I'm not really familiar with the American graduate system, so I'd like to get an idea about what the profile of candidates look like (for candidates in the area of analysis/PDEs) for Courant Institute (NYU), Berkeley, UCLA, Johns Hopkins, Princeton, Chicago, Stanford, University of Texas at Austin, and Duke.
The past threads on grad admissions help quite a bit, but I'd still like some personalized advice and I'd appreciate if you could point out among the previous applicants someone with similar interests and target schools.
I've taken my bachelor's and I'm doing my master's degree from a smallish (not American) university. Top grades (and all courses taken were advanced). Rather well-known advisor. Four "REUs" in other (quite prestigious) institutions. Good projects in progress. Plenty of experience with conferences (attendance and presentations).