I'm an engineering undergrad with low CGPA, trying to get a Math PhD position in the US. My college is top 5 in India.
Mathematics GRE Score- 820/990 (83 percentile).
1. Currently working under Professor Kapil Hari Paranjape on Algebraic Geometry for 6 months.
2. Completed the Visiting Students' Research Program at TIFR, Mumbai. I worked on Commutative Algebra under Professor S Subramaniam.
3. Bronze medal- Singapore Math Olympiad (Senior section) and Honourable mention (Open section). I availed a $60,000 scholarship to attend higher secondary school in Singapore.
4. Summer internship at ISI, Kolkata on Ring Theory.
5. Blog on algebra/topology/set theory. Link: http://www.cozilikethinking.wordpress.com
I have original proofs of Hilbert's Basis Theorem, Eisenstein's criterion (slight generalization), amongst others.
6. Special project in Algebraic Topology (following Hatcher's book)
7. Edit Commutative Algebra notes for a Masters' student in Berlin School of Mathematics
8. Extensive questions/answers on math.stackexchange.com. Around 2500 credit points.
Could someone suggest colleges that I could apply to? I'd appreciate realistic suggestions. I am aiming as low as 150-200