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UID:20260416T211926EDT-9368l6aCvF@132.216.98.100
DTSTAMP:20260417T011926Z
DESCRIPTION:Title: The Two-Point Weyl Law on Manifolds without Conjugate Po
 ints\n\n\n	Abstract: In this talk\, we discuss the asymptotic behavior of t
 he spectral function of the Laplace-Beltrami operator on a compact Riemann
 ian manifold $M$ with no conjugate points. The spectral function\, denoted
  $\Pi_\lambda(x\,y)\,$ is defined as the Schwartz kernel of the orthogonal
  projection from $L^2(M)$ onto the eigenspaces with eigenvalue at most $\l
 ambda^2$. In the regime where $(x\,y)$ is restricted to a sufficiently sma
 ll neighborhood of the diagonal in $M\times M$\, we obtain a uniform logar
 ithmic improvement in the remainder of the asymptotic expansion for $\Pi_\
 lambda$ and its derivatives of all orders. This generalizes a result of B\
 'erard which established an on-diagonal estimate for $\Pi_\lambda(x\,x)$ w
 ithout derivatives. Furthermore\, when $(x\,y)$ avoids a compact neighborh
 ood of the diagonal\, we obtain the same logarithmic improvement in the st
 andard upper bound for the derivatives of $\Pi_\lambda$ itself. We also di
 scuss an application of these results to the study of monochromatic random
  waves.\n	\n	Zoom link: https://umontreal.zoom.us/j/81706136500?pwd=UVFZeXhW
 d1RpY29GeE1nS2RkK0V3Zz09\n\nMeeting ID: 817 0613 6500\n\nPasscode: 872949
 \n	 \n
DTSTART:20220408T183000Z
DTEND:20220408T193000Z
SUMMARY:Blake Keeler (McGill University)
URL:https://www.mcgill.ca/mathstat/channels/event/blake-keeler-mcgill-unive
 rsity-338907
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