I am interested in problems typically tackled in theoretical computer science departments as well as seperate problems found in mathematics departments. Both would be more proof based. Is it easy to move from one to the other?
Example: Say I would like to work on proofs under the theory of computation (on the CS side) as well as geometric and topological proofs coming from problems in particle theory (maybe more on the mathematical physics side). Should I be in TCS or a math department, or would I be free enough to move around? Might I have more room to move in a mathematics department versus a TCS department?