BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gunther Cornelissen (Utrecht University) DTSTART:20201207T121500Z DTEND:20201207T131500Z DTSTAMP:20260423T023043Z UID:WarsawNT/15 DESCRIPTION:Title: An analogy between number theory and spectral geometry\nby Gunther C ornelissen (Utrecht University) as part of Warsaw Number Theory Seminar\n\ n\nAbstract\nSunada’s construction of non-isometric\, isospectral manifo lds proceeds in the same way as Gassmann’s construction of non-isomorphi c number fields with the same zeta function\, using a group G with two non -conjugate subgroups H and K such that the permutation representations giv en by G acting on their cosets are isomorphic. In Gassmann’s example\, G was the permutation group on 6 letters and H and K the groups generated b y (12)(34) and (13)(24)\, and (12)(34) and (12)(56)\, respectively. These can be realized as covering groups of a compact Riemann surface of genus 2 . Recently\, the speaker and collaborators showed that isomophism of numbe r fields can be detected by equality of suitable L-series. This talk is ab out the finding the analogous result for manifolds. The result says that i f two manifolds are finite Riemannian covers of a developable orbifold\, a nd such that a certain homological condition is satisfied\, then the manif olds are isometric if and only if the spectra of finitely many Laplacians twisted by suitable unitary representations of the fundamental group are e qual. The result is explicit: in the above example\, one needs 56 spectral equalities corresponding to 180-dimensional representations. (Joint work with Norbert Peyerimhoff.)\n LOCATION:https://researchseminars.org/talk/WarsawNT/15/ END:VEVENT END:VCALENDAR