Best Programs for Certain Topics?

[frogeyedpeas]

Hi,

I'm preparing to apply for Grad School in the coming fall, I'll be out of school for 3 years now (worked as a software engineer, now trying my best to pursue childhood dreams again xD)

I have a list of specialized topics that I enjoy working on in my spare time but I can't find a resource to actually tail up the best schools for certain topics, so I wanted to throw this as the board:

Does anyone work/is interested in working on:

1. Higher Teichmuller Theory
2. Proof Verification
- I heard CMU is a decent spot for this?
3. Discrete Operator Theory
- Rutgers, and UNC are good places for this
4. Computer Algebra
- Rutgers, and UNC again (since it overlaps a great deal)
5. Nonlinear Non Convex Optimization (I specialize in 0-1 IP but i'm down to learn a shit ton here)

If I can get a school that is really strong in say 3+ of these topics that'll be pretty sweet. But i'm having a hard time finding one.

[djysyed]

UIC has David Dumas (Teichmuller Theory) and Jan Vershalde (Computer Algebra).