BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Konstantin Druzhkov DTSTART:20250305T162000Z DTEND:20250305T180000Z DTSTAMP:20260423T010458Z UID:GDEq/127 DESCRIPTION:Title: I nvariant reduction for PDEs. II: The general mechanism\nby Konstantin Druzhkov as part of Geometry of differential equations seminar\n\n\nAbstra ct\nGiven a local (point\, contact\, or higher) symmetry of a system of pa rtial differential equations\, one can consider the system that describes the invariant solutions (the invariant system). It seems natural to expect that the invariant system inherits symmetry-invariant geometric structure s in a specific way. We propose a mechanism of reduction of symmetry-invar iant geometric structures\, which relates them to their counterparts on th e respective invariant systems. This mechanism is homological and covers t he stationary action principle and all terms of the first page of the Vino gradov C-spectral sequence. In particular\, it applies to invariant conser vation laws\, presymplectic structures\, and internal Lagrangians. A versi on of Noether's theorem naturally arises for systems that describe invaria nt solutions. Furthermore\, we explore the relationship between the C-spec tral sequences of a system of PDEs and systems that are satisfied by its s ymmetry-invariant solutions. Challenges associated with multi-reduction un der non-commutative symmetry algebras are also clarified.\n LOCATION:https://researchseminars.org/talk/GDEq/127/ END:VEVENT END:VCALENDAR