December 18, 2018

2004 CRM-Fields Prize Lecture
Professor Donald Dawson,
Carleton University/McGill University

November 4, 2004 --3:30 p.m.

Stochastic Dynamics of Evolving Populations (audio)

In this lecture we give an overview of some mathematical developments that have been motivated by and contributed to the study of evolving population systems such as those that arise in molecular and evolutionary biology, evolutionary economics, and evolutionary computation. Mathematical formulations of these systems have led to classes of stochastic processes that are sufficiently rich to describe spatially and hierarchically structured interacting populations and their genealogical structures. These processes are formulated in terms of interacting particle systems and measure-valued Markov processes on structured spaces. Basic tools for the study of particle systems and measure-valued processes have been developed over the past 25 years. These include martingale problem methods, dual processes, countable particle representations, canonical representations, Palm measures, coupling methods, multi-scale asymptotics, large deviations, etc. Using these methods considerable progress has been achieved in understanding some universality classes of behaviors of spatially and hierarchically structured systems in different fitness landscapes and space and time scales. In recent years progress has also been made on some interesting classes of more complex interactions but the development and analysis of populations with complex interactions remains an active and challenging area of research.

January 2004. - The directors of the The Centre de recherches mathématiques (CRM) of l'Université de Montréal, Christian Léger, and the Fields Institute for Research in Mathematical Sciences, Kenneth R. Davidson, are pleased to announce that the CRM-Fields Prize for 2004 is awarded to Professor Donald Dawson in recognition of his exceptional achievement and work in probability.

The Centre de recherches mathématiques and the Fields Institute established the joint CRM-Fields prize in 1994 with the goal of recognizing exceptional work in the mathematical sciences. The recipient is chosen by the Advisory Committee of the CRM together with the Scientific Advisory Panel of the Fields Institute. The candidate's research should have been conducted primarily in Canada or in affiliation with a Canadian university. The main selection criterion is excellence in research.

Donald Dawson, this year's recipient, is one of the world's leading probabilists, having made seminal contributions to the study of spatially distributed stochastic processes and infinite-dimensional branching systems, among those being the Dawson-Watanabe superprocess. He received his B.Sc. from McGill in 1958 and his doctorate from MIT in 1963.

Professor Dawson taught at both McGill University and Carleton University, where he is now Professor Emeritus. His leadership within the Canadian mathematical community includes a term as Director of the Fields Institute from 1996 to 2000. He is a Fellow of the Royal Society of Canada, as well as of the International Statistical Institute and the Institute of Mathematical Statistics.

Other honours include 1991 Gold Medal Lecture of the Statistical Society of Canada, the 1994 Jeffery-Williams lecture of the CMS, an invited lecture at the 1994 ICM, as well as the Fields Institute's Distinguished Lecture Series in the Statistical Sciences. His numerous editorial contributions include serving as co-editor-in-chief of the Canadian Journal of Mathematics. He has served his profession through numerous NSERC and CMS committees, and is currently President-Elect of the Bernoulli Society for Mathematical Statistics and Probability.

Previous recipients are H.S.M. (Donald) Coxeter, George A. Elliott, James Arthur, Robert V. Moody, Stephen A. Cook, Israel Michael Sigal, William T. Tutte, John B. Friedlander, John McKay and Edwin Perkins.


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