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Escape of mass for measures invariant under the diagonal group

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

May 13, 2015 (10:20 AM PDT - 11:10 AM PDT)
Speaker(s): Uri Shapira (Technion---Israel Institute of Technology)
Location: MSRI: Simons Auditorium
  • thin subgroup

  • discrete subgroups

  • SL(n-Z)

  • compact orbit

  • unimodular lattices

  • ergodic measure

  • convergence of measure

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



Let A denote the diagonal group in SL(n,R) acting on the space of unimodular lattices in R^n. In this talk I will explain a construction of a sequence of A-invariant ergodic probability measures (supported on compact A-orbits) which converge to the zero measure. In fact the "geometry" of these orbits will be described in some detail. 

23529?type=thumb Shapira.Notes 180 KB application/pdf Download
Video/Audio Files


H.264 Video 14243.mp4 292 MB video/mp4 rtsp://videos.msri.org/data/000/023/454/original/14243.mp4 Download
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