Logarithm laws, diophantine approximation, and the geometry of numbers.
Jayadev Athreya (Yale)

In joint work with G. A. Margulis, we prove a logarithm law governing the cusp excursions of unipotent flows on non-compact homogeneous spaces, in particular, hyperbolic surfaces and the space of unimodular lattices in Euclidean space. Our main tool is a result of independent interest, a measurable analogue of the Minkowski convex body theorem. We also describe several connections to diophantine approximation.

Colloquium, Department of Mathematics, Rice University
September 25, 2008, 4-5PM HB 227

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