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. Topics on current projects:

• A generic approach to the topology of moduli spaces of G-Higgs bundles (i.e. without specifying the group G).
• Geometry of moduli spaces of rank 2 quadratic pairs.
• A motivic description of the moduli spaces of Bradlow pairs.
• Topology of free group representations in real Lie groups.

Papers

1.	Representations of surface groups in the projective general linear group, Int. J. Math., 22, 2 (2011), 223-279
2.	(with P. Gothen) Rank two quadratic pairs and surface group representations, Geom. Dedicata, 161, 1 (2012), 335-375.
3.	(with P. Gothen) The singular fiber of the Hitchin map, Int. Math. Res. Not., 2013, No. 5 (2013), 1079-1121.
4.	(with O. García-Prada) Higgs bundles for the non-compact dual of the unitary group, Illinois J. Math., 55, No. 3, to appear.

Preprints

1.	Geometry of moduli of rank 2 quadratic pairs, arXiv:1206.3876v1.
2.	(with V. Muñoz and J. Sánchez) Motives and the Hodge Conjecture for moduli spaces of pairs, arXiv:1207.5120v1.
3.	(with O. García-Prada) Connectedness of the moduli of Sp(2p,2q)-Higgs bundles, arXiv:1209.2336.

Other stuff

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