I am an Indian student enrolled in the PhD program in Mathematics at Central Michigan University (a relatively unknown program). I have a weak background in my undergrad. I did Mechanical Engineering (at BITS Pilani, for people who know about Indian colleges), and had a low CGPA (6.7/10) with bad grades in Math subjects.
1. Dean's Research Assistantship. This is the most prestigious fellowship given to any incoming student at Central Michigan University.
2. Nominated by the Department to attend a workshop on Tropical Geometry at MSRI, Berkeley.
3. Pursued Mechanical Engineering at BITS Pilani, India, and then switched to Mathematics.
4. Only candidate to clear the Algebra qualifying exam. I got around 90%. The passing mark was 70%
5. GRE: 336/340. Subject GRE: 97 percentile.
6. Math blog: cozilikethinking.wordpress.com
7. Singapore Math Olympiad: Bronze
8. GPA: 3.85/4
9. Selected for the Master's program at Chennai Mathematical Institute. Interview calls from TIFR Bombay and Bangalore. Selected for the program at Bangalore. I also attended the VSRP program at TIFR Bombay.
10. NET rank: 28
11. Six month internship with Prof Kapil Hari Paranjape on Differential Geometry.
12. Awarded the Keppel Magus Scholarship to complete high school in Singapore. Only student selected from Kolkata.
The thing that has changed in the recent past is that I got my Subject GRE score today: 97 percentile (900).
I had a fallout with one of the professors who had initially told me he would write me a strong reco. Now I'm taking recos from other professors, and I think they will be good, but generic.
I've done some original research in Algebraic Geometry as part of my Masters' thesis. We have proved the result we wanted. However, I will not be able to submit the preprint with my application as my thesis advisor does not want me to.
Should I apply to MIT, Stanford, Berkeley or Chicago? Does just my Subject GRE score warrant that. How about Cornell, Wisconsin-Madison or University of Michigan? Does the blog help in any way?