Geometry Seminar
Hitchin-Ngô Lab Seminar - Geometric structures from cyclic Higgs bundles via parallel distributions of planes
Speaker: Colin Davalo (Università di Torino)Date: Tuesday, 20 October 2026 - 11:30-12:30Place: Aula Naranja, ICMAT
Abstract:
The non-abelian Hodge correspondence identifies the moduli space of polystable \(G\)-Higgs bundles with the space of representations of surface groups into \(G\) for every simple group \(G\). A difficult question in general is to determine which Higgs bundles give rise to representations that discrete and/or are the holonomies of geometric structures. In recent years several results in this direction have been obtained for cyclic Higgs bundles, especially in rank 2. In this talk I will present some recent joint work with Parker Evans for a family of cyclic Higgs bundles for the exceptional real split group \(G_2'\) introduced by Collier and Toulisse. We show that the representations associated to these bundles are the holonomies of geometric structures modelled on a flag manifold on a fiber bundle over the surface. The main principle of our construction uses a parallel distribution of planes along the minimal surface in the symmetric space that is constructed from the cyclic Higgs bundle. This construction allows us to also reinterpret previous constructions of geometric structures in other rank 2 groups. Moreover these parallel distributions of planes prove also useful in general to show the discreteness and Anosov property for the corresponding representations.
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