I am a grad student in the Mathematics and Physics departments at the University of North Texas (in Denton, TX). I have been an avid reader of the seminar notes John Baez has put on his website. Up until recently, I have mostly just read through some books on category theory, but there is nothing like doing exercises and having others point out errors for making one really learn a subject.
I am interested in the foundations of quantum mechanics, phase transitions, critical phenomena, the foundations of thermodynamics, renewal processes, game theory, logic, and category theory. My Physics research is mostly about stochastic processes and the response of complex systems to purturbation. My Mathematics research currently involves the topological games, in particular, determining whether and under what conditions certain topological games are dual. I am interested in category theory as a way to better understand the connections between the various subdisciplines in Mathematics/Physics/Computer Science, and for its usefulness as a way to organize mathematical knowledge.