The question is meant to be broad in that recommendations with mentions of the particular areas within type theory research are greatly appreciated. Also, the research need not be conducted in computer science departments. Thanks in advance.
Any such list is always subjective, but the best approach to answer this question is:
- Look at journals/conferences in the area you're interested in. For type theory, I'd look at LICS, LMCS, POPL, ICFP, and JFP.
- Find papers that seem interesting, or are in the area you're interested in.
- Look at the schools the authors are from.
There's another important underlying point here, which is the for graduate studies, the school matters much less than the supervisor. So you're far better off looking for the research you're interested in, and then trying to work with the people conducting it, then to choose a school first and then try to find a supervisor and area.