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Totally geodesic submanifolds of Teichmüller space and moduli space
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Authors : ... (Author of the conference)
... (Publisher )
30F60 - Teichmüller theory
32G15 - Moduli of Riemann surfaces, Teichmüller theory
... (Publisher )
Abstract :
We consider "higher dimensional Teichmüller discs", by which we mean complex submanifolds of Teichmüller space that contain the Teichmüller disc joining any two of its points. We prove results in the higher dimensional setting that are opposite to the one dimensional behavior: every "higher dimensional Teichmüller disc" covers a "higher dimensional Teichmüller curve" and there are only finitely many "higher dimensional Teichmüller curves" in each moduli space. The proofs use recent results in Teichmüller dynamics, especially joint work with Eskin and Filip on the Kontsevich-Zorich cocycle. Joint work with McMullen and Mukamel as well as Eskin, McMullen and Mukamel shows that exotic examples of "higher dimensional Teichmüller discs" do exist.
MSC Codes : 30F60 - Teichmüller theory
32G15 - Moduli of Riemann surfaces, Teichmüller theory
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Information on the Video
Language : EnglishAvailable date : 28/02/17 Conference Date : 14/02/2017 Subseries : Research talks arXiv category : Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 01:02:54 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-02-14_Wright.mp4 
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Information on the Event
Event Title : Espace de Teichmüller. Billards polygonaux, échanges d'intervalles / Teichmüller Space, Polygonal Billiard, Interval ExchangesDates : 13/02/2017 - 17/02/2017 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1713.html
Citation Data
DOI : 10.24350/CIRM.V.19119303Cite this video as: (2017). Totally geodesic submanifolds of Teichmüller space and moduli space. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19119303 URI : http://dx.doi.org/10.24350/CIRM.V.19119303 |
See Also
- [Multi angle] Simplicity of the Lyapunov spectrum revisited / Author of the conference ....
- [Multi angle] Limits of geodesic push-forwards of horocycle measures / Author of the conference ....
- [Multi angle] Interval exchange transformations from tiling billiards / Author of the conference ....
- [Multi angle] Unique ergodicity of geodesic flow in an infinite translation surface / Author of the conference ....
Bibliography
- Wright, A. (2017). Totally geodesic submanifolds of Teichmüller space.
- Eskin, A., Filip, S., & Wright, A. (2017). The algebraic hull of the Kontsevich-Zorich cocycle - https://arxiv.org/abs/1702.02074
- McMullen, C.T., Mukamel, R.E., & Wright, A. (2016). Cubic curves and totally geodesic subvarieties of moduli space - http://www.math.harvard.edu/~ctm/papers/home/text/papers/gothic/gothic.pdf
