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2025 IHES Summer School – Statistical Aspects of Nonlinear Physics
26 videos

2025 IHES Summer School – Statistical Aspects of Nonlinear Physics

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Fuzzy Sphere Meets Conformal Bootstrap 2025
20 videos

Fuzzy Sphere Meets Conformal Bootstrap 2025

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2025 - T2 - WS2 - Low-dimensional phenomena: geometry and dynamics

Collection 2025 - T2 - WS2 - Low-dimensional phenomena: geometry and dynamics

Organizer(s) Bromberg, Kenneth ; Haïssinsky, Peter ; Hamenstädt, Ursula ; Maloni, Sara ; Sambarino, Andrés ; Schapira, Barbara
Date(s) 23/06/2025 - 27/06/2025
linked URL https://indico.math.cnrs.fr/event/11570/
17 17

Exotic maximal surface group representations into Diff(S1)

By Nicolas Tholozan

The Euler class of a surface group representation into $\mathrm{Diff}(\mathbb S^1)$ satisfies the Milnor—Wood inequality, and representations with maximal Euler class are semi-conjugated to Fuchsian representations by a theorem of Matsumoto. In higher regularity, Ghys proved a stronger rigidity theorem: for $k\geq3$, a maximal circle action by diffeomorphisms of class $\mathrm{C}^k$ is $\mathrm{C}^k$-conjugated to some Fuchsian action. In particular it is minimal, dilating, and Hölder conjugated to any Fuchsian action. I will explain that all these results fail in regularity $\mathrm{C}^1$, by associating « exotic » maximal $\mathrm{C}^1$ actions to discrete and faithful surface group representations into $\mathrm{PSL}(2,\mathbb C)$. This is based on discussions with Selim Ghazouani and Françoise Dal'bo.

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