Seminario Geometría
Hitchin-Ngô Lab Seminar - Branched real projective structures and cyclic Higgs bundles
Ponente: Nicholas Rungi (ICMAT)Fecha: martes 20 de octubre de 2026 - 10:00-11:00Lugar: Aula Naranja, ICMAT
Resumen:
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.
