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UID:20251102T201122EST-69871HgVWK@132.216.98.100
DTSTAMP:20251103T011122Z
DESCRIPTION:Title: Maximizing Laplace eigenvalues with density in higher di
 mensions\n\nAbstract: We will discuss the problem of maximizing the k-th L
 aplace eigenvalue with density on a closed Riemannian manifold of dimensio
 n m ≥ 2. The Euler–Lagrange equation identifies critical densities with th
 e energy densities of harmonic maps into spheres\, linking spectral optimi
 zation to harmonic-map theory. Unlike the case m = 2\, where a priori mult
 iplicity bounds yield existence and regularity\, higher dimensions allow u
 nbounded multiplicities.\n\nIn the talk\, we will present topological tens
 or products techniques that handle this setting and prove the existence of
  maximizing densities for all m ≥ 3. For regularity\, optimizers are smoot
 h away from a singular set\; when m ≥ 7\, this set can have any prescribed
  integer dimension up to m − 7\, as we will illustrate with examples on th
 e m-sphere. These techniques have potential for other eigenvalue-optimizat
 ion problems in higher dimensions where unbounded multiplicities arise.\n
 \nReferences: \n\nD. Vinokurov\, Maximizing higher eigenvalues in dimensio
 ns three and above\, preprint\, arXiv:2506.09328 [math.SP] (2025).\n\nJoin
  Zoom Meeting\n\nhttps://umontreal.zoom.us/j/89528730384?pwd=IF10Cg8C0Yfog
 aBlL6F1NboPaQvAaV.1\n\nMeeting ID: 895 2873 0384\n\nPasscode: 077937\n
DTSTART:20251031T180000Z
DTEND:20251031T190000Z
SUMMARY:Denis Vinokurov (Université de Montréal)
URL:/mathstat/channels/event/denis-vinokurov-universit
 e-de-montreal-368611
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