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SUMMARY:Barak Weiss (Tel Aviv University)
DTSTART:20210208T171500Z
DTEND:20210208T183000Z
DTSTAMP:20260423T021322Z
UID:NEDNT/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/15/">C
 lassification and statistics of cut-and-project sets</a>\nby Barak Weiss (
 Tel Aviv University) as part of New England Dynamics and Number Theory Sem
 inar\n\nLecture held in Online.\n\nAbstract\nWe introduce a class of so-ca
 lled “Ratner-Marklof-Strombergsson measures”. These are probability me
 asures supported on cut-and-project sets in Euclidean space of dimension d
 >1 which are invariant and ergodic for the action of the groups ASL_d(R) o
 r SL_d(R) (affine or linear maps preserving orientation and volume). We cl
 assify the measures that can arise in terms of algebraic groups and homoge
 neous dynamics. Using the classification\, we prove analogues of results o
 f Siegel\, Weil and Rogers about a Siegel summation formula and identities
  and bounds involving higher moments. We deduce results about asymptotics\
 , with error estimates\, of point-counting and patch-counting for typical 
 cut-and-project sets. Joint work with Rene Ruehr and Yotam Smilansky.\n
LOCATION:https://researchseminars.org/talk/NEDNT/15/
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