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SUMMARY:Perturbations of Fefferman spaces over (almost) CR manifolds - Arm
 an Taghavi-Chabert (Technical University of Lodz)
DTSTART:20240906T103000Z
DTEND:20240906T113000Z
UID:TALK219901@talks.cam.ac.uk
DESCRIPTION:In 1976\, Charles Fefferman constructed\, in a canonical way\,
  a Lorentzian conformal structure on a circle bundle over a given strictly
  pseudoconvex Cauchy-Riemann (CR) manifolds of hypersurface type. It is al
 so known\, notably through the work of Sir Roger Penrose and his associate
 s\, and that of the Warsaw group led by Andrzej Trautman\, that CR three-m
 anifolds underlie Einstein Lorentzian four-manifolds whose Weyl tensors ar
 e said to be algebraically special. I will show how these two perspectives
  are related to each other\, by presenting modifications of Fefferman&rsqu
 o\;s original construction\, where the conformal structure is "perturbed" 
 by some semi-basic one-form\, which encodes additional data on the CR thre
 e-manifold.\nMetrics in such a perturbed Fefferman conformal class whose R
 icci tensor satisfies certain degeneracy conditions are only defined off s
 ections of the Fefferman bundle\, which may be viewed as "conformal infini
 ty". The prescriptions on the Ricci tensor can then be reduced to differen
 tial constraints on the CR three-manifold in terms of a "complex density" 
 and the CR data of the perturbation one-form. One such constraint turns ou
 t to arise from a non-linear\, or gauged\, analogue of a second-order diff
 erential operator on densities\, closely related to so-called BGG operator
 s. A solution thereof provides a criterion for the existence of a CR funct
 ion and\, under certain conditions\, for CR embeddability. Our setup allow
 s us to reinterpret previous works by Lewandowski\, Nurowski\, Tafel\, Hil
 l\, and independently\, by Mason.\nTime permitting\, I will discuss the hi
 gher-dimensional story.\nThis talk is based on arXiv:2303.07328 and arXiv:
 2309.16986.
LOCATION:Seminar Room 2\, Newton Institute
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