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SUMMARY:Tunneling and Weyl laws for the d-bar operator - Michael Hitrik  (
 University of California\, Los Angeles)
DTSTART:20260113T140000Z
DTEND:20260113T150000Z
UID:TALK238195@talks.cam.ac.uk
DESCRIPTION:We study the number of exponentially small singular values for
  the semiclassical d-bar operator on exponentially weighted L^2 spaces on 
 a compact Riemann surface. Accurate upper and lower bounds on the number o
 f such singular values are established with the help of auxiliary notions 
 of upper and lower bound weights. Assuming that the Laplacian of the expon
 ential weight changes sign along a curve\, we construct optimal such weigh
 ts by solving a free boundary problem\, which yields a Weyl asymptotics fo
 r the counting function of exponentially small singular values. We also pr
 ovide a precise description of the leading term in the Weyl asymptotics\, 
 in the regime of small exponential decay rates. This is joint work with Jo
 hannes Sjostrand and Martin Vogel.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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