At the moment, I'm mostly spending my time trying to map the landscape of type theories (in the broad sense of the word) and their categorical semantics. Of special interest to me are intuitive semantic presentations of initial - or fully abstract/complete, in CS terms - models of syntactic calculi. The two approaches that spring to mind, in particular, are the constructions of these models either as categories of games and strategies or as categories of geometric objects like (generalised) tangles. I'm hoping that a good understanding of this "big picture" will help relate diverse concepts coming from fields like computer science, physics, geometry (homotopy theory), logic, and linguistics, through the comparison of categories and type theories coming from these areas.
Master's thesis on topos-theoretic approaches to quantum kinematics, a survey article of the field, unifying some of the definitions and results and presenting some new ones.
Bachelor's thesis on principal bundles and gauge theory, a set of lecture notes that was intended to form an addition to the then existing literature by connecting the mathematical and physical parts of the story.