During my PhD I have worked with different types of problems. Here I explain a little bit what is my PhD thesis about. Feel free to ask me about more details (the pdf will come as soon as my PhD document is ready).
I studied principal bundles on effective orbifolds. In particular, I defined the holonomy group of a connection, proved that it is a Lie group and showed that the Ambrose-Singer theorem holds for principal orbibundle connections.
I have been studying formal deformation problems. In particular, together with my advisor, we gave an explicit description of the obstructions of a deformation problem in terms of the L_\infty-algebra that controls it.
I have been studying deformations of Lie algebroid morphisms. In particular, we found a deformation complex that controls the moduli space of deformations of morphisms up to equivalence. Besides, we use it to describe deformations of subalgebroids and study some examples.
Together with João Mestre and Ivan Struchiner, we are working on deformations of Cartan's realization problem.