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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