The idea that many algebraic invariants in number theory should have analytic analogues forms one of the central themes of arithmetic geometry today. Iwasawa theory takes this theme a step further, insisting that certain p-adic limits of algebraic invariants should have p-adic analytic relatives, an idea that has proven very fruitful. The PIs are organizing the conference Iwasawa 2010 at the University of Toronto from July 5-9, 2010, in coordination with the Fields Institute. This conference is the latest in a biannual series of international conferences on Iwasawa theory, and the first to be held in North America. The series has consistently attracted a worldwide audience, and speakers are invited upon consultation with a distinguished scientific committee. The award will provide travel support for U.S. speakers and junior researchers to the conference.
Number theory attempts to answer fundamental questions in arithmetic, such as: what are the solutions to a given polynomial equation? Iwasawa theory is a major area of research in number theory that provides, among other things, a means of relating the solutions of certain such equations to interesting mathematical functions (known as p-adic L-functions). The award will provide travel support for U.S. mathematicians to the international conference Iwasawa 2010 organized at the University of Toronto in coordination with the Fields Institute, during the period July 5-9, 2010. In particular, support for U.S. graduate students and postdoctoral researchers will provide them with the opportunity to learn from some of the foremost experts in the field. Moreover, the conference will educate the experts on new techniques and developments in Iwasawa theory, thereby promoting even greater progress on its many open problems and new directions of research.
The NSF award provided funding for two conferences in the field of algebraic number theory, one of the most active areas of research in mathematics today. Specifically, the conferences were devoted to research in the subfield of Iwasawa theory. This area originated from the work of Kenkichi Iwasawa in a series of papers in the 1950s and 1960s. Since then, Iwasawa theory has taken a central position in the field of algebraic number theory, having played a role in many of the most important developments in the field. Today, the area of Iwasawa theory is more active than ever, continuing to grow at a rapid pace. The first of the two conferences, Iwasawa 2010, was a five-day international held at the University of Toronto in July 2010. It was fifth in a series of biannual conferences devoted to research in the subject and the first to be held in North America. In addition to the NSF award, funding was provided by the Fields Insistute for Research in Mathematical Sciences. Twenty speakers, including seven from the U.S., gave hour-long reports on the state of their art in the field to an audience of about seventy. Included in this audience were more than ten U.S. graduate students and a few U.S. postdoctoral fellows who received NSF funding to attend. The conference provided them a great opportunity to gain a familiarity with current research in the area which is otherwise hard to obtain, thereby aiding in their development as research mathematiicians. The research reported on by the speakers is by an large being or has been published in major mathematical journals. The second conference, Workshop on Iwasawa theory, was a smaller follow-up meeting at the University of Arizona in October 2011. The nine speakers who delivered hour-long talks at this conference included some of the most distinguished number theorists in the nation. Among the audience of approximately forty were more than 10 U.S. graduate students who received NSF support to attend, as well as a number of local graduate students. As with Iwasawa 2010, the research reported on by the speakers is being published in esteemed journals. Both conferences can be counted as great successes not just in the education of young researchers but in providing a forum for top researchers in the field of algebraic number theory to interact, form new collaborations, and keep abreast of the latest developments in field of Iwasawa theory.
