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SUMMARY:Mary Sandoval (Trinity College)
DTSTART:20230517T220000Z
DTEND:20230517T230000Z
DTSTAMP:20260423T021239Z
UID:VSGS/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VSGS/73/">De
 tecting Orbifold Singularities via the Orbifold Length Spectra</a>\nby Mar
 y Sandoval (Trinity College) as part of Virtual seminar on geometry with s
 ymmetries\n\n\nAbstract\nIn this talk\, we will consider the geodesic flow
  on a compact Riemannian orbifold $\\mathcal{O}$. Assuming the set of clos
 ed geodesics on the orbifold is non-empty\, we consider the following ques
 tion:  Is it possible to detect orbifold singularities via the length spec
 trum of $\\mathcal{O}$ and the length spectrum of the associated orthonorm
 al frame bundle of the orbifold? The answer is a qualifed yes\, provided t
 hat the closed geodesic flow on $\\mathcal{O}$ intersects with the singula
 r set of the orbifold\, and the non-trivial isotropy group of the singular
 ity ``closes up" the geodesic. Assuming these conditions are satisfied\, w
 e consider a second question: Given a singularity on a closed geodesic\, w
 hat aspects of the isotropy group can be determined by the dynamics of the
  geodesic flow for closed geodesics that pass through the singularity? Par
 tial results to this second question will be discussed. The proofs will us
 e some recent results from the spectral theory of leaf spaces of regular a
 nd singular Riemannian foliations.\n
LOCATION:https://researchseminars.org/talk/VSGS/73/
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