BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Elizabeth Stanhope (Lewis & Clark College) DTSTART:20250611T160000Z DTEND:20250611T170000Z DTSTAMP:20260423T021403Z UID:VSGS/110 DESCRIPTION:Title: U sing Hodge spectra to detect orbifold singularities\nby Elizabeth Stan hope (Lewis & Clark College) as part of Virtual seminar on geometry with s ymmetries\n\n\nAbstract\nA Riemannian orbifold is a mildly singular genera lization of a Riemannian manifold. A fundamental question in the Laplace s pectral geometry of Riemannian orbifolds is whether or not a singular orbi fold can be isospectral to a manifold. This question is open for the spect rum of the Laplacian acting on functions. We will see that combining infor mation from the spectrum of the Laplacian on functions with information fr om the spectrum of the Hodge Laplacian on 1-forms allows us to detect orbi fold singularities in some cases. For example\, a singular Riemannian orb ifold of dimension 3 or less cannot be both 0 and 1-isospectral to a Riema nnian manifold. The proof relies on the heat invariants associated to the $p$-spectrum of the corresponding Hodge Laplacian. We will also discuss a few inverse spectral results for the individual $p$-spectra themselves.\n LOCATION:https://researchseminars.org/talk/VSGS/110/ END:VEVENT END:VCALENDAR