Stable Maps and a Universal Hitchin Component

par Max Riestenberg (MPIMS Leipzig)

lundi 6 oct. 2025, 16:00 → 17:15 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

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 → 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 RP¹ to the flag variety of SL(n,R), to a harmonic map from H² to the symmetric space of SL(n,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 Peter Smillie.