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Local spectral gap

Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015

May 11, 2015 (03:50 PM PDT - 04:40 PM PDT)
Speaker(s): Alireza Salehi Golsefidy (University of California, San Diego)
Location: MSRI: Simons Auditorium



(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. 

23519?type=thumb Golesefidy. Notes 157 KB application/pdf Download
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