Research and Publications

My Ph.D research was on the classical approach to Fermat's last theorem using cyclotomic field theory. My thesis advisor was Prof. Dinakar Ramakrishnan . Currently I am working on the class number of the cyclotomic field. More details will be posted soon.

Publications



Resources for Number Theory

Several resources are available for number theorists, including lists of number theorists, preprint servers, archives, and computational resources such as PARI and the elliptic curve calculator. All these and more can be found on the Number theory web. ( link to the site in Brisbane, Australia. There are other mirror sites available).

Fermat's Last Theorem and Cyclotomic fields
Starting with Kummer, a long list of mathematicians including Mirimanoff, Pollaczek, Furtwangler, Morishima, Eichler, Inkeri, and Vandiver tried to use algebraic number theory , and the theory of cyclotomic fields in particular, to solve Fermat's last theorem. They met with a great deal of success, especially on what is known as the First case, as chronicled in P. Ribenboim's "Thirteen lectures on Fermat's Last Theorem." Ultimately, though, the theory of elliptic curves and modular forms in what is now called arithmetic geometry proved more powerful, and Andrew Wiles was able to prove the "theorem" in 1995 in its entirety. ( Here is an article by G. Faltings on Wiles' proof and an interview with Wiles about the proof. For a detailed list of resources available on Fermat's last theorem, go to Eric Weisstein's treasure trove on Fermat's last theorem.

Notes from a lecture of mine on this topic

But the work on cyclotomic fields has by itself yielded many fundamental results that are useful in many branches of number theory and arithmetic geometry quite independent of their relevance to Fermat's last theorem, as can be seen from L. Washington's "Introduction to cyclotomic fields" or S. Lang's "Cyclotomic fields."