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SUMMARY:Spectral Cluster Bounds for Orthonormal Functions - Jean-Claude Cu
 enin (Loughborough University)
DTSTART:20260116T114500Z
DTEND:20260116T124500Z
UID:TALK242014@talks.cam.ac.uk
DESCRIPTION:In this talk\, we will consider Lq bounds for spectral cluster
 s (linear combinations of eigenfunctions) of the Laplace-Beltrami operator
  on a compact manifold. These bounds are classical for a single cluster. W
 e will consider N orthonormal clusters and seek bounds on the Lq norm of t
 heir square function. The main challenge is to obtain an optimal dependenc
 e on N. The results have applications to the spectral theory of Schrodinge
 r operators and to Kakeya-type problems. The talk is based on joint work w
 ith Nhi Nguyen and Xiaoyan Su.
LOCATION:Seminar Room 1\, Newton Institute
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