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SUMMARY:Guofang Wei (University of California\, Santa Barbara)
DTSTART:20221012T160000Z
DTEND:20221012T170000Z
DTSTAMP:20260423T021337Z
UID:VSGS/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VSGS/60/">Si
 ngular Weyl's law with Ricci curvature bounded below</a>\nby Guofang Wei (
 University of California\, Santa Barbara) as part of Virtual seminar on ge
 ometry with symmetries\n\n\nAbstract\nWeyl's law describes the asymptotic 
 behavior of eigenvalues of the Laplace Beltrami operator. Its study  has a
  long history and is important in mathematics and physics. In a joint work
  with J. Pan (GAFA 2022)\, using equivariant convergence\, we constructed 
 first examples of Ricci limit spaces with symmetry whose Hausdorff dimensi
 on may not be an integer and the Hausdorff dim of the singular set is bigg
 er than the Hausdorff dim of the regular set. With in-depth study of metri
 c and measure of the examples\, and the delicate analysis of the heat kern
 els\, in a very recent joint work with X. Dai\, S. Honda\, J. Pan we show 
 the surprising results that for compact RCD(K\,N)/Ricci limit spaces\, Wey
 l's law may not hold for any power\, and in the case when power law holds\
 , it is in terms of the Hausdorff measure of the singular set instead of t
 he regular set.\n
LOCATION:https://researchseminars.org/talk/VSGS/60/
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