BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sebastian Egger (Technion) DTSTART:20201029T150000Z DTEND:20201029T160000Z DTSTAMP:20260423T021706Z UID:MPHA/20 DESCRIPTION:Title: We ll-defined spectral position for Neumann domains\nby Sebastian Egger ( Technion) as part of TAMU: Mathematical Physics and Harmonic Analysis Semi nar\n\n\nAbstract\nA Laplacian eigenfunction on a two-dimensional Riemanni an manifold provides a natural partition generated by specific gradient fl ow lines of the eigenfunction. The restricted eigenfunction onto the parti tion's components satisfies Neumann boundary conditions and the components are therefore coined 'Neumann domains'. Neumann domains represent a compl ementary path to the famous nodal-domain partition to study elliptic eigen functions where the latter is associated with the Dirichlet Laplacian. A v ery basic but fundamental property of nodal domains is that the restricted eigenfunction onto a nodal domain always gives the ground-state of the Di richlet Laplacian. That feature becomes significantly more complex for Neu mann domains due to the presence of possible cusps and cracks. In this tal k\, we focus on this problem and show that the spectral position for Neuma nn domains is well-defined. Moreover\, we provide explicit examples of Neu mann domains displaying a fundamentally different behavior in their spectr al position than their nodal-domain counterparts.\n LOCATION:https://researchseminars.org/talk/MPHA/20/ END:VEVENT END:VCALENDAR