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.
The preprint versions of (most of) these papers can be found at arXiv.
S. Bradlow, B. Collier, O. García-Prada, P. Gothen, A. Oliveira, A general Cayley correspondence and higher rank Teichmüller spaces, Annals of Mathematics, 200, No. 3, (2024) 803-892.
E. Franco, P. Gothen, A. Oliveira, A. Peón-Nieto, Narasimhan--Ramanan branes and wobbly Higgs bundles, International Journal of Mathematics, 35, No. 9, 2441006 (2024).
D. Alfaya, A. Oliveira, Lie algebroid connections, twisted Higgs bundles and motives of moduli spaces, Journal of Geometry and Physics, 201 (2024) 105195.
A. Oliveira, Principal bundles on 2-dimensional CW-complexes with disconnected structure group, Glasgow Mathematical Journal, 64 (2022), 675-690.
E. Franco, P. Gothen, A. Oliveira, A. Peón-Nieto, Unramified covers and branes on the Hitchin system, Advances in Mathematics, 377 (2021), 107493.
I. Biswas, T. Gómez, A. Oliveira, Complex Lagrangians in a hyperKaehler manifold and the relative Albanese, Complex Manifolds, 7 (2020), 230-240.
M. Aparicio-Arroyo, S. Bradlow, B. Collier, O. García-Prada, P. Gothen, A. Oliveira, SO(p,q)-Higgs bundles and higher Teichmüller components, Inventiones mathematicae, 288 (2019), 197-299.
P. Gothen, A. Oliveira, Topological mirror symmetry for parabolic Higgs bundles, Journal of Geometry and Physics, 137 (2019), 7-34.
M. Aparicio-Arroyo, S. Bradlow, B. Collier, O. García-Prada, P. Gothen, A. Oliveira, Exotic components of SO(p,q) surface group representations, and their Higgs bundle avatars, C. R. Acad. Sci. Paris, Ser. I, 356 (2018), 666-673.
O. García-Prada, A. Oliveira, Connectedness of Higgs bundle moduli for complex reductive Lie groups, Asian Journal of Mathematics, 21, No.5 (2017), 791-810.
O. García-Prada, A. Oliveira, Maximal Higgs bundles for adjoint forms via Cayley correspondence, Geometriae Dedicata, 190, No.1 (2017), 1-22.
A. Oliveira, Quadric bundles applied to non-maximal Higgs bundles, Travaux Mathématiques, 24 (2016), 201-220.
A. Oliveira, Representations, Higgs bundles and components: an overview, CIM Bulletin, 36 (2016), 17-23.
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.
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.
A. Oliveira, Torelli Theorem for the Moduli Spaces of Rank 2 Quadratic Pairs, Communications in Algebra, 43, 8 (2015), 3051-3072.
V. Muñoz, J. Sánchez, A. Oliveira, Motives and the Hodge Conjecture for moduli spaces of pairs, Asian Journal of Mathematics, 19, No. 2 (2015), 281-306.
O. García-Prada, A. Oliveira, Connectedness of the moduli of Sp(2p,2q)-Higgs bundles, Quarterly Journal of Mathematics, 65 (3) (2014), 931-956.
P. Gothen, A. Oliveira, The singular fiber of the Hitchin map, International Mathematics Research Notices, 2013, No. 5 (2013), 1079-1121.
P. Gothen, A. Oliveira, Rank two quadratic pairs and surface group representations, Geometriae Dedicata, 161, 1 (2012), 335-375.
O. García-Prada, A. Oliveira, Higgs bundles for the non-compact dual of the unitary group, Illinois Journal of Mathematics, 55, No. 3 (2011), 1155-1181.
A. Oliveira, Representations of surface groups in the projective general linear group, International Journal of Mathematics, 22, 2 (2011), 223-279.
E. Franco, R. Hanson, J. Horn, A. Oliveira, Fourier-Mukai transforms and normalization of nodal curves, arXiv:2405.11860.
Quadric bundles and their moduli spaces, arXiv:1610.05568.
Higgs bundles, quadratic pairs and the topology of moduli spaces, PhD Thesis, 2008.