Notice
Rod Gover - An introduction to conformal geometry and tractor calculus (Part 4)
- document 1 document 2 document 3
- niveau 1 niveau 2 niveau 3
Descriptif
After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in this framework. Motivated by the need to develop a more effective approach to such problems we are led into the idea of conformal geometry and a conformally invariant calculus; this``tractor calculus'' is then developed explicitly. We will discuss how to calculate using this, and touch on applications to the construction of conformal invariants and conformally invariant differential operators. The second part of the course is concerned with the application of conformal geometry and tractor calculus for the treatment of conformal compactification and the geometry of conformal infinity. The link with Friedrich’s conformal field equations will be made. As part of this part we also dedicate some time to the general problem of treating hypersurfaces in a conformal manifold, and in particular arrive at a conformal Gauss equation. Finally we show how these tools maybe applied to treat aspects of the asymptotic analysis of boundary problems on conformally compact manifolds.
Documentation
Liens
Dans la même collection
-
Lionel Mason - Perturbative formulae for scattering of gravitational wave
MASON Lionel J.
The Christodoulou Klainerman proof of existence of asymptotically simple space-times shows that it is reasonable to consider the scattering of
-
Andras Vasy - Microlocal analysis and wave propagation (Part 4)
In these lectures I will explain the basics of microlocal analysis, emphasizing non elliptic problems, such as wave propagation, both on manifolds without boundary, and on manifolds with boundary. In
-
Alexander Strohmaier - Workshop
STROHMAIER Alexander
I will explain how one can formulate and formalize the Gupta Bleuler framework for the Quantization of the electromagnetic field in an
-
-
Andras Vasy - Microlocal analysis and wave propagation (Part 1)
VASY András
In these lectures I will explain the basics of microlocal analysis, emphasizing non elliptic problems, such as wave propagation, both on
-
-
Alain Bachelot - Waves in the Anti-de Sitter space-time Ads
BACHELOT Alain
In this talk we address some issues concerning the wave propagation in the 4D+1 anti de Sitter space time : the role of the conformal
-
Semyon Dyatlov - Spectral gaps for normally hyperbolic trapping
DYATLOV Semyon
Motivated by wave decay for Kerr and Kerr de Sitter black holes, we study spectral gaps for codimension 2 normally hyperbolic trapped sets with
-
Andras Vasy - Microlocal analysis and wave propagation (Part 3)
In these lectures I will explain the basics of microlocal analysis, emphasizing non elliptic problems, such as wave propagation, both on manifolds without boundary, and on manifolds with boundary. In
-
Maciej Zworski - From redshift effect to classical dynamics : microlocal proof of Smale's conjecture
ZWORSKI Maciej
Dynamical zeta functions of Selberg, Smale and Ruelle are analogous to the Riemann zeta function with the product over primes replaced by
-
Pieter Blue - Decay for fields outside black holes
BLUE Pieter
I will discuss energy and Morawetz (or integrated local decay) estimates for fields outside black holes. These results build on results for
-
Jérémie Szeftel - General relativity (Workshop)
SZEFTEL Jérémie
In order to control locally a space time which satisfies the Einstein equations, what are the minimal assumptions one should make on its
Avec les mêmes intervenants et intervenantes
-
Rod Gover - An introduction to conformal geometry and tractor calculus (Part 2)
GOVER Ashwin Roderick
After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal
-
Rod Gover - An introduction to conformal geometry and tractor calculus (Part 3)
GOVER Ashwin Roderick
After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal
-
Rod Gover - An introduction to conformal geometry and tractor calculus (Part 1)
GOVER Ashwin Roderick
After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling
Sur le même thème
-
"Le mathématicien Petre (Pierre) Sergescu, historien des sciences, personnalité du XXe siècle"
HERLéA Alexandre
Alexandre HERLEA est membre de la section « Sciences, histoire des sciences et des techniques et archéologie industrielle » du CTHS. Professeur émérite des universités, membre effectif de l'Académie
-
Webinaire sur la rédaction des PGD
LOUVET Violaine
Rédaction des Plans de Gestion de Données (PGD) sous l’angle des besoins de la communauté mathématique.
-
Alexandre Booms : « Usage de matériel pédagogique adapté en géométrie : une transposition à interro…
« Usage de matériel pédagogique adapté en géométrie : une transposition à interroger ». Alexandre Booms, doctorant (Université de Reims Champagne-Ardenne - Cérep UR 4692)
-
D. Stern - Harmonic map methods in spectral geometry
STERN Daniel
Over the last fifty years, the problem of finding sharp upper bounds for area-normalized Laplacian eigenvalues on closed surfaces has attracted the attention of many geometers, due in part to
-
P. Burkhardt - Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flow
BURKHARDT-GUIM Paula
We propose a class of local definitions of weak lower scalar curvature bounds that is well defined for C0 metrics. We show the following: that our definitions are stable under greater-than-second
-
R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions
BAMLER Richard H.
We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow.
-
C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
LI Chao
In this talk, I will discuss some recent developments on the topology of closed manifolds admitting Riemannian metrics of positive scalar curvature. In particular, we will prove if a closed PSC
-
Y. Lai - A family of 3d steady gradient Ricci solitons that are flying wings
LAI Yi
We find a family of 3d steady gradient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing, we show that the scalar curvature does not vanish at
-
T. Ozuch - Noncollapsed degeneration and desingularization of Einstein 4-manifolds
OZUCH Tristan
We study the noncollapsed singularity formation of Einstein 4-manifolds. We prove that any smooth Einstein 4-manifold close to a singular one in a mere Gromov-Hausdorff (GH) sense is the result
-
D. Tewodrose - Limits of Riemannian manifolds satisfying a uniform Kato condition
TEWODROSE David
Presentation of a joint work with G. Carron and I. Mondello where we study Kato limit spaces.
-
A. Mondino - Time-like Ricci curvature bounds via optimal transport
MONDINO Andrea
The goal of the talk is to present a recent work in collaboration with Cavalletti (SISSA) on optimal transport in Lorentzian synthetic spaces. The aim is to set up a “Lorentzian analog” of the
-
M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem
LESOURD Martin
The study of positive scalar curvature on noncompact manifolds has seen significant progress in the last few years. A major role has been played by Gromov's results and conjectures, and in
