Good work hard work good hard work work hard good work hard

>>5764633
>33
>dubs

I'm in graduate school for math. I went there to do research, but I wasn't expecting to have to do as much teaching as I'm doing. I hate teaching.

>>5764633 (dubs)
Hi, I am in graduate school for physics. I'm here to do research in high energy, but I only just got here so I'm not in a group yet. I want to someday be a professor, but as long as I'm doing research then that is good.
Right now I'm TAing and grading for a lab, which isn't really my thing to be honest. Labs have always thrown me off a little, and this one is structured in a non-standard way.
>>5764641
What specific area of mathematics are you interested in?

>>5764753
>What specific area of mathematics are you interested in?
I'm in low-dimesional topology. The specific thing I'm working on is the following: some guys came up with a system of coordinates that parametrize representations (nice functions) from certain 3-manifolds to SL(n,C). This is cool because the coordinates work nicely for triangulations, so we can take, say, the figure eight knot complement and actually compute all possible representations into SL(3,C).

The technique these guys used involves things called Cluster Algebras, which I hear you physics people are sort of interested in as well. Recently, people have figured out how to generalize the first part of the construction, replacing SL(n,C) with lots of other Lie Groups. I'm trying to carry that work forward. My goal is that you give me a (nice) 3-manifold, I triangulate it, run some quick computations on a finite number of points, and come back with every possible representation into, say, the Lie Group G2.

The really weird thing about this is that the work for SL(n,C) has a physical interpretation: we can compute the volume of the manifold as an invariant. For the other Lie Groups, what I'll be computing is some kind of invariant, but (as far as I know) there's no physical interpretation of that invariant yet. Perhaps it will be something like a higher-dimensional analogue of the Dehn Invariant, or perhaps it will be something boring. I hope it's something nobody's ever seen before.

(Sage for my blog.)

>>5764785
bump for your blog because i like it

>>5764785
Sounds neat, though definitely a little over my head. My math degree was only a B.A. (the number of additional courses to the phys degree was quite small compared to the B.S.), so while I recognize terms it's a lot of stuff I only have very basic experience with at most. Someday I would like to learn more mathematics if I am able too; I decided to go with physics around when I started college, but I feel like I could just as easily have gone for mathematics; it is some really neat stuff, particularly the little taste of (relatively) higher-level mathematics I got at the end of the B.A.