Diophantine Approximation and Analytic Number Theory: A Tribute to Cam Stewart (10w5032)

Arriving in Banff, Alberta Sunday, May 30 and departing Friday June 4, 2010


(University of British Columbia)

(Université de Montréal)

Jeff Thunder (Northern Illinois University)

(University of Ottawa and CSE)


Recent significant developments in the area of Analytic Number Theory, such as
the work of Green and Tao on primes in arithmetic progression, and the work of
Goldston, Pintz and Yildrim on small gaps between primes, have gained the attention of both experts in the area, and the greater mathematical community. The reason for this increased level of interest stems from the fact that statements about prime numbers are so simple, and yet the proofs of such statements often require methods of considerable depth, or else have remained elusive. These developments have spawned a considerable amount of new research, and also new forums for researchers to develop their ideas. These forums include the special program in Analytic Number Theory in 2005-2006 at the Centre de Recherches Mathematiques, the upcoming 2009-2010 program in Analytic Number Theoryat The Institute for Advanced Study, and workshops at various research centers such as the workshop on Gaps between Primes in 2005 at The American Institute of Mathematics, and those at the Banff International Research Station which will be elaborated on below. As a result of much of this research, methods developed within the scope of Analytic Number Theory have found connection to various other mathematical areas, both within Number Theory, and beyond. One particular area of study which has been affected by these developments is the classical area of Diophantine equations. Such connections were the scope of the 2004 BIRS workshop on Diophantine approximation and Analytic Number Theory and the 2006 BIRS workshop on Analytic Methods for Diophantine Equations. A central figure in both of these research areas is Professor C.L. Stewart of the University of Waterloo. The contributions of Professor Stewart are numerous and of considerable influence.
From his early work on primitive divisors in Lucas-Lehmer sequences, to his notable joint papers with Paul Erdos on Diophantine equations and prime factors of arithmetical forms, with Alan Baker on effective irrationality measures, with Andras Sarkozy on uniform distribution and prime factors of formed sets, with Tarlak Shorey on pure powers in linear recurrences, with Kunrui Yu on the ABC conjecture, and many other significant research contributions, Professor Stewart has been a leader in his research area, and a foremost contributor within the Canadian Mathematical community.
The purpose of the proposed workshop is twofold. Of primary importance is to bring together the world experts on the connections between the areas of Analytic Number Theory and Diophantine Analysis in order to further this active field of research, while exposing the younger researchers in this field to the major developments currently underway. As a byproduct of having these researchers in one place, the workshop will also be intended to pay tribute to the research contributions of Professor Stewart.