Labourie's conjecture and Higgs bundles at high energy

Abstract: For S a closed surface of genus at least 2, Hitchin representations from pi_1(S) to PSL(n,R) naturally generalize Fuchsian representations to PSL(2,R). Labourie proved that every Hitchin representation comes with an invariant minimal surface in the corresponding symmetric space. Motivated by the mapping class group action and potential Kahler metrics on the space of Hitchin representations, he conjectured that uniqueness holds as well.

In this talk we'll explain how we used Higgs bundles to produce large area minimal surfaces that give counterexamples to Labourie's conjecture, and we'll overview related advances in the theory of Higgs bundles at high energy. This is all joint with Peter Smillie.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

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CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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