Geometric approach to Hitchin components via punctual Hilbert schemes | Vidéo | Carmin.tv

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Geometric approach to Hitchin components via punctual Hilbert schemes

De Alexander Thomas

Apparaît dans la collection : Teichmüller Theory: Classical, Higher, Super and Quantum / Théorie de Teichmüller : classique, supérieure, super et quantique

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.

Informations sur la vidéo

Date de captation 09/10/2020
Date de publication 23/10/2020
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19656703
Citer cette vidéo Thomas, Alexander (09/10/2020). Geometric approach to Hitchin components via punctual Hilbert schemes. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19656703
URL https://dx.doi.org/10.24350/CIRM.V.19656703

Domaine(s)

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

Codes MSC

Document(s)

https://www.cirm-math.fr/RepOrga/2216/Slides/Thomas_Slides.pdf

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