June 20, 2024

Distinguished Lecture Series in Statistical Science
April 23 and 24, 2003 - 3:30 p.m.

Don Dawson
Mathematics and Statistics, Carleton University and McGill University

Probabilistic Phenomena in Mathematics and Science

Probability has a long history going back to the 17th century with major landmarks in the works of Fermat, Pascal, Bernoulli, Bayes, de Moivre, Laplace and Gauss but it was in the 20th century that it blossomed into one of the core areas of the mathematical sciences. This development was fed from two sides. On the one hand the developments in analysis including measure theory and partial differential equations were an essential ingredient for the development of the subject as we know it today. On the other hand the transformation from the deterministic world view to a probabilistic viewpoint in physics - statistical mechanics, Brownian motion, quantum physics, the role of probability in evolutionary biology and population genetics and the probabilistic modelling of social phenomena including Bachelier's now celebrated introduction of probabilistic models of financial markets served as a powerful catalyst for this development. Probability now plays a central role in science and mathematics. Probability and statistics link the mathematical world of theoretical models and the empirical world of experimentation and data collection. In particular probability provides a rich universe of models and also serves as an essential component in the development of statistical methodology for the analysis of empirical data. Moreover probability also plays a special and increasingly central role in mathematics in that it forms a natural link between the continuum world of analysis and physics and the discrete world of combinatorics, computer science, Monte Carlo simulation and bioinformatics. Today probability is an essential tool in the study of many fields including statistical physics, complex manufacturing and communications networks, finance, risk assessment, image analysis, analysis of algorithms, perception in artificial and natural systems and genetics and ecology.

In response to challenging problems arising across this spectrum of applications, the subject has undergone a remarkable development with the emergence of new probabilistic objects and methodologies. In the first lecture I will sketch some strands of these developments with emphasis on some probabilistic structures that not only capture the essence of an entire range of probabilistic phenomena and but also appear in unexpected places.

The second lecture will trace more recent developments in the theory of stochastic processes with emphasis on their applications to multiagent systems, hierarchically structured populations and spatially distributed systems.


Donald Dawson received his Honours B.Sc. in Mathematics and Physics from McGill University in 1958 and his doctorate from MIT in 1963. He has taught at both McGill University and Carleton University and is currently Professor Emeritus and Distinguished Research Professor at Carleton and Adjunct Professor at McGill. He has been a co-director of the Carleton-Ottawa Laboratory for Research in Statistics and Probability since 1982 and served as Director of the Fields Institute from 1996-2000. His research interests include large deviation theory, stochastic differential equations, stochastic partial differential equations, measure-valued processes and applications of probability to statistical physics, genetics, finance and communications. He is a Fellow of the Royal Society of Canada. He has given numerous invited lectures; including the 1991 Gold Medal Lecture of the Statistical Society of Canada, the 1994 Jeffery-Williams lecture of the Canadian Mathematical Society, an invited lecture at the 1994 International Congress of Mathematicians in Zurich, and a plenary lecture at the 1996 World Congress of the Bernoulli Society in Vienna. He has been a member of the editorial boards of a number of journals and Co-Editor-in-Chief of the Canadian Journal of Mathematics from 1988 to 1993. He has served on a number of NSERC committees including the Mathematics and Statistical Sciences GSC's, Research Manpower, Postdoctoral Fellowship, International Relations and the 1995 Task Force on Strategy Implementation.

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