<em>Lecturers</em>

Steven Bradlow (University of Illinois at Urbana-Champaign)

Oscar García-Prada (Instituto de Ciencias Matemáticas, CSIC, Madrid)

<em>Abstract</em>

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.

<em>About the courses</em>

The course is the seventh of a series of courses aimed at graduate students and researchers in the area of algebraic geometry and researchers from other areas. The courses usually take place at the Instituto Superior Técnico (Lisbon) but this year's edition will take place at the University of Porto.