Cohomology in algebra, geometry, physicsand statistics

Perturbations of Fefferman’s conformal structures

Speaker’s name:

Arman Taghavi-Chabert

Speaker’s affiliation:

Warsaw University

Place:

ZOOM meeting

Date:

Wednesday, 22. February 2023 - 13:30 to 14:30

Abstract:

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

JoinZoomMeeting

https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09

MeetingID:99598413922

Passcode:Galois

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

JoinZoomMeeting

https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09

MeetingID:99598413922

Passcode:Galois