Open Questions and Recent Developments in Iwasawa Theory

Trustees Of Boston University, Boston

Investigators

Abstract

In June of 2005, Boston University will host a weeklong international conference entitled "Open questions and recent developments in Iwasawa theory". Over five days, the conference will cover a broad range of topics in Iwasawa theory with an emphasis towards the main conjecture in its many guises and non-commutative Iwasawa theory. Iwasawa theory has seen major advances in the last few years (e.g. the Skinner-Urban proof of the cyclotomic main conjecture for modular forms and the Coates, Fukaya, Kato, Sujatha and Venjakob proposal of a non-abelian main conjecture) making it important to have experts come together to discuss these results and make them more widely available to the mathematical community. A key aspect of the conference will be an emphasis on the future direction of Iwasawa theory. Indeed, each speaker will be asked to present open questions and conjectures that they feel are important to the development of the field. Iwasawa theory is a subfield of number theory whose fundamental questions relate algebraic information (e.g. solutions to polynomial equations) to analytic information (e.g. values of functions arising from calculus). The merging of these two disparate ideas is what makes Iwasawa theory such a mysterious and powerful field. One can use Iwasawa theory to study the arithmetic of a variety of geometric objects such as elliptic curves. Since the theory of elliptic curves has applications to coding theory and cryptography, advances in Iwasawa theory could lead to advances in these two subjects