I am currently interested in principal Hitchin fibrations and surface group representations into real forms. I am member of the Differential Geometry Research Group at the Mathematical Institute of the University of Heidelberg, and we are looking at the relation between Higgs bundles and projective structures.
For my D.Phil thesis I have studied the monodormy action for the SL(2,R) Hitchin fibration and also looked at U(p,q) and SU(p,q) Higgs bundles. Some of the work that I have done is here:
- "Monodromy action for the SL2 Hitchin fibration", ArXiv:1111.2550v1
- "On the geometry of U(p,p) and SU(p,p) Higgs bundles", in preparation.
- "Spectral data for U(p,1) and SU(p,1) Hitchin fibrations" , in preparation.
- "Monodromy of Higgs bundles", Transfer report, Oxford University.2010
- "Aproximación simpléctica a la mecánica lagrangiana". Master's Thesis. Advisor: J.E. Solomin. 2008
- "Geometric approach to Lagrangian mechanics". Survey done for Henrique Bursztyn`s course Symplectic Geometry. 2008
- “Non-autonomous systems” for the course Non linear systems, 2007.
- "Linear groups" for the course Abstract Algebra, 2007 (with Pablo de Caria)
- “Simplex method for bounded variables” for the course Linear programming, 2007 (with Pablo de Caria)
- “Minimal cost flow” for the course Linear programming, 2007 (with Pablo de Caria)
- "Topics on probabilities" for the course Topics on probabilities, 2007.
- “Poisson equations” for the course Elements of applied Mathematics, 2005 (with Pablo de Caria)