BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marcus Marrocos (Universidade Federal do Amazonas) DTSTART:20260211T160000Z DTEND:20260211T170000Z DTSTAMP:20260423T052923Z UID:VSGS/123 DESCRIPTION:Title: O n the generic irreducibility of the spectrum of the Laplacian on homogeneo us spaces.\nby Marcus Marrocos (Universidade Federal do Amazonas) as p art of Virtual seminar on geometry with symmetries\n\n\nAbstract\nWe discu ss the generic irreducibility of Laplace eigenspaces on compact homogeneou s spaces $M=G/K$ with $G$-invariant metrics. While Uhlenbeck’s theorem s uggests that\, for generic metrics\, Laplace eigenvalues are simple\, $G$- invariance forces multiplicities. Since each eigenspace carries a natural representation of $G$\, the appropriate substitute is representation-theor etic simplicity: each eigenspace should be an irreducible $G$-module. Buil ding on Schueth’s viewpoint for compact Lie groups with left-invariant m etrics\, we present the framework developed for homogeneous spaces\, empha sizing the results of Petrecca--Röser and the remarks in de Oliveira--Mar rocos on real versus complex irreducibility and on structural sources of e igenvalue collisions in higher rank. We conclude with a discrete analogue: generic spectra of weighted Laplacians on Cayley graphs.\n LOCATION:https://researchseminars.org/talk/VSGS/123/ END:VEVENT END:VCALENDAR