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Translation surfaces and dynamics on moduli spaces - part 3

By Ferrán Valdez

Appears in collection : An introduction to dynamics on surfaces and random walks / Géométrie et Dynamiques sur les surfaces

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.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.20208003
  • Cite this video Valdez, Ferrán (22/07/2024). Translation surfaces and dynamics on moduli spaces - part 3. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20208003
  • URL https://dx.doi.org/10.24350/CIRM.V.20208003

Bibliography

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

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