Geometry of Higgs Bundles - IST Courses on Algebraic Geometry - 2013

Departamento de Matemática, Faculdade de Ciências da Universidade do Porto
Tuesday, 25 June, 2013

Higgs bundles appear in several guises including (a) as solutions to gauge-theoretic equations for connections and sections of a bundle (b) as holomorphic realizations of fundamental group representations or, equivalently, local systems and (c) as special cases of principal bundles with extra structure (principal pairs). Each point of view leads to a construction of a moduli space, i.e. a geometric object whose points parametrize equivalence classes of Higgs bundles. The first part of this mini course will explain these different points of view and describe how they are related. We will then explore some key topological and geometric features of the moduli spaces. We will confine attention to Higgs bundles over closed Riemann surfaces


Steven Bradlow (University of Illinois at Urbana-Champaign) and Oscar García-Prada (Instituto de Ciencias Matemáticas, CSIC, Madrid)