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2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

Collection 2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

Organizer(s) Canary, Richard ; Garcia-Faide, Elba ; Labourie, François ; Li, Qiongling ; Neitzke, Andrew ; Pozzetti, Beatrice ; Wienhard, Anna
Date(s) 19/05/2025 - 27/05/2025
linked URL https://indico.math.cnrs.fr/event/11569/
10 23

Stable maps and a universal Hitchin component

By Peter Smillie

Let $X$ be a pinched Cartan-Hadamard manifold, and $Y$ a symmetric space of non-compact type. We define a notion of stability for coarse Lipschitz maps $f: X \to Y$, and show that every stable map from $X$ to $Y$ is at bounded distance from a unique harmonic map. As an application, we extend any positive quasi-symmetric map from $\mathbb{RP}^1$ to the flag variety of $\textrm{SL}_n(\mathbb{R})$ to a harmonic map from $\mathbb H^2$ to the symmetric space of $\textrm{SL}_n(\mathbb{R})$. This allows us to define a universal Hitchin component in the style suggested by Labourie and Fock-Goncharov. This is all joint work with Max Riestenberg.

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Citation data

  • DOI 10.57987/IHP.2025.T2.WS1.010
  • Cite this video Smillie, Peter (22/05/2025). Stable maps and a universal Hitchin component. IHP. Audiovisual resource. DOI: 10.57987/IHP.2025.T2.WS1.010
  • URL https://dx.doi.org/10.57987/IHP.2025.T2.WS1.010

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