BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Maxim Grigoriev (Lebedev Physical Institute\, Institute for Theore tical and Mathematical Physics of Moscow State University) DTSTART:20200706T120000Z DTEND:20200706T140000Z DTSTAMP:20260423T024833Z UID:GDEq/11 DESCRIPTION:Title: Pr esymplectic structures and intrinsic Lagrangians\nby Maxim Grigoriev ( Lebedev Physical Institute\, Institute for Theoretical and Mathematical Ph ysics of Moscow State University) as part of Geometry of differential equa tions seminar\n\n\nAbstract\nIt is well-known that a Lagrangian induces a compatible presymplectic form on the equation manifold (stationary surface \, understood as a submanifold of the respective jet-space). Given an equa tion manifold and a compatible presymplectic form therein\, we define the first-order Lagrangian system which is formulated in terms of the intrinsi c geometry of the equation manifold. It has a structure of a presymplectic AKSZ sigma model for which the equation manifold\, equipped with the pres ymplectic form and the horizontal differential\, serves as the target spac e. For a wide class of systems (but not all) we show that if the presymple ctic structure originates from a given Lagrangian\, the proposed first-ord er Lagrangian is equivalent to the initial one and hence the Lagrangian pe r se can be entirely encoded in terms of the intrinsic geometry of its sta tionary surface. If the compatible presymplectic structure is generic\, th e proposed Lagrangian is only a partial one in the sense that its stationa ry surface contains the initial equation manifold but does not necessarily coincide with it. I also plan to briefly discuss extension of this constr uction to gauge PDEs (gauge theories in BV framework).\n LOCATION:https://researchseminars.org/talk/GDEq/11/ END:VEVENT END:VCALENDAR