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Translation surfaces and dynamics on moduli spaces - part 3

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Authors : Valdez, Ferrán (Author of the conference)
CIRM (Publisher )

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Abstract : In this course we give a proof of a central result in the theory of translation surfaces known as $Masur's$ $criterion$. The aim is to introduce the audience to the subject and illustrate how one can understand ergodic properties of the geodesic flow on an individual translation surface by studying the behaviour of its $SL(2,\mathbb{R})$-orbit on moduli space. The course is divided in 4 parts. Exercise sessions (TP) are also planned.

- Basic notions about translation surfaces.
- Moduli spaces of translation surfaces.
- Dynamical aspects of translation flows.
- Proof of Masur's criterion.

Keywords : translation surfaces; dynamics of geodesic flows

MSC Codes :
20G15 - Linear algebraic groups over arbitrary fields
37E35 - Flows on surfaces
37F34 - Teichmüller theory; moduli spaces of holomorphic dynamical systems

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : French
    Available date : 06/09/2024
    Conference Date : 22/07/2024
    Subseries : Research School
    arXiv category : Dynamical Systems ; Metric Geometry
    Mathematical Area(s) : Dynamical Systems & ODE ; Geometry
    Format : MP4 (.mp4) - HD
    Video Time : 01:31:51
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2024-07-26_Valdez_3.mp4

Information on the Event

Event Title : An introduction to dynamics on surfaces and random walks / Géométrie et Dynamiques sur les surfaces
Event Organizers : Gaye, Masseye ; Quint, Jean-François
Dates : 22/07/2024 - 26/07/2024
Event Year : 2024
Event URL : https://conferences.cirm-math.fr/3294.html

Citation Data

DOI : 10.24350/CIRM.V.20208003
Cite this video as: Valdez, Ferrán (2024). Translation surfaces and dynamics on moduli spaces - part 3. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20208003
URI : http://dx.doi.org/10.24350/CIRM.V.20208003

See Also

Bibliography

  • ATHREYA, Jayadev S. et MASUR, Howard. Translation Surfaces. Graduate Studies in Mathematics 242. American Mathematical Society, 2024.195 p. -



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