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