English
Geometric approach to Hitchin components via punctual Hilbert schemes
Multi angle
Auteurs : Thomas, Alexander (Auteur de la Conférence)
CIRM (Editeur )
14C05 - Parametrization (Chow and Hilbert schemes)
14D21 - applications of vector bundles and moduli spaces in mathematical physics
30F60 - Teichmüller theory
53C15 - General geometric structures on manifolds (almost complex, contact, symplectic, almost product structures, etc.)
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2216/Slides/Thomas_Slides.pdf
CIRM (Editeur )
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Résumé :
I will describe a program to describe Hitchin components as the moduli space of some new geometric structure on the surface. This geometric structure generalizes the complex structure. Its construction uses the punctual Hilbert scheme of the plane. It should give a unified description of Hitchin components without fixed complex structure on the surface. I also present a generalization to character varieties for non split real groups in the spirit of G-Higgs bundles.
Keywords : Hitchin component; higher Teichmüller theory; geometric structures; punctual Hilbert scheme
Codes MSC : Keywords : Hitchin component; higher Teichmüller theory; geometric structures; punctual Hilbert scheme
14C05 - Parametrization (Chow and Hilbert schemes)
14D21 - applications of vector bundles and moduli spaces in mathematical physics
30F60 - Teichmüller theory
53C15 - General geometric structures on manifolds (almost complex, contact, symplectic, almost product structures, etc.)
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2216/Slides/Thomas_Slides.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 23/10/2020 Date de captation : 09/10/2020 Sous collection : Research talks arXiv category : Differential Geometry ; Mathematical Physics Domaine : Geometry ; Mathematical Physics Format : MP4 (.mp4) - HD Durée : 01:07:52 Audience : Researchers Download : https://videos.cirm-math.fr/2020-10-08_Thomas.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Teichmüller Theory: Classical, Higher, Super and Quantum / Théorie de Teichmüller : classique, supérieure, super et quantiqueOrganisateurs de la rencontre : Ohshika, Ken'ichi ; Papadopoulos, Athanase ; Penner, Robert C. ; Wienhard, Anna Dates : 05/10/2020 - 10/10/2020 Année de la rencontre : 2020 URL Congrès : https://conferences.cirm-math.fr/2216.html
Données de citation
DOI : 10.24350/CIRM.V.19656703Citer cette vidéo: Thomas, Alexander (2020). Geometric approach to Hitchin components via punctual Hilbert schemes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19656703 URI : http://dx.doi.org/10.24350/CIRM.V.19656703 |
Voir aussi
- [Multi angle] Equivalent curves on surfaces / Auteur de la Conférence Xu, Binbin.
- [Multi angle] Algebraic intersection on translation surfaces / Auteur de la Conférence Massart, Daniel.
- [Multi angle] Automorphisms of curve and pants complexes in profinite content / Auteur de la Conférence Funar, Louis.
- [Multi angle] Local systems and Satake duality / Auteur de la Conférence Fock, Vladimir.
Bibliographie
- FOCK, Vladimir et THOMAS, Alexander. Higher complex structures. International Mathematics Research Notices, 2018. - https://doi.org/10.1093/imrn/rnz283
- THOMAS, Alexander. Higher Complex Structures and Higher Teichm\" uller Theory. arXiv preprint arXiv:2007.00382, 2020. - https://arxiv.org/abs/2007.00382
- THOMAS, Alexander. Higher Complex Structures and Flat Connections. arXiv preprint arXiv:2005.14445, 2020. - https://arxiv.org/abs/2005.14445
- THOMAS, Alexander. Generalized Punctual Hilbert Schemes and $\mathfrak {g} $-complex structures. arXiv preprint arXiv:1910.08504, 2019. - https://arxiv.org/abs/1910.08504
