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Geometric approach to Hitchin components via punctual Hilbert schemes
Multi angle
Authors : Thomas, Alexander (Author of the conference)
CIRM (Publisher )
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.)
Additional resources :
https://www.cirm-math.fr/RepOrga/2216/Slides/Thomas_Slides.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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.)
Additional resources :
https://www.cirm-math.fr/RepOrga/2216/Slides/Thomas_Slides.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 23/10/2020 Conference Date : 09/10/2020 Subseries : Research talks arXiv category : Differential Geometry ; Mathematical Physics Mathematical Area(s) : Geometry ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 01:07:52 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-10-08_Thomas.mp4 
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Information on the Event
Event Title : Teichmüller Theory: Classical, Higher, Super and Quantum / Théorie de Teichmüller : classique, supérieure, super et quantiqueEvent Organizers : Ohshika, Ken'ichi ; Papadopoulos, Athanase ; Penner, Robert C. ; Wienhard, Anna Dates : 05/10/2020 - 10/10/2020 Event Year : 2020 Event URL : https://conferences.cirm-math.fr/2216.html
Citation Data
DOI : 10.24350/CIRM.V.19656703Cite this video as: 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 |
See Also
- [Multi angle] Equivalent curves on surfaces / Author of the conference Xu, Binbin.
- [Multi angle] Algebraic intersection on translation surfaces / Author of the conference Massart, Daniel.
- [Multi angle] Automorphisms of curve and pants complexes in profinite content / Author of the conference Funar, Louis.
- [Multi angle] Local systems and Satake duality / Author of the conference Fock, Vladimir.
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
