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Cohomology in algebra, geometry, physicsand statistics

Perturbations of Fefferman’s conformal structures

Speaker’s name: 
Arman Taghavi-Chabert
Speaker’s affiliation: 
Warsaw University


ZOOM meeting
Wednesday, 22. February 2023 - 13:30 to 14:30
In 1976, Charles Fefferman constructed, in a canonical way, a conformal structure of Lorentzian
signature on a circle bundle over any given strictly pseudo-convex Cauchy-Riemann (CR) manifolds
of hypersurface type.

It is also known, notably through the work of Roger Penrose and his associates, and of the Warsaw
group led by Andrzej Trautman, that CR three-folds underlie four-dimensional Einstein Lorentzian
metrics whose Weyl tensors are said to be algebraically special.

In this talk, I will show how these algebraically special Einstein metrics find a natural formulation
as exact perturbations of Fefferman’s original construction. The additional CR data required turns
out to be constrained by a non-linear, or gauged, analogue of a second-order (BGG) differential
operator, and is related to the existence of CR functions.
We shall open the  seminar room and  ZOOM at 13.15 for coffee and close at 15:00