BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Konstantin Druzhkov DTSTART:20230920T162000Z DTEND:20230920T180000Z DTSTAMP:20260423T041527Z UID:GDEq/93 DESCRIPTION:Title: In ternal Lagrangians as variational principles\nby Konstantin Druzhkov a s part of Geometry of differential equations seminar\n\n\nAbstract\nThe pr inciple of stationary action deals with Lagrangians defined on jets. Howev er\, for some reason\, the intrinsic geometry of the corresponding equatio ns knows about their variational nature. It turns out that the explanation is quite simple: each stationary-action principle reproduces itself in te rms of the intrinsic geometry. More precisely\, each admissible Lagrangian gives rise to a unique integral functional defined on some particular cla ss of submanifolds of the corresponding equations. Such submanifolds can b e treated as almost solutions since (informally speaking) they are compose d of initial-boundary conditions lifted to infinitely prolonged equations. Intrinsic integral functionals produced by variational principles are rel ated to so-called internal Lagrangians. This relation allows us to introdu ce the notion of stationary point of an internal Lagrangian\, formulate th e corresponding intrinsic version of Noether's theorem\, and discuss the n ondegeneracy of presymplectic structures of differential equations. Despit e the generality of the approach\, its application to gauge theories prove s to be challenging. Perhaps the construction needs some modification in t his case.\n LOCATION:https://researchseminars.org/talk/GDEq/93/ END:VEVENT END:VCALENDAR