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Post-edited Totally geodesic submanifolds of Teichmüller space and moduli space

Auteurs : Wright, Alexander (Auteur de la Conférence)
CIRM (Editeur )

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Teichmüller disc totally geodesic surface square root of an Abelian differential affine invariant submanifold isoperiodic foliation rank Jenkins-Strebel differential questions of the audience

Résumé : 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.

Codes MSC :
30F60 - Teichmüller theory
32G15 - Moduli of Riemann surfaces, Teichmüller theory

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 28/02/17
    Date de captation : 14/02/2017
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 01:02:54
    Domaine : Dynamical Systems & ODE
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : http://videos.cirm-math.fr/2017-02-14_Wright.mp4

Informations sur la rencontre

Nom du congrès : Espace de Teichmüller. Billards polygonaux, échanges d'intervalles / Teichmüller Space, Polygonal Billiard, Interval Exchanges
Organisteurs Congrès : Chaika, Jon ; Hubert, Pascal ; Lanneau, Erwan ; Skripchenko, Alexandra ; Zorich, Anton
Dates : 13/02/2017 - 17/02/2017
Année de la rencontre : 2017
URL Congrès : http://conferences.cirm-math.fr/1713.html

Citation Data

DOI : 10.24350/CIRM.V.19119303
Cite this video as: Wright, Alexander (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

Voir aussi


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

  2. Eskin, A., Filip, S., & Wright, A. (2017). The algebraic hull of the Kontsevich-Zorich cocycle - https://arxiv.org/abs/1702.02074

  3. 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