BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Maxim Grigoriev DTSTART:20211117T162000Z DTEND:20211117T180000Z DTSTAMP:20260423T010251Z UID:GDEq/54 DESCRIPTION:Title: Pr esymplectic gauge PDEs and Batalin-Vilkovisky formalism\nby Maxim Grig oriev as part of Geometry of differential equations seminar\n\nLecture hel d in room 303 of the Independent University of Moscow.\n\nAbstract\nGauge PDE is a geometrical object underlying what physicists call a local gauge field theory defined at the level of equations of motion (i.e. without sp ecifying Lagranian) in terms of BV-BRST formalism. Although gauge PDE can be defined as a PDE equipped with extra structures\, the generalization is not entirely straightforward as\, for instance\, two gauge PDEs can be eq uivalent even if the underlying PDEs are not. As far as Lagrangian gauge s ystems are concerned the powerful framework is provided by the BV formalis m on jet-bundles. However\, just like in the case of usual PDEs it is diff icult to encode the BV extension of the Lagrangian in terms of the intrins ic geometry of the equation manifold while working on jet-bundles is often very restrictive\, especially in analyzing boundary behaviour\, e.g.\, in the context of AdS/CFT correspondence. We show that BV Lagrangian (or its weaker analogs) can be encoded in the compatible graded presymplectic str ucture on the gauge PDE. In the case of genuine Lagrangian systems this pr esymplectic structure is related to a certain completion of the canonical BV symplectic structure. A presymplectic gauge PDE gives rise to a BV form ulation of the underlying system through an appropriate generalization of the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) sigma-model constructi on followed by taking the symplectic quotient. The construction is illustr ated on the standard examples of gauge theories with particular emphasis o n the Einstein gravity\, where this naturally leads to an elegant presympl ectic AKSZ representation of the BV extension of the Cartan-Weyl formulati on of gravity.\n LOCATION:https://researchseminars.org/talk/GDEq/54/ END:VEVENT END:VCALENDAR