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.

Check the working paper version, as well as older versions on Mathematics ArXiv. - Equivariant Elliptic Cohomology and Rigidity

*American Journal of Mathematics***123**(2001), 647-677.

Check the working paper version, as well as older Mathematics ArXiv. - Rational S
^{1}-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.