Hausdorff dimension estimates for bounded orbits on homogeneous spaces of Lie groups

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• Kleinbock, D (Brandeis University)
• Thursday 03 July 2014, 13:30-14:20
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact Mustapha Amrani.

Interactions between Dynamics of Group Actions and Number Theory

This work is motivated by studying badly approximable vectors, that is, ${f x}in {f R}^{n$ such that $|q{f x} – {f p}| ge cq}{-1/n}$ for all ${f p}in {f Z}^n$, $qin {f N}$. Computing the Hausdorff dimension of the set of such ${f x}$ for fixed $c$ is an open problem. I will present some estimates, based on the interpretation of a badly approximable vector via a trajectory on the space of lattices, and then use exponential mixing to estimate from above the dimension of points whose trajectories stay in a fixed compact set. Joint work with Ryan Broderick.

This talk is part of the Isaac Newton Institute Seminar Series series.

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