BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Maxim Grigoriev (Moscow State University and Mons University) DTSTART:20241009T113000Z DTEND:20241009T123000Z DTSTAMP:20260502T044907Z UID:PHK-cohomology-seminar/110 DESCRIPTION:Title: Graded geometry of local gauge theories\nby Maxim Gri goriev (Moscow State University and Mons University) as part of Prague-Hra dec Kralove seminar Cohomology in algebra\, geometry\, physics and statist ics\n\n\nAbstract\nGauge PDEs generalize AKSZ sigma models to the case of general local gauge theories. Despite being very flexible and invariant th ese geometrical objects are usually infinite-dimensional and are difficult to define explicitly\, just like standard infinitely-prolonged PDEs. We p ropose a notion of a weak gauge PDE where the nilpotency of the BRST diffe rential is relaxed in a controllable way. In this approach a nontopologica l local gauge theory can be described in terms of a finite-dimensional geo metrical object. Moreover\, among such objects one can find a minimal one which is unique in a certain sense. In the case of a Lagrangian system\, t he respective weak gauge PDE naturally arises from the presymplectic struc ture. We prove that any weak gauge PDE determines the standard jet-bundle BV formulation of the underlying gauge theory\, giving an unambiguous fiel d-theoretical interpretation of these objects. The relation to the covaria nt phase space and the multisymplectic approaches is also discussed. The f ormalism is illustrated by a variety of models including (super) gravity\, (chiral) Yang-Mills\, and a non-Lagrangian self-dual Yang-Mills theory.\n LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/110/ END:VEVENT END:VCALENDAR