Hitchin-Ngô Lab Seminar
19 October 2026
(Venue: Aula Naranja, ICMAT, Madrid)
10:00 - 11:00: Andrea Tamburelli (Università di Pisa)
Title: Pseudo-Kähler geometry of Hitchin representations in PSL(3,R)
Abstract: It is classically known that the Teichmüller space of a smooth, closed, oriented surface of genus g>1 is a ball of dimension 6g-6, which can be endowed with a Kahler metric, the Weil-Petersson metric, defined in terms of holomorphic quadratic differentials on the surface. In this talk, we will see how such a metric has a natural pseudo-Kahler extension on the Hitchin component for SL(3,R), in which the Teichmüller space embeds totally geodesically. The construction is based on the geometry of equivariant affine spheres and provides an alternative approach to the recent work of Collier-Toulisse-Wentworth for the SL(3,R) Hitchin component. Joint work with Nicholas Rungi.
11:00 - 11:30: Coffee break
11:30 - 12:30: Andrea Seppi (Università di Torino)
Title: A complex hyperKähler extension of the Weil-Petersson metric
Abstract: It is a classical fact, going back to Weil and Ahlfors around 1960, that the Teichmüller space has a natural Kähler structure, called the Weil-Petersson metric. Many interesting extensions have been studied: Donaldson in 2003 constructed a hyperKähler extension on the space of quasi-Fuchsian manifolds, Loustau-Sanders then built a complex bi-Kähler extension, whereas in my work with Mazzoli and Tamburelli we constructed a para-hyperKähler extension on an analogue space of Anti-de Sitter manifolds. In this talk, I will explain that all these extensions are in fact restrictions of a natural, holomorphic, "complex hyperKähler'' structure defined on a larger space. If time permits, I will describe the crucial role played by minimal immersions in the complex Lie group PSL(2,C).
20 October 2026
(Venue: Aula Naranja, ICMAT, Madrid)
10:00 - 11:00: Nicholas Rungi (ICMAT)
Title: Branched real projective structures and cyclic Higgs bundles
Abstract: A classical consequence of the uniformisation theorem, for a closed surface S of genus g>1, is that hyperbolic structures on S can be described in terms of Fuchsian representations of its fundamental group into PSL(2,R). The so-called higher Teichmüller theory aims to provide a generalisation of this correspondence. For instance, representations in the Hitchin component for SL(3,R) arise as holonomies of properly convex real projective structures on S, which generalise hyperbolic structures. The main goal of this talk is to show that this phenomenon extends beyond the Hitchin component once one allows projective structures with branch points. The first part of the talk will be devoted mainly to an introduction to these branched structures, together with some examples and a statement of the main results. In the second part, we will explain how cyclic Higgs bundles can be used to construct interesting examples of such structures. This is joint work with Gianluca Faraco.
11:00 - 11:30: Coffee break
11:30 - 12:30: Colin Davalo (Università di Torino)
Title: Geometric structures from cyclic Higgs bundles via parallel distributions of planes.
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.
Past Seminars
17 September 2026
(Venue: Aula Naranja, ICMAT, Madrid)
10:00 - 11:00: Steven Bradlow (University of Illinois Urbana-Champaign)
Title: Geometric structures and Higgs bundles
Abstract: Under the right conditions surface group representations, i.e. homomorphisms from the fundamental group of a topological surface into a Lie group, are intimately connected to geometric structures modeled on homogeneous spaces, and also to Higgs bundles on Riemann surfaces. This creates opportunities for using Higgs bundles to investigate geometric structures, and also for using geometric structures to shed light on Higgs bundles. This - mostly expository - talk will explore these themes.
11:00 - 11:30: Coffee break
11:30 - 12:30: Juming Zhang (Nankai University)
Title: 4-cyclic Higgs bundles, ∂-alternating surfaces, and QIE representations
Abstract: We introduce ∂-alternating surfaces in complex pseudo-hyperbolic spaces of signature (2,q) or (q+1,1), which generalize maximal surfaces in real pseudo-hyperbolic geometry, and establish a natural correspondence between these surfaces and harmonic 4-cyclic Higgs bundles. Under this correspondence, the Gauss map of the surface agrees with the harmonic map arising from non-Abelian Hodge theory. When the underlying surface is closed, we prove that the associated equivariant harmonic maps are bi-Lipschitz embedded minimal surfaces and that the corresponding surface-group representations into PU(2,q+1) are discrete, faithful, and their orbit maps are quasi-isometric embeddings. We also construct domains of discontinuity in the symmetric space and its Shilov boundary, whose quotients form fiber bundles over the underlying surface. This is joint work with Qiongling Li.
18 September 2026
(Venue: Aula Naranja, ICMAT, Madrid)
11:30 - 12:30 Marcos Jardim (Unicamp, Campinas)
Title: Stability conditions for coherent systems on integral curves
Abstract: We present stability conditions for the category of coherent systems on an integral curve. We define a three-parameter family of pre-stability conditions in its derived category using tilting, and then investigate when these conditions qualify as stability conditions. Additionally, we examine the semistability of specific objects under these conditions, namely: torsion, free, and complete tilted systems, without relying on the support property. Joint work with Leonardo Roa-Leguizamón and Renato Vidal Martins.