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

By Alexander Thomas

Appears in 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.

Information about the video

Date of recording 09/10/2020
Date of publication 23/10/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19656703
Cite this video 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

Domain(s)

Bibliography

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

MSC codes

Document(s)

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

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