Hi. I am an applicant from India, currently in the final year of a B.Tech Electrical and Electronics Engineering course in an Indian university. I plan to apply to physics PhD programs in the US. I have taken very few courses in physics proper (2 theory+lab courses) and mathematics (4 courses) apart from a host of physics related engineering courses (for eg, Thermal Engineering, Engineering Mechanics, Solid and Fluid Mechanics, Electron devices etc). I have had two productive research internships, one in math and one in physics, and for the former, I received a national fellowship. The latter was in condensed matter theory and I am still continuing the work. The math internship was in Group theory, in particular, Special Groups, Lie Algebra and Group Representation. I hope to get substantially strong recommendation letters. I have scored 930 in PGRE (88th percentile), 330 in GRE (Verbal: 163 & 92nd percentile, Quant: 167 & 94th percentile, AW 4.5 & 80th percentile) and 114 in TOEFL ibt (R-29, L-30, S-27, W-28). I am not sure if I should apply to a top university given the fact that I have few courses in physics, on paper (i.e transcript). But I have completed a few online courses, for example, edx 8.05x Mastering Quantum Mechanics from MIT. My current interest is in Condense matter theory. Should I apply to any of these: Princeton, Stanford, Caltech, Harvard, MIT or UC Berkeley? Has anyone with a similar non traditional background been admitted to theory in any of these? How can I boost my application?