Mathematical physics for graduate school

Right now I am going into my senior year as a physics major. I am
interested in applying to graduate school, and I want to study
mathematical physics. In particular, I think I would enjoy studying
ways to place physical theories like quantum field theory or general
relativity on rigorous mathematical foundations.

Although I am a physics major, I have managed to take lots of math
classes. In particular, I will have as many topology and analysis
classes as a typical math major at Caltech, and I have taken a year
long course in Algebra and had some more applied math courses (PDEs,
dynamical systems, things of that nature). I generally feel like I
enjoy my math classes at least as much if not more than my
corresponding physics classes.

This summer I have been thinking about places where I might apply to
graduate school. I have had success finding physics programs where I
think there are faculty who study the things that I am interested in
(interestingly, these sorts of "mathematical physics" programs seem
much more common in the UK.) Since I have taken lots of math classes, I
was wondering if I could potentially go to graduate school in
mathematics. I would want to focus on mathematical physics in
particular, and somehow I think I might enjoy math graduate school more
than physics graduate school. I haven't been able to identify math
departments where mathematical physics is well represented.

If anyone can help me with looking for math graduate schools that suit
my needs, (or less importantly physics ones) it would be
extraordinarily helpful to me. If anybody has other advice relating to
my graduate school search, please feel free to tell me.

Thanks for your help,
Sincerely,
George Hagstrom

.

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