I am planning on pursuing a ph.d. in mathematics, however, really my research interests often lie in the intersection of mathematics, logic, and theoretical computer science. Thus, in many of the universities I would like to apply to, I do not have very many common research interests with the mathematics faculty, but instead with the computer science or philosophy faculty.
Is it fine to mention that my primary research interests are actually outside the mathematics department in my letters of intent, should I try to word it to sound more like I am simply interested in interdisciplinary collaboration with other departments, or would even that harm my chances of getting accepted?
I suppose another question I have implicitly is: "...Or would it be better for me to apply for a ph.d. in Computer Science instead if the person at the university who most matches my research interests is in the computer science department?", or at least, what other factors should I consider to determine which way I should go (Math, or Computer Science) for a given university?
For what it's worth, my undergraduate degree is in mathematics with a minor in computer science.