BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Boris Doubrov DTSTART:20230517T162000Z DTEND:20230517T180000Z DTSTAMP:20260423T023048Z UID:GDEq/90 DESCRIPTION:Title: Ov erdetermined systems of PDEs related to representations of semi-simple Lie algebras\nby Boris Doubrov as part of Geometry of differential equati ons seminar\n\n\nAbstract\nWe explore a class of finite-type systems of PD Es whose symbol is determined by an (arbitrary) irreducible representation of a graded semisimple Lie algebra.\n\nWe show that trivial equations wit h such symbol correspond to rational homogeneous varieties\, non-trivial l inear equations define symbol-preserving deformations of such varieties. I n particular\, we determine when such deformations exist. In terms of the corresponding PDE system this corresponds to the question when compatibili ty conditions imply that the system is equivalent to trivial. The answer t o this question is given in terms of certain Lie algebra cohomology\, whic h can be effectively computed using the results for the theory of semisimp le Lie algebras.\n\nWe solve local equivalence problem for such systems un der fiber+symbol preserving transformations and show how this is related t o the projective geometry of submanifolds. Finally\, we discuss the case o f non-linear systems with the same symbol and show that under certain addi tional conditions their solution spaces admit remarkable geometric structu res.\n LOCATION:https://researchseminars.org/talk/GDEq/90/ END:VEVENT END:VCALENDAR