Geometry and Dynamics of Cyclic Higgs Bundles in the Slodowy Slices

par Samuel Bronstein (MPIMS Leipzig)

lundi 10 nov. 2025, 16:00 → 17:15 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

The nonabelian Hodge correspondence provides a parametrization of the character variety of a surface group in a semisimple Lie group G by objects called Higgs bundles (which we will introduce). Among them, cyclic Higgs bundles stand out as candidates for representations with strong geometric properties. The Slodowy slice is a natural set of deformations of a Fuchsian representation in G, whose properties are yet to be described. In this talk, I will present some cases in which we are able to prove that representations in the cyclic Slodowy slice are Anosov, hence discrete and faithful, and correspond to some geometric structure that we describe. This is joint work with Colin Davalo and Qiongling Li.