April 22, 2019

Fields-Carleton Distinguished Lecture Series

Dr. Don Dawson
Carleton University,
School of Mathematics and Statistics

March 23, 2011 (Wednesday) 6:00pm
General public talk

Some episodes in the mathematics and science of random phenomena

Room 5050 Minto Centre
There will be a reception after the talk

March 25, 2011 (Friday) 3:30pm,
Specialized talk for mathematical sciences

Spatial structures and universality classes in stochastic systems

4351 Herzberg Laboratories
Coffee will be served at 3:00pm

Lecture I: Some episodes in the mathematics and science of random phenomena

Probability, the field of mathematics that studies random phenomena, has a long history going back to the 17th century but it was in the 20th century that it blossomed into one of the core areas of the mathematical sciences. This development was driven by the transformation from the deterministic viewpoint of classical physics to the probabilistic viewpoint of statistical physics and quantum physics, and the emerging role of probability in evolutionary biology and population genetics. The probabilistic modelling of social phenomena including the introduction of probabilistic models of financial markets also served as a powerful catalyst for this development. Probability now plays a central role in science and mathematics. In mathematics it forms a natural link between the continuum world of analysis and physics and the discrete world of combinatorics, computer science, and Monte Carlo methods. Over the past 50 years probability has developed into an essential research tool in the study of many fields including statistical physics statistics, complex biological and communications networks, economics, finance, genomics, genetics and ecology. The scientific challenges posed by these fields have stimulated some exciting mathematical advances which in turn have provided new scientific insights and tools. In this lecture I will take a look at some of the major developments in this story and the current synergetic nature of research in the mathematical sciences.

Lecture II: Spatial structures and universality classes in stochastic systems

The classical invariance principle establishes that the scaling limit of a large class of discrete stochastic processes is given by Brownian motion. Expanding on this, the idea that the large space and time scale behaviour of many physical systems can be classified into "universality classes" and that the structure of such classes is highly dimension-dependent is one of the great developments in statistical physics. In the realm of population processes, universality classes related to super-Brownian motion have emerged from a surprising range of particle systems and random combinatorial objects. This lecture will present a review some of these developments. I will also describe ongoing work using the idea of hierarchical mean-field limit as one approach to understanding this phenomenon as well as to identify multitype generalizations of these universality classes.

Donald Dawson received his B.Sc.(Hon.) in Mathematics and Physics from McGill University in 1958 and his doctorate from MIT in 1963. He taught at both McGill University and Carleton University. He first came to Carleton in 1970 and was appointed Professor Emeritus and Distinguished Research Professor in 1999. He served as Director of the Fields Institute from 1996-2000 and as the President of the Bernoulli Society for Mathematical Statistics and Probability for 2003-2005. He served as Associate Editor of the Canadian Journal of Statistics (1980-87), Co-Editor-in-Chief of the Canadian Journal of Mathematics (1988-1993) and on the editorial Boards of the Annals of Probability and Electronic Journal of Probability.
Professor Dawson gave 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, a plenary lecture at the 1996 World Congress of the Bernoulli Society in Vienna, and the Fields Institute Distinguished Lecture Series in the Statistical Sciences in 2003.
He is a Fellow of the Royal Society of Canada, Institute of Mathematical Statistics and International Statistical Institute and received a Max Planck Award of the for International Cooperation from the Humboldt Foundation in 1996 and the CRM-Fields prize in 2004. He received an honourary degree Dr. Sci. from McGill University in 2005. He was elected to the Royal Society (London) in 2010.
His research interests include probability and stochastic processes and their applications to complex systems, statistical physics, genetics and evolutionary biology. He has published over 100 scientific papers and 7 monographs and has supervised 27 Ph.D. students and 30 postdoctoral fellows.

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