BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:James Kennedy (University of Lisbon) DTSTART:20201119T160000Z DTEND:20201119T170000Z DTSTAMP:20260423T004514Z UID:MPHA/21 DESCRIPTION:Title: Sp ectral partitions of metric graphs\nby James Kennedy (University of Li sbon) as part of TAMU: Mathematical Physics and Harmonic Analysis Seminar\ n\n\nAbstract\nWe introduce a theory of partitions of metric graphs via sp ectral-type functionals\, inspired by the theory of spectral minimal parti tions of domains but also with a view to understanding how to detect "clus ters" in metric graphs.\n\nThe goal is to associate with any given partiti on a spectral energy built around eigenvalues of differential operators li ke the Laplacian\, and then minimize (or maximize) this energy over all ad missible partitions. Since metric graphs are essentially one-dimensional m anifolds with singularities (the vertices)\, the range of well-posed probl ems is much greater than on domains. We first sketch a general existence t heory for optimizers of such partition functionals\, and discuss a number of natural functionals and optimization problems.\n\nWe also illustrate ho w changing the functionals and the classes of partitions under considerati on -- for example\, imposing Dirichlet versus standard conditions at the c ut vertices or considering min-max versus max-min type functionals -- may lead to qualitatively different optimal partitions which seek out differen t features of the graph.\n\nFinally\, we show how for many problems the op timal energies behave very similarly to the eigenvalues of the Laplacian ( with Dirichlet or standard vertex conditions)\, in terms of Weyl asymptoti cs\, upper and lower bounds\, and interlacing inequalities.\n\nThis is bas ed on joint works with Matthias Hofmann\, Pavel Kurasov\, Corentin Léna\, Delio Mugnolo and Marvin Plümer.\n LOCATION:https://researchseminars.org/talk/MPHA/21/ END:VEVENT END:VCALENDAR