given bounded Apollonian circle packing.
Dec 8

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