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SUMMARY:Jonas Henkel (University of Marburg)
DTSTART:20261104T160000Z
DTEND:20261104T170000Z
DTSTAMP:20260714T040434Z
UID:VSGS/134
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VSGS/134/">T
 he Spectrum of the Laplacian under Deformations of Homogeneous Metrics</a>
 \nby Jonas Henkel (University of Marburg) as part of Virtual seminar on ge
 ometry with symmetries\n\n\nAbstract\nThe spectrum of the Laplace-Beltrami
  operator is a key geometric feature of a compact Riemannian manifold\, re
 flecting the subtle connections between analysis\, geometry\, and symmetry
 . While classical representation-theoretic methods yield explicit formulas
  for symmetric and normal homogeneous spaces via the Casimir operator\, co
 ntinuous metric deformations typically break these standard algebraic stru
 ctures. \n\nIn this talk\, we discuss a framework to compute the Laplace-B
 eltrami spectrum under multi-parameter deformations\, focusing on canonica
 l variations of homogeneous principal bundles. By algebraically realizing 
 these deformed metrics as naturally reductive spaces on larger product gro
 ups\, we reduce the analytical eigenvalue problem to a tractable algebraic
  branching problem. We apply this method to derive explicit formulas for t
 he spectra of the classical families of homogeneous $3$-$(\\alpha\,\\delta
 )$-Sasaki manifolds and Stiefel manifolds. Finally\, we illustrate how the
 se explicit formulas can be used to study variational problems in global a
 nalysis\, such as the linear stability of the associated Einstein metrics 
 under Perelman's $\\nu$-entropy and the occurrence of symmetry-breaking Ya
 mabe bifurcations. \n\nThis is joint work with Ilka Agricola and Leandro C
 agliero.\n
LOCATION:https://researchseminars.org/talk/VSGS/134/
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