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SUMMARY:Emmett Wyman (Rochester)
DTSTART:20211028T151500Z
DTEND:20211028T161500Z
DTSTAMP:20260423T024518Z
UID:HASS21/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HASS21/5/">E
 igenfunctions restricted to submanifolds and their Fourier coefficients</a
 >\nby Emmett Wyman (Rochester) as part of Harmonic Analysis and Symmetric 
 Spaces 2021\n\n\nAbstract\nConsider a Laplace-Beltrami eigenfunction on so
 me compact manifold\, and restrict it to a compact submanifold. We may wri
 te the restricted eigenfunction as a combination of eigenbasis elements in
 trinsic to the submanifold\, whose coefficients we will call Fourier coeff
 icients. What does the spectral decomposition of the restricted eigenfunct
 ion look like? How much of the mass of the Fourier coefficients is concent
 rated near the eigenvalue? Do the Fourier coefficients "feel" the geometry
  of the submanifold or ambient manifold? If so\, how?\n\nI will present jo
 int work with Yakun Xi and Steve Zelditch on such questions. Indeed\, vari
 ous aspects of these Fourier coefficients reflect the geometry of the subm
 anifold and ambient space. Of particular importance are configurations of 
 "geodesic bi-angles\," which consist of a pair of geodesics\, one in the a
 mbient manifold and one intrinsic to the submanifold\, with shared endpoin
 ts. These bi-angles arise in the wavefront set analysis a la the Duisterma
 at-Guillemin theorem.\n
LOCATION:https://researchseminars.org/talk/HASS21/5/
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