I'm curious as to how competitive my profile is, and what sort of schools I could get into at best. Here is some info. I go to a top Canadian school, doing the honours joint math and physics program. My interest lies very strongly in mathematical physics, particularly because I enjoy the content of physics, but prefer to study it from a mathematically rigourous point of view. Course wise, my biggest fear is that I'm spread too thin and that I lack a strong enough math background (no algebra other than linear). Upper division math courses i've taken: complex analysis, real analysis, intro topology, pdes, (graduate) mathematics of quantum mechanics, and in the coming semester (graduate) mathematics of general relativity, a differential geometry topics (graduate) course and maybe something else. I've had an NSERC USRA (Canadian equivalent of REU) in math after second year (but produced no results), and did summer research in physics this past summer (and right now I am submitting a short paper on some results, for which I would be the first author -- this is in physics, so will this improve my chances for math/ematical physics?). I should have good references. I am also a teaching assistant this year for a first year math course. I haven't taken the GRE subject test yet (I will probably do that next year during my master's -- planning on studying very hard), but I was wondering what level of a profile I'm shaping up to have, and how much a high GRE score would bolster me. Any thoughts? Thanks.
EDIT: Wow how did I forget my GPA. It's 3.72 overall (should be about 3.8 by the end of the year, doing better these last two years), and basically every course I took was for my major so major GPA is roughly the same.