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SUMMARY:Para-CR geometry and curves - Wojciech Krynski (Polska Akademia Na
 uk)
DTSTART:20240904T133000Z
DTEND:20240904T143000Z
UID:TALK219883@talks.cam.ac.uk
DESCRIPTION:We study para-CR geometry in dimension 2n + 1. For a given par
 a-CRstructure\, we introduce a canonically associated family of curves\, w
 hich we refer toas Lewy curves by analogy to a construction in CR geometry
  studied in [F]. We showthat for n > 1\, the curves define a path geometry
  exclusively in the flat case (in whichthey coincide with chains). We prov
 e that in the generic case\, the Lewy curves aresolutions to a system of O
 DEs of order n. However\, orders between 2 and n are alsopossible. Further
 more\, we discuss the sub-maximal cases and provide a characterizationof t
 he Lewy curves in terms of invariants of ODEs. We also discuss relations t
 othe twistor construction given in [D]\, generalized to higher dimensions.
  The talk isbased on joint work with O. Makhmali [KM].[F] J. J. Faran\, Le
 wy&rsquo\;s curves and chains on real hypersurfaces\, Trans. AMS.\, 1981.[
 D] M. Dunajski. Twistor theory of dancing paths\, SIGMA\, 2022.[KM] W. Kry
 nski\, O. Makhmali\, Lewy curves in para-CR geometry\, arXiv:2406.04798\,2
 024.
LOCATION:Seminar Room 2\, Newton Institute
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