BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Samuel Z. Lin (Dartmouth College) DTSTART:20210127T190000Z DTEND:20210127T200000Z DTSTAMP:20260423T021217Z UID:VSGS/20 DESCRIPTION:Title: Ge ometric Structure and the Laplace Spectrum\nby Samuel Z. Lin (Dartmout h College) as part of Virtual seminar on geometry with symmetries\n\n\nAbs tract\nThe Laplace spectrum of a compact Riemannian manifold is defined to be the set of positive eigenvalues of the associated Laplace operator. In verse spectral geometry is the study of how this set of analytic data rela tes to the underlying geometry of the manifold.\n\nA (compact) geometric s tructure is defined to be a compact Riemannian manifold equipped with a lo cally homogeneous metric. Geometric structures played an important role in the study of two and three-dimensional geometry and topology. In dimensio n two\, the only geometric structures are those of constant curvature. Fur thermore\, Berger showed that they are determined up to local isometries b y their Laplace spectra.\n\nIn this work\, we study the following question : “To what extend are the three-dimensional geometric structures determi ned by their Laplace spectra?” Among other results\, we provide strong e vidence that the local geometry of a three-dimensional geometric structure is determined by its Laplace spectrum\, which is in stark contrast with r esults in higher dimensions. This is a joint work with Ben Schmidt (Michig an State University) and Craig Sutton (Dartmouth College).\n LOCATION:https://researchseminars.org/talk/VSGS/20/ END:VEVENT END:VCALENDAR