Hi everyone. I'm an overseas student looking to apply for some (possibly out of reach) top tier universities and want to know about my chances of getting in. Here is a quick summary of pertinent parts of my application.

Currently: final semester of two year MSc (Applied Mathematics), top university in my country

General GRE:

Q: 170 (96%)

V: 165 (96%)

W: 6.0 (99%)

Maths GRE: 890 (92%)

Research experience: 1 summer project on fluid mechanics + student conference, masters thesis on rarefied gas dynamics which my supervisor is rapt about, writing a paper soon, original work

GPA: 4.00, average score of 90% in masters

Prizes: freshman maths award, scholarship in masters all semesters for academic merit, dean's list first and third year undergrad (not second year because exchange)

Have tutored every maths subject completed in my first two years of undergrad, as well as a few from my third year and one from my masters.

Extra useful info: masters supervisor works at Caltech half the year as a professor (which means supervision in that semester is indeed challenging ): )

Wish to apply for: MIT, Caltech, Harvard, Stanford, UC Berkeley, all under Applied Maths, although I will probably apply for engineering too. Will, of course, apply for others, but my chances at these concern me the most at the moment.

Am I being too wishful here? Any tips for what I can do? I suspect I could email some potential supervisors, but I've been told that is of limited utility at American universities.