My interest in Mathematics was in algebraic topology, and its connections with index theory and mathematical physics. In particular, one of the most fascinating fields of math is Elliptic Cohomology. The main problem in this field (as posed by Ed Witten) is to find a geometric interpretation of elliptic cohomology and find its connection with String Theory. I didn't solve this problem 
, but I gave it a shot.
Here is a list of my publications in this area:
- Equivariant K-Theory and Equivariant Cohomology, appendix joint with Allen Knutson
Mathematische Zeitschrift 243 (2003), 423-448. - Equivariant Elliptic Cohomology and Rigidity
American Journal of Mathematics 123 (2001), 647-677. - Rational S1-Equivariant Elliptic Cohomology joint with John Greenlees and Michael Hopkins
Preprint (2000).
This version was continued by John Greenlees and published in Topology 44 (2005), 1213-1279. - Ph.D. Thesis
Defended in May 1998, submitted in June 1999.
Here's a little note posted by Alan Edelman with a problem that I solved in my very first semester at MIT.