English
Totally geodesic submanifolds of Teichmüller space and moduli space
Post-edited
Auteurs : Wright, Alexander (Auteur de la Conférence)
CIRM (Editeur )
30F60 - Teichmüller theory
32G15 - Moduli of Riemann surfaces, Teichmüller theory
CIRM (Editeur )
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
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 28/02/17 Date de captation : 14/02/2017 Sous collection : Research talks arXiv category : Dynamical Systems Domaine : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Durée : 01:02:54 Audience : Researchers Download : https://videos.cirm-math.fr/2017-02-14_Wright.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Espace de Teichmüller. Billards polygonaux, échanges d'intervalles / Teichmüller Space, Polygonal Billiard, Interval ExchangesOrganisateurs de la rencontre : 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
Données de citation
DOI : 10.24350/CIRM.V.19119303Citer cette vidéo: 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
- [Multi angle] Simplicity of the Lyapunov spectrum revisited / Auteur de la Conférence Hamenstädt, Ursula.
- [Multi angle] Limits of geodesic push-forwards of horocycle measures / Auteur de la Conférence Forni, Giovanni.
- [Multi angle] Interval exchange transformations from tiling billiards / Auteur de la Conférence Davis, Diana.
- [Multi angle] Unique ergodicity of geodesic flow in an infinite translation surface / Auteur de la Conférence Rafi, Kasra.
Bibliographie
- 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
