BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Emilio Franco (Universidad Autónoma de Madrid) DTSTART:20230110T160000Z DTEND:20230110T170000Z DTSTAMP:20260423T022719Z UID:Geolis/108 DESCRIPTION:Title: Lagrangians of Hecke cycles in the moduli space of Higgs bundles\nby Emilio Franco (Universidad Autónoma de Madrid) as part of Geometria em Li sboa (IST)\n\n\nAbstract\nThe moduli space of Higgs bundles over a curve i s a well known (singular) variety with an extremely rich geometry\, in par ticular it is hyperKähler and becomes an integrable system after being eq uipped with the so called Hitchin morphism which\, to any Higgs bundle\, a ssociates a finite cover of the base curve named spectral curve. Associate d to the hyperKähler structure\, Kapustin and Witten introduced in 2007\, BBB and BAA-branes\, predicting that they occur in pairs dual under mirro r symmetry. An example of BBB-brane is a hyperKähler bundle supported on hyperKähler subvariety\, and an example of BAA-brane is a flat bundle sup ported on a complex Lagrangian subvariety. Hitchin described in 2019 a fam ily of subintegral systems lying on the critical loci of the Hitchin integ rable system parametrized by spectral curves with a fixed number of singul arities. The critical subsystem obtained by considering spectral curves wi th maximal number of singularities is a hyperKähler subvariety and the au thor\, along with Oliveira\, Peón-Nieto and Gothen\, studied the BBB-bran es constructed over it\, and their image under Fourier-Mukai transform\, w hich are supported on complex Lagrangian subvarieties. Surprinsingly\, Hit chin showed that the critical subsystem obtained by considering spectral c urves with 1 singularity is not a hyperKähler subvariety and he conjectur ed that only the critical subsystem with a maximal number of singularities is hyperKähler.\n\nIn this work\, joint with Hanson\, Horn and Oliveira\ , we study the critical subsystems with any number of singularities\, show ing that their image under Fourier-Mukai is supported on a certain family of complex Lagrangian subvarieties which we describe.\n LOCATION:https://researchseminars.org/talk/Geolis/108/ END:VEVENT END:VCALENDAR