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Translation surfaces and dynamics on moduli spaces - part 1
Multi angle
Authors : Valdez, Ferrán (Author of the conference)
CIRM (Publisher )
20G15 - Linear algebraic groups over arbitrary fields
37E35 - Flows on surfaces
37F34 - Teichmüller theory; moduli spaces of holomorphic dynamical systems
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 : - 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
20G15 - Linear algebraic groups over arbitrary fields
37E35 - Flows on surfaces
37F34 - Teichmüller theory; moduli spaces of holomorphic dynamical systems
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : 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 : 01:26:40 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-07-22_Valdez_1.mp4 
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Information on the Event
Event Title : An introduction to dynamics on surfaces and random walks / Géométrie et Dynamiques sur les surfacesEvent 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.20207103Cite this video as: Valdez, Ferrán (2024). Translation surfaces and dynamics on moduli spaces - part 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20207103 URI : http://dx.doi.org/10.24350/CIRM.V.20207103 |
See Also
- [Multi angle] Translation surfaces and dynamics on moduli spaces - part 3 / Author of the conference Valdez, Ferrán.
- [Multi angle] Translation surfaces and dynamics on moduli spaces - part 2 / Author of the conference Valdez, Ferrán.
- [Multi angle] Geodesic flow on surfaces without conjugate points - part 3 / Author of the conference War, Khadim Mbacke.
- [Multi angle] Geodesic flow on surfaces without conjugate points - part 2 / Author of the conference War, Khadim Mbacke.
- [Multi angle] Topology of horocyclic flow on geometrically infinite surface - part 3 / Author of the conference Lo, Cheikh.
- [Multi angle] Random walks on groups - part 3 / Author of the conference Aoun, Richard.
- [Multi angle] Random walks on groups - part 2 / Author of the conference Aoun, Richard.
- [Multi angle] Geodesic flow on surfaces without conjugate points - part 1 / Author of the conference War, Khadim Mbacke.
- [Multi angle] Topology of horocyclic flow on geometrically infinite surface - part 1 / Author of the conference Lo, Cheikh.
- [Multi angle] Topology of horocyclic flow on geometrically infinite surface - part 2 / Author of the conference Anonymous, A..
- [Multi angle] Random walks on groups - part 1 / Author of the conference Aoun, Richard.
Bibliography
- ATHREYA, Jayadev S. et MASUR, Howard. Translation Surfaces. Graduate Studies in Mathematics 242. American Mathematical Society, 2024.195 p. -
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