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On the algebraic hull of the Kontsevich-Zorich cocycle and applications to finiteness theorems
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Authors : Eskin, Alex (Author of the conference)
CIRM (Publisher )
14D07 - Variation of Hodge structures
30F30 - Differentials on Riemann surfaces
32G15 - Moduli of Riemann surfaces, Teichmüller theory
32G20 - Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30]
37D25 - Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
CIRM (Publisher )
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Abstract :
We give a necessary and sufficient condition for the existence of infinitely many non-arithmetic Teichmuller curves in a stratum of abelian differentials. This is joint work with Simion Filip and Alex Wright.
MSC Codes : 14D07 - Variation of Hodge structures
30F30 - Differentials on Riemann surfaces
32G15 - Moduli of Riemann surfaces, Teichmüller theory
32G20 - Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30]
37D25 - Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
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Information on the Video
Film maker : Vichi, Pascal ; Hennenfent, GuillaumeLanguage : English Available date : 20/07/15 Conference Date : 06/07/15 Subseries : Research talks arXiv category : Dynamical Systems ; Algebraic Geometry ; Geometric Topology Mathematical Area(s) : Dynamical Systems & ODE ; Topology ; Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 01:00:00 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-07-06_Eskin.mp4 
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Information on the Event
Event Title : Dynamics and geometry in the Teichmüller space / Dynamique et géométrie dans l'espace de TeichmüllerEvent Organizers : Hubert, Pascal ; Lanneau, Erwan ; Zorich, Anton Dates : 06/07/15 - 10/07/15 Event Year : 2015 Event URL : http://conferences.cirm-math.fr/1115.html
Citation Data
DOI : 10.24350/CIRM.V.18791003Cite this video as: Eskin, Alex (2015). On the algebraic hull of the Kontsevich-Zorich cocycle and applications to finiteness theorems. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18791003 URI : http://dx.doi.org/10.24350/CIRM.V.18791003 |
Bibliography
- [1] Eskin, A., & Mirzakhani, M. (2014). Invariant and stationary measures for the $SL(2,\mathbb{R})$ action on Moduli space.
- [2] Filip, S. (2014). Semisimplicity and rigidity of the Kontsevich-Zorich cocycle.
- [3] Wright, A. (2014). The field of definition of affine invariant submanifolds of the moduli space of abelian differentials.
