Wow, time flies! I’m now a Ph.D. student at UT Austin, and you can find some of my writing and stuff on my department home page. Things I’m thinking about these days include… * Quadratic differentials, spectral networks, and connections on Riemann surfaces (for a reading course). * Classical and quantum gauge theories on compact surfaces (for a math club talk). * What the is going on in this paper (for a graduate geometry seminar). * Markov algorithms (maybe for a middle school summer program somewhere, someday).
I’m a master’s student interested in mathematical physics. Or is it physical mathematics? Here are some things I’ve been wondering about lately… * The general boundary formulation of quantum field theory. * Whether or not it would be pedagogically useful to introduce topology as a special case of pretopology.
Welcome, Aaron! It might be good if you used your full name, although I don't think anybody will try to force you.
I have also thought that pretopological spaces are pedagogically simpler than topological spaces. I also like to motivate uniform spaces as a uniform version of pretopological rather than topological spaces (although we do have the theorem that any pretopological uniform space is topological). On the other hand, now that I'm getting to locale theory, I'm not as interested in pretopological spaces ….