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

  • Topological mirror symmetry for parabolic Higgs bundles, (with P. Gothen) , Journal of Geometry and Physics 137 (2019)
  • SO(p,q)-Higgs bundles and higher Teichmüller components (with M. Aparicio-Arroyo, S. Bradlow, B. Collier, O. García-Prada, P. Gothen) , Inventiones mathematicae 288 (2019)
  • Connectedness of Higgs bundle moduli for complex reductive Lie groups (with O. García-Prada) , Asian Journal of Mathematics 21 (2017)
  • Motives and the Hodge Conjecture for moduli spaces of pairs (with Vicente Muñoz, Jonathan Sánchez ) , Asian Journal of Mathematics 19 (2015)
  • The singular fiber of the Hitchin map (with P. Gothen) , International Mathematics Research Notices 2013 (2011)

• Adittional information

  I am interested in the study of the geometry and topology of moduli spaces of (mainly Higgs-) bundles over algebraic curves. So I work with objects from Algebraic Geometry, an absolutely central area in modern Mathematics.

  Indeed, such study has an outstanding network of connections with many other areas of Mathematics, like  Differential Geometry, Algebraic Topology, Symplectic Geometry, Lie Theory and several others, including Theoretical Physics (like Mirror Symmetry).

  This is actually one of the beauties of this theory: it's source of several unexpected "bridges" between apparently different areas of Mathematics.

  I'm part of an extremelly successfull and dynamic worldwide network connection, composed by world top mathematicians. I have access to funding to travel, so a potential student of mine will travel a lot to make contacts with those mathematicians and of course participate in conferences or so. Such research contacts are crucial for every mathematician, and especially to PhD students.

  For more information, please check my website: https://sites.google.com/view/aoliveira.

  For an example (somehow now a little outdated) of a little part of my research, please take a look at the survey availble on page 17 of http://www.cim.pt/docs/98/pdf, written for a general mathematician.

  My arXiv personal area can be reached from here: https://arxiv.org/a/oliveira_a_1.html

  Topics on current projects I'm involved in (a potential student would work in one of these or other):

  • Study of higher Teichmüller components of the moduli spaces of Higgs bundles for real Lie groups.
  • Relate the existence of higher Teichmüller components of these moduli spaces with positivity property of the corresponding real Lie group.
    
  • Study of branes in the moduli space of Higgs bundles and their relation with mirror symmetry.
  • Study the motives ofmoduli spaces of lambda-connections.
  • Study the normality of Higgs bundle moduli.
  • Study of the moduli space of the so-called skew-symmetric pairs.

Research and Events