Totally geodesic submanifolds of Teichmüller space and moduli space | Vidéo | Carmin.tv

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Totally geodesic submanifolds of Teichmüller space and moduli space

By Alexander Wright

Appears in collection : Espace de Teichmüller. Billards polygonaux, échanges d'intervalles / Teichmüller Space, Polygonal Billiard, Interval Exchanges

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.

Information about the video

Date of recording 14/02/2017
Date of publication 28/02/2017
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19119303
Cite this video Wright, Alexander (14/02/2017). Totally geodesic submanifolds of Teichmüller space and moduli space. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19119303
URL https://dx.doi.org/10.24350/CIRM.V.19119303

Domain(s)

Dynamical Systems

Bibliography

Wright, A. (2017). Totally geodesic submanifolds of Teichmüller space. <arXiv:1702.03249> - https://arxiv.org/abs/1702.03249
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

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