BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:André Oliveira (Univ. Porto) DTSTART:20210122T140000Z DTEND:20210122T150000Z DTSTAMP:20260423T010636Z UID:GPL/4 DESCRIPTION:Title: Lie algebras and higher Teichmüller components\nby André Oliveira (Univ. Porto) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nConsider t he moduli space M(G) of G-Higgs bundles on a compact Riemann surface X\, f or a real semisimple Lie group G. Hitchin components in the split real for m case and maximal components in the Hermitian case were\, for several yea rs\, the only known source of examples of higher Teichmüller components of M(G). These components (which are not fully distinguished by topologica l invariants) are important because the corresponding representations of t he fundamental group of X have special properties\, generalizing Teichmü ller space\, such as being discrete and faithful. Recently\, the existence of new such higher Teichmüller components was proved for G = SO(p\,q) w hich\, in general\, is not neither split nor Hermitian.\n\nIn this talk I will explain the new Lie theoretic notion of magical nilpotent\, which giv es rise to the classification of groups for which such components exist. I t turns out that this classification agrees with the one of Guichard and W ienhard for groups admitting a positive structure. We provide a parametriz ation of higher Teichmüller components\, generalizing the Hitchin sectio n for split real forms and the Cayley correspondence for maximal component s in the Hermitian (tube type) case.\n\nThis is joint work with S. Bradlow \, B. Collier\, O. García-Prada and P. Gothen.\n LOCATION:https://researchseminars.org/talk/GPL/4/ END:VEVENT END:VCALENDAR