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Documents  30F60 | enregistrements trouvés : 3

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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. 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 ...

30F60 ; 32G15

In this somewhat speculative talk I will briefly describe recent results with Xuwen Zhu on the boundary behaviour of the Weil-Petersson metric (on the moduli space of Riemann surfaces) and ongoing work with Jesse Gell-Redman on the associated Laplacian. I will then describe what I think happens for the wave equation in this context and what needs to be done to prove it.

30F60 ; 32G15 ; 35L05

We will present a geometric criterion for the ergodicity of the billiard flow in a polygon with non-rational angles and discuss its application to the Diophantine case.

37D40 ; 37D50 ; 30F10 ; 30F60 ; 32G15

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