Study of geometric and topological properties of moduli spaces. The following are the main projects I worked on:

• Proof of irreducibility of moduli of semistable Chains and applications to U(p,q)-Higgs bundles. Joint work with Bradlow, Garcia-Prada and Heinloth, concluded.
• Proof topological mirror symmetry for parabolic Higgs bundles in rank 2 and 3. Joint work with Oliveira, concluded.
• Study of wall crossing for chains via quiver bundles. Joint with Nozad, concluded.
• Determination of the connected components of the moduli space of SO(p,q)-Higgs bundles and identification of "exotic" components; these can be viewed as coming from a generalized Cayley correspondence and are related to positivity of surface group representations. Joint work with Aparicio, Bradlow, Collier, Garcia-Prada and Oliveira, concluded February 2018.
• Study of BBB-branes coming from fixed points of the action of torsion line bundles on the moduli space of Higgs bundles and proof that their dual BAA-branes are coming from Hecke modifications. Joint work with Franco, Oliveira and Peon-Nieto. Preliminary version concluded February 2018.
• Other projects are in progress.