I will be applying to graduate schools in mathematics for Fall 2009. From what I've heard, the UCSB mathematics department is decent though not as good as some of the other mathematics departments I've been looking at (like Texas at Austin, Michigan, Illinois at UC, and University of Washington). However, my interest is in mathematical physics (i.e. QFT, relativity, the intersections between differential geometry and physics, representation theory, etc.) and I hear that UCSB is well known in theoretical physics and two professors have joint appointments with the mathematics and physics departments. Therefore I am wondering if as a mathematics graduate student (I wouldn't want to apply to the physics program because lots of the core physics courses do not interest me much whereas most of pure math appeals to me), I'll be able to take advantage of the breakthrough mathematical physics work being done there. Any opinions on the matter?