Category Theory Seminar!
It looks like not only is this seminar going to go off, but one of the tenured faculty is going to set it up as a seminar associated to the department’s VIGRE grant, partly because his grad student needs a VIGRE seminar on his transcript this semester and this would be the closest to his actual research interests. Here’s the rough description I sent off to the professor, which will be more or less the outline on the books:
As I’ve envisioned it, the seminar will start with 2-3 weeks (maybe 4, depending on how smoothly it goes) of basic information, to cover:
1) categories, functors, and natural transformations
2) limits, adjunctions, representable functors, universals (Yoneda lemma?)
3) monoidal and monoidal closed categories
At that point most of the basic language is in place to do applications. We can then branch out to survey various applications in 1-3 weeks each, including (but not limited to):
1) “quantum topology” (applications to knot theory and related fields)
2) elementary topoi (applications to foundations)
3) lambda calculi (applications to functional programming semantics)
4) Lawvere’s “sketches” (applications to universal algebra)
5) n-categories (applications to mathematical physics)
These branches could be dealt with by interested seminar participants as time permits.
I’m hoping that the material could be made accessible to even a good senior undergraduate, but if the VIGRE seminar format is such that it’s more appropriate to restrict to graduate students and up, that can work too.
I’m surely not going to measure up to John Baez’ quantum gravity seminar, especially not on my first time out, but I’m really excited about it anyhow. When we start up I’ll try to get some regular attendee take notes so I can follow Baez’ lead in scanning/posting them.