SCIENTIFIC PROGRAMS AND ACTIVITIES

October 23, 2014

2002 CRM-Fields Prize Winner
Professor John B. Friedlander

Lecture "Sieve Methods and the Distribution of Primes"
October 22, 2002
3:30 p.m.

The Centre de recherches mathématiques and the Fields Institute are pleased to announce the winner of the 2002 CRM-Fields Prize: John B. Friedlander of the University of Toronto.

Abstract

Many of the most famous old conjectures in mathematics arise from the theory of numbers and, of those, quite a few are concerned with prime numbers. One example is the Goldbach conjecture which predicts that every even integer, at least four, can be written as the sum of two primes.

Questions about the distribution of primes began to see important progress during the nineteenth century, for the most part due to new developments in harmonic analysis and the theory of functions of a complex variable. Unfortunately these analytic techniques seem not to be capable of being adapted to the counting of primes in any but the simplest subsequences of the integers, such as for example the primes occurring in a short interval.

Another line of attack, the ancient and elementary sieve method, seems more versatile and indeed can be formulated so as to provide an entry into rather general questions of this nature. Based on new ideas due to Brun and others during the first three quarters of the twentieth century, one was able to prove theorems which in various senses gave approximations to the desired conjectures. Whereas however, in contrast to the analytic method, one could say something worthwhile about a great many different problems, one could never seem (again in contrast to the analytic method) to prove the conjecture that was really wanted. Moreover, there were theoretical reasons which seemed to render this failure an inevitable outcome of the method.

Today, the most famous conjectures seem still to be out of reach. Nevertheless, during the past twenty years it has become possible, by modifying the sieve method and then combining it with data achieved by analytic methods, to prove results about prime numbers which had been inaccessible to either method alone.

The lecture will present a survey of some the older and the more recent developments of these topics.

Professor Friedlander is one of the world's foremost analytic number theorists, and is a recognized leader in the theory of prime numbers and L-functions. He received his B.Sc. from the University of Toronto in 1965, an M.A. from the University of Waterloo in 1966, and a Ph.D. from Penn State in 1972. He was a lecturer at M.I.T. in 1974-76, and has been on the faculty of the University of Toronto since 1977, where he served as Chair during 1987-91. He has also spent several years at the Institute for Advanced Study where he has collaborated with E.Bombieri and many others.

Friedlander is a Fellow of the Royal Society of Canada (1988), was an invited lecturer at the 1994 ICM in Zürich and delivered the CMS Jeffery-Williams Lecture in 1999. He has contributed significantly to mathematics in other ways, especially in Canada, through his role at NSERC (Mathematics GSC, 1991-94), as Mathematics Convenor of the Royal Society of Canada (1990-93), and as a Council member (1989-95) and Scientific Advisory Panel member (1996-2000) of the Fields Institute. He has served on the Editorial Board of the Canadian Journal of Mathematics and the Canadian Mathematics Bulletin for the past 4 years.