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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 Golsefidy (University of California, San Diego)
Location: SLMath: Eisenbud Auditorium
Tags/Keywords

  • Kazhdan's property T

  • locally compact groups

  • discrete subgroups

  • Random walks

  • discrete group actions

  • compact Lie group

  • p-adic Lie group

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14235
Abstract

(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. 
Supplements
23519?type=thumb Golesefidy. Notes 157 KB application/pdf Download
Video/Audio Files

14235

H.264 Video 14235.mp4 342 MB video/mp4 rtsp://videos.msri.org/data/000/023/430/original/14235.mp4 Download
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