Français
Local index theory for Lorentzian manifolds
Multi angle
Authors : Bär, Christian (Author of the conference)
CIRM (Publisher )
35L05 - Wave equation (hyperbolic PDE)
58J20 - Index theory and related fixed point theorems
58J32 - Boundary value problems on manifolds
58J45 - Hyperbolic equations
35L02 - First-order hyperbolic equations
CIRM (Publisher )
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Abstract :
We prove a local version of the index theorem for Dirac-type operators on globally hyperbolic Lorentzian manifolds with Cauchy boundary. In case the Cauchy hypersurface is compact, we do not assume self-adjointness of the Dirac operator on the spacetime or of the associated elliptic Dirac operator on the boundary.In this case, integration of our local index theorem results in a generalization of previously known index theorems for globally hyperbolic spacetimes that allows for twisting bundles associated with non-compact gauge groups. This is joint work with Alexander Strohmaier.
Keywords : Dirac-type operator; globally hyperbolic Lorentzian
MSC Codes : Keywords : Dirac-type operator; globally hyperbolic Lorentzian
35L05 - Wave equation (hyperbolic PDE)
58J20 - Index theory and related fixed point theorems
58J32 - Boundary value problems on manifolds
58J45 - Hyperbolic equations
35L02 - First-order hyperbolic equations
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 12/04/2022 Conference Date : 29/03/2022 Subseries : Research talks arXiv category : Differential Geometry ; Mathematical Physics Mathematical Area(s) : PDE ; Geometry ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 00:58:38 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-03-29_Bar.mp4 
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Information on the Event
Event Title : Geometry and analysis on non-compact manifolds / Géométrie et analyse sur les variétés non compactesEvent Organizers : Ammann, Bernd ; Carron, Gilles ; Groe, Nadine ; Nistor, Victor Dates : 28/03/2022 - 01/04/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2548.html
Citation Data
DOI : 10.24350/CIRM.V.19902003Cite this video as: Bär, Christian (2022). Local index theory for Lorentzian manifolds. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19902003 URI : http://dx.doi.org/10.24350/CIRM.V.19902003 |
See Also
- [Multi angle] Regularity in Besov spaces of parabolic PDEs / Author of the conference Schneider, Cornelia.
- [Multi angle] On the mass of asymptotically hyperbolic manifolds and initial data set / Author of the conference Sakovich, Anna.
- [Multi angle] Proper actions of Lie groups and numeric invariants of Dirac operators / Author of the conference Piazza, Paolo.
- [Multi angle] Segal axioms and resolution of Liouville conformal field theory / Author of the conference Guillarmou, Colin.
Bibliography
- BÄR, Christian et STROHMAIER, Alexander. A rigorous geometric derivation of the chiral anomaly in curved backgrounds. Communications in Mathematical Physics, 2016, vol. 347, no 3, p. 703-721. - https://doi.org/10.1007/s00220-016-2664-1
- BÄR, Christian et STROHMAIER, Alexander. An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary. American Journal of Mathematics, 2019, vol. 141, no 5, p. 1421-1455. - https://doi.org/10.1353/ajm.2019.0037
- BÄR, Christian et STROHMAIER, Alexander. Local index theory for Lorentzian manifolds. arXiv preprint arXiv:2012.01364, 2020. - https://arxiv.org/abs/2012.01364
