CIRM - Videos & books Library - Totally geodesic submanifolds of Teichmüller space and moduli space

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Authors : Wright, Alexander (Author of the conference)
CIRM (Publisher )

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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

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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https://videos.cirm-math.fr/2017-02-14_Wright.mp4

Information on the Event

Event Title : Espace de Teichmüller. Billards polygonaux, échanges d'intervalles / Teichmüller Space, Polygonal Billiard, Interval Exchanges
Event Organizers : Chaika, Jon ; Hubert, Pascal ; Lanneau, Erwan ; Skripchenko, Alexandra ; Zorich, Anton
Dates : 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.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

Bibliography

Wright, A. (2017). Totally geodesic submanifolds of Teichmüller space. - 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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