Rod Gover - An introduction to conformal geometry and tractor calculus (Part 1)
- document 1 document 2 document 3
- niveau 1 niveau 2 niveau 3
- audio 1 audio 2 audio 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.
Thème
Notice
Documentation
Liens
Dans la même collection
-
Thomas Backdahl - Symmetry operators, conserved currents and energy momentum tensorsBackdahlThomas
Conserved quantities, for example energy and momentum, play a fundamental role in the analysis of dynamics of particles and fields. For
-
Alain Bachelot - Waves in the Anti-de Sitter space-time AdsBachelotAlain
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
-
Alexander Strohmaier - WorkshopStrohmaierAlexander
I will explain how one can formulate and formalize the Gupta Bleuler framework for the Quantization of the electromagnetic field in an
-
Jérémie Joudioux - Hertz potentials and the decay of higher spin fieldsJoudiouxJérémie
The study of the asymptotic behavior of higher spin fields has proven to be a key point in understanding the stability properties of
-
Lionel Mason - Perturbative formulae for scattering of gravitational wave
The Christodoulou Klainerman proof of existence of asymptotically simple space-times shows that it is reasonable to consider the scattering of
-
Claudio Dappiaggi - On the role of asymptotic structures in the construction of quantum states for …DappiaggiClaudio
In the algebraic approach to quantum field theory on curved backgrounds, there exists a special class of quantum states for free fields,
-
Lars Andersson - Symmetry operators and energies
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in
-
Christian Gérard - Construction of Hadamard states for Klein‐Gordon fields
we will review a new construction of Hadamard states for quantized Klein-‐Gordon fields on curved spacetimes, relying on pseudo differential
-
Jérémie Szeftel - General relativity (Workshop)SzeftelJérémie
In order to control locally a space time which satisfies the Einstein equations, what are the minimal assumptions one should make on its
-
Rod Gover - Geometric Compactification, Cartan holonomy, and asymptotics
Conformal compactification has long been recognised as an effective geometric framework for relating conformal geometry, and associated field theories `
-
Philippe G LeFloch - Weakly regular spacetimes with T2 symmetryLeFlochPhilippe G.
I will discuss the initial value problem for the Einstein equations and present results concerning the existence and asymptotic behavior of
-
Pieter Blue - Decay for fields outside black holes
I will discuss energy and Morawetz (or integrated local decay) estimates for fields outside black holes. These results build on results for
Avec les mêmes intervenants
-
Rod Gover - An introduction to conformal geometry and tractor calculus (Part 4)GoverAshwin 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)GoverAshwin 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 2)GoverAshwin 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
Sur le même thème
-
Webinaire sur la rédaction des PGDLouvetViolaine
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)
-
J. Fine - Knots, minimal surfaces and J-holomorphic curvesFineJoël
I will describe work in progress, parts of which are joint with Marcelo Alves. Let L be a knot or link in the 3-sphere. I will explain how one can count minimal surfaces in hyperbolic 4-space
-
D. Tewodrose - Limits of Riemannian manifolds satisfying a uniform Kato conditionTewodroseDavid
I will present a joint work with G. Carron and I. Mondello where we study Kato limit spaces. These are metric measure spaces obtained as Gromov-Hausdorff limits of smooth n-dimensional Riemannian
-
D. Stern - Harmonic map methods in spectral geometrySternDaniel
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
-
M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass TheoremLesourdMartin
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
-
P. Burkhardt - Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flowBurkhardt-GuimPaula
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
-
J. Wang - Topological rigidity and positive scalar curvatureWangJian
In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with
-
C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensionsLiChao
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
-
D. Semola - Boundary regularity and stability under lower Ricci boundsSemolaDaniele
The theory of non smooth spaces with lower Ricci Curvature bounds has undergone huge developments in the last thirty years. On the one hand the impetus came from Gromov’s precompactness theorem
-
A. Mondino - Time-like Ricci curvature bounds via optimal transportMondinoAndrea
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
-
Y. Lai - A family of 3d steady gradient Ricci solitons that are flying wingsLaiYi
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