Faculty

• André Oliveira

  andre.oliveira@fc.up.pt

• Research Area

  Moduli spaces of bundles over algebraic curves

• Institution

  University of Porto

• PhD

  Institution: University of Porto
  Year: 2008

• Main research publications

  • Topology of moduli spaces of free group representations in real reductive groups (with Ana Casimiro, Carlos Florentino, Sean Lawton) , Forum Mathematicum 28 (2016)
  • Motives and the Hodge Conjecture for moduli spaces of pairs (with Vicente Muñoz, Jonathan Sánchez ) , Asian Journal of Mathematics 19 (2015)
  • Connectedness of the moduli of Sp(2p,2q)-Higgs bundles (with Oscar García-Prada) , Quarterly Journal of Mathematics 65 (2014)
  • The singular fiber of the Hitchin map (with Peter Gothen) , International Mathematics Research Notices 2013 2013 (2013)
  • Representations of surface groups in the projective general linear group , International Journal of Mathematics 22 (2011)

• Adittional information

  My research centers in a mix of Algebraic Geometry, Differential Geometry and Algebraic Topology and their relationships with the equations of Mathematical Physics. More precisely, I am interested in the study of the geometry and topology of moduli spaces of (mainly Higgs-) bundles over curves. My arXiv personal area can be reached from here: https://arxiv.org/a/oliveira_a_1.html
  
  Topics on current projects:

  • Study of connected components of the moduli space Higgs bundles for the groups SO(p,q)
  • Relate the existence of exotic connected components of these moduli spaces with positivity property of the corresponding real Lie group.
    
  • Study of branes in the moduli space of Higgs bundles arising from fixed points by tensorisation by finite-order line bundles.
  • Study the normality of Higgs bundle moduli.
  • Study of the moduli space of the so-called skew-symmetric pairs.

Research and Events