Inaugural G. de B. Robinson Award
Presentations and Lectures

Friday, April 18, 1997
at the Fields Institute

Recipients will offer public lectures on the prize-winning papers which were selected from the Canadian Journal of Mathematics (1994-95). Sponsored by the Canadian Mathematical Society and The Fields Institute for Research in Mathematical Sciences.

2:30 - 2:45 p.m. Introduction and Comments
Dr. Katherine Heinrich, Canadian Mathematical Society
2:45 - 3:30 p.m. Public Lecture
Dr. Henri R. Darmon, Mathematics and Statistics, McGill University
"Thaine's Method for Circular Units and a Conjecture of Gross" We formulate a conjecture analogous to Gross' refinement of the Stark conjectures on special values of abelian L-series at s=0. Some evidence for the conjecture can be obtained, thanks to the fundamental ideas of F. Thaine.

3:30 - 3:45 p.m. Break and Refreshments
3:45 - 4:30 p.m. Public Lecture
Dr. Steven N. Evans, Statistics, University of California, Berkeley
Dr. Edwin A. Perkins, Mathematics, University of British Columbia
"Measure-Valued Branching Diffusions with Singular Interactions"
The usual super-Brownian motion is a measure-valued process that arises as a high density limit of a system of branching Brownian particles in which the branching mechanism is critical. In this work we consider analogous processes that model the evolution of a system of two such populations in which there is inter-species competition or predation.

We first consider a competition model in which inter-species collisions may result in casualties on both sides. Using a Girsanov approach, we obtain existence and uniqueness of the appropriate martingale problem in one dimension. In two and three dimensions we establish existence only. However, we do show that, in three dimensions, any solution will not be absolutely continuous with respect to the law of two independent super-Brownian motions. Although the supports of two independent super-Brownian motions collide in dimensions four and five, we show that there is no solution to the martingale problem in these cases.

We next study a predation model in which collisions only affect the ``prey'' species. Here we can show both existence and uniqueness in one, two and three dimensions. Again, there is no solution in four and five dimensions. As a tool for proving uniqueness, we obtain a representation of martingales for a super-process as stochastic integrals with respect to the related orthogonal martingale measure.