Local spectral gap
Location: MSRI: Simons Auditorium
Kazhdan's property T
locally compact groups
discrete group actions
compact Lie group
p-adic Lie group
(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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