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SUMMARY:Valentin Lychagin
DTSTART:20221207T162000Z
DTEND:20221207T180000Z
DTSTAMP:20260423T010012Z
UID:GDEq/77
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDEq/77/">On
  normal forms of differential operators</a>\nby Valentin Lychagin as part 
 of Geometry of differential equations seminar\n\nLecture held in room 303 
 of the Independent University of Moscow.\n\nAbstract\nIn this talk\, we cl
 assify linear (as well as some special nonlinear) scalar diff\nerential op
 erators of order $k$ on $n$-dimensional manifolds with respect to the diff
 eomorphism pseudogroup.\n                                                 
                                Cases\, when $k = 2$\, $\\forall n$\, and $
 k = 3$\, $n = 2$\, were discussed before\, and now we consider cases $k\\g
 e5$\, $n = 2$ and $k\\ge4$\, $n = 3$ and $k\\ge3$\, $n\\ge4$. In all these
  cases\, the fields of rational differential invariants are generated by t
 he 0-order invariants of symbols.\n\nThus\, at first\, we consider the cla
 ssical problem of Gl-invariants of $n$-ary forms. We'll illustrate here th
 e power of the differential algebra approach to this problem and show how 
 to find the rational Gl-invariants of $n$-are forms in a constructive way.
 \n\nAfter all\, we apply the $n$ invariants principle in order to get (loc
 al as well as global) normal forms of linear operators with respect to the
  diffeomorphism pseudogroup.\n\nDepending on available time\, we show how 
 to extend all these results to some classes of nonlinear operators.\n
LOCATION:https://researchseminars.org/talk/GDEq/77/
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