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SUMMARY:Ilya Khayutin (Northwestern University)
DTSTART:20211202T171500Z
DTEND:20211202T183000Z
DTSTAMP:20260423T021900Z
UID:NEDNT/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/36/">T
 wo-step equidistribution for bi-quadratic torus packets</a>\nby Ilya Khayu
 tin (Northwestern University) as part of New England Dynamics and Number T
 heory Seminar\n\nLecture held in Online.\n\nAbstract\nA major challenge to
  the asymptotic analysis of a sequence of probability measures on a homoge
 neous space\, invariant under diagonalizable groups\, is the possibility o
 f accumulation on intermediate homogeneous subspaces. In this aspect highe
 r rank homogeneous flows cannot be expected to share the rigidity properti
 es of unipotent ones. In particular\, the linearization technique fails fo
 r diagonalizable flows. \n\nIn a joint work in progress with A. Wieser we 
 show how in favorable situations one can actually use the existence of int
 ermediate homogeneous spaces in our benefit. We show that periodic measure
 s on some packets of periodic torus orbits on PGL4(Z)\\PGL4(R) converge in
  the limit to a measure with a non-trivial Haar component. The proof goes 
 by establishing high entropy for the limit measure. The method utilizes th
 e intermediate homogeneous space to split the analysis into two more tract
 able steps.\n
LOCATION:https://researchseminars.org/talk/NEDNT/36/
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