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SUMMARY:Boris Kruglikov (UiT the Arctic University of Norway)
DTSTART:20201223T162000Z
DTEND:20201223T180000Z
DTSTAMP:20260423T023020Z
UID:GDEq/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDEq/24/">Di
 spersionless integrable hierarchies and GL(2) geometry</a>\nby Boris Krugl
 ikov (UiT the Arctic University of Norway) as part of Geometry of differen
 tial equations seminar\n\n\nAbstract\n(joint work with Evgeny Ferapontov)\
 n\nParaconformal or GL(2) geometry on an n-dimensional manifold M is defin
 ed by a field of rational normal curves of degree n - 1 in the projectiviz
 ed cotangent bundle $\\mathbb{P}T^*M$. In dimension n=3 this is nothing bu
 t a Lorentzian metric. GL(2) geometry is known to arise on solution spaces
  of ODEs with vanishing Wünschmann invariants.\n\nWe show that GL(2) stru
 ctures also arise on solutions of dispersionless integrable hierarchies of
  PDEs such as the dispersionless Kadomtsev-Petviashvili (dKP) hierarchy. I
 n fact\, they coincide with the characteristic variety (principal symbol) 
 of the hierarchy. GL(2) structures arising in this way possess the propert
 y of involutivity. For n=3 this gives the Einstein-Weyl geometry.\n\nThus 
 we are dealing with a natural generalization of the Einstein-Weyl geometry
 . Our main result states that involutive GL(2) structures are governed by 
 a dispersionless integrable system whose general local solution depends on
  2n - 4 arbitrary functions of 3 variables. This establishes integrability
  of the system of Wünschmann conditions.\n
LOCATION:https://researchseminars.org/talk/GDEq/24/
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