Higgs Bundles and the Topology of Higher Teichmüller Spaces

Explore the fascinating world of higher Teichmüller spaces in this comprehensive lecture by Oscar Garcia-Prada from ICMAT. Delve into the generalization of Teichmüller spaces for non-compact real Lie groups of higher rank, building upon the well-known identification of Teichmüller space for compact surfaces with a connected component of the moduli space of representations. Discover how the theory of Higgs bundles, combined with the non-abelian Hodge correspondence and the recently developed Cayley correspondence, provides powerful tools for investigating the topology of these higher Teichmüller spaces. Gain insights into this advanced mathematical topic and its connections to fundamental group representations, moduli spaces, and Lie group theory.