Analytic Methods for Diophantine Equations (06w5101)

Some of the oldest questions in mathematics stem from the desire to find integer solutions to equations. From the equation in Pythagoras' theorem, to Fermat's last theorem, professional and amateur mathematicians alike are thrilled in trying to determine solutions, or to prove there are none. With such a venerable topic it is not surprising that there are many competing approaches to such questions, some whose time has already come, some that are very hot methods right now, and some whose time is yet to come. At this meeting (Analytic Methods for Diophantine Equations, May 13-May18, 2006) at BIRS there are participants from many of the different schools of thought in this subject; it will be an interesting opportunity for them to come together and find common ground.

During the last academic year two of the world's major research institutes, the Centre de Recherche Mathematiques in Montreal, and the Mathematical Sciences Research Institute in Berkeley, have hosted semester long programmes on different aspects on these questions, and many of the participants in those programmes, as well as some special extra invitees will be at this meeting. We can hope for some exciting interactions.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is administered by the Pacific Institute for the Mathematical Sciences, in collaboration with the Mathematics of Information Technology and Complex Systems Network (MITACS), the Berkeley-based Mathematical Science Research Institute (MSRI) and the Instituto de Matematicas at the Universidad Nacional Autonoma de Mexico (UNAM).