André Oliveira

 

Research Interests

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.

Topics on current projects:
  • Study of connected components of the moduli space Higgs bundles for the groups SO(p,q).
  • Study of the topological mirror test for the moduli spaces of parabolic Higgs bundles on a curve.
  • Study of the moduli space of the so-called skew-symmetric pairs.
  • Study of certain types of dual branes on the moduli spaces of Higgs bundles.


Published or Accepted Papers

13. O. García-Prada, A. Oliveira, Maximal Higgs bundles for adjoint forms via Cayley correspondence, Geom. Dedicata, to appear.
12. O. García-Prada, A. Oliveira, Connectedness of Higgs bundle moduli for complex reductive Lie groups, Asian. J. Math., to appear.
11. A. Oliveira, Quadric bundles applied to non-maximal Higgs bundles, Travaux Mathématiques, 24 (2016), 201-220.
10. A. Oliveira, Representations, Higgs bundles and components: an overview, CIM Bulletin, 36 (2016), 17-23.
9. A. Casimiro, C. Florentino, S. Lawton, A. Oliveira, On the homotopy type of free group character varieties, Boletim Soc. Port. Mat., Special Number, May 2016, 53-57.
8. A. Casimiro, C. Florentino, S. Lawton, A. Oliveira, Topology of moduli spaces of free group representations in real reductive groups, Forum Mathematicum, 28, 2 (2016), 275-294.
7. A. Oliveira, Torelli Theorem for the Moduli Spaces of Rank 2 Quadratic Pairs, Comm. Algebra, 43, 8 (2015), 3051-3072.
6. V. Muñoz, J. Sánchez, A. Oliveira, Motives and the Hodge Conjecture for moduli spaces of pairs, Asian. J. Math., 19, No. 2 (2015), 281-306.
5. O. García-Prada, A. Oliveira, Connectedness of the moduli of Sp(2p,2q)-Higgs bundles, Quarterly J. Math., (2014), 65 (3), 931-956.
4. P. Gothen, A. Oliveira, The singular fiber of the Hitchin map, Int. Math. Res. Not., 2013, No. 5 (2013), 1079-1121.
3. P. Gothen, A. Oliveira, Rank two quadratic pairs and surface group representations, Geom. Dedicata, 161, 1 (2012), 335-375.
2. O. García-Prada, A. Oliveira, Higgs bundles for the non-compact dual of the unitary group, Illinois J. Math., 55, No. 3 (2011), 1155-1181.
1. A. Oliveira, Representations of surface groups in the projective general linear group, Int. J. Math., 22, 2 (2011), 223-279.


Preprints

1. P. Gothen, A. Oliveira, Topological mirror symmetry for parabolic Higgs bundles.
2. A. Oliveira, Quadric bundles and their moduli spaces.


Other stuff

1. Higgs bundles, quadratic pairs and the topology of moduli spaces, PhD Thesis, 2008.
2. Representations of the fundamental group of a surface in PGL(n,R), Talk.
3. Quadratic pairs and the Hitchin map, Talk.