Cursos IST em Geometria Algébrica 2013

O curso é o sétimo de uma série destinada a estudantes graduados e investigadores na área da geometria algébrica e de outras áreas. Os cursos usualmente decorrem no Instituto Superior Técnico (Lisboa) mas esta edição decorrerá na Universidade do Porto. Para informação mais completa e actualizada consulte a respectiva página web no CMUP.

Conferencistas

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

Resumo

Higgs bundles appear in several guises including

1. as solutions to gauge-theoretic equations for connections and sections of a bundle
2. as holomorphic realizations of fundamental group representations or, equivalently, local systems and
3. 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.

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