Local spectral gap
Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015
Location: MSRI: Simons Auditorium
Kazhdan's property T
locally compact groups
discrete subgroups
Random walks
discrete group actions
compact Lie group
p-adic Lie group
22E40 - Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
22F10 - Measurable group actions [See also 22D40, 28Dxx, 37Axx]
14235
(Joint with R. Boutonnet, A. Ioana) The notion of local spectral gap for general measure preserving actions will be defined. We prove that the left translation action of a dense subgroup of a simple Lie group has local spectral gap if the subgroup has algebraic entries. This extends to the non-compact setting recent works of Bourgain-Gamburd and Benoist-de Saxce. We also extend Bourgain-Yehudayoff’s result. The application of this result to Banach-Ruziewicz problem, delayed random-walk, and monotone expanders will be explained.
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14235
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