Prize Speakers

Cecil Graham Doctoral Dissertation Award:
2011-
Elsa Hansen (Queen's)
Applications of Optimal Control Theory to Infectious Disease Modeling

Mathematical modeling has become an important tool for assessing the potential impact of different interventions on disease spread and providing guidelines to help inform public policy. We use Pontryagin's Maximum Principle to discuss how different types of population-level interventions should be administered to minimize certain cost functions with special emphasis on how additional constraints such as i) limited resources and ii) de novo resistance can modify these results. A distinguishing feature of this work is the focus on models that lend themselves to analytic solutions. Although these models are necessarily simpler, this approach has much to offer. For example our analysis provides results that do not depend on specific parameter values and therefore facilitates an understanding of the general mechanisms involved. Furthermore, our analysis often leads to analytic expressions that can be generalized to more detailed models.

David Titley Peloquin (McGill)
Backward Perturbation Analysis of Least Squares Problems

Given an approximate solution to a certain problem, backward perturbation analysis involves finding a perturbation in the data of minimal size (in some norm) such that the approximate solution is an exact solution of the perturbed problem. The size of the minimal perturbation is referred to as the 'backward error'. This type of analysis has many practical applications in matrix computations. For instance, it can be used to design reliable stopping criteria for iterative solution methods.
We perform a backward perturbation analysis of the linear least squares and related problems. We give bounds on, and estimates of, the backward error. We also present theoretical results and numerical experiments on the convergence of the backward error and its estimates in commonly-used iterative methods.
This talk is based on joint work with my PhD co-supervisors Xiao-Wen Chang and Chris Paige of McGill University, as well as Serge Gratton and Pavel Jiranek of CERFACS.

2012 -
Brendan Pass, University of Alberta
Multi-marginal optimal transportation

The multi-marginal optimal transportation problem is the general problem of coupling several (say m) probability measures (called marginals) as efficiently as possible, relative to a prescribed surplus function; this is the challenge faced, for example, by a large company trying to divide its work force into several teams. When m=2, this problem has been studied extensively and has many applications, but results for more than two marginals are relatively scarce.
In this talk, I will present a result on the geometric structure of the optimal coupling. This structure depends on a family of semi-Riemannian metrics, derived from the mixed, second order partial derivatives of the surplus function. I will then discuss an application to the hedonic pricing problem in mathematical economics.

CAIMS Research Prize:
Troy Day (Queen's)
Computability, Gödel’s Incompleteness Theorem, and an Inherent limit on the Predicability of Evolution

I will briefly review a main way in which mathematical modeling has been used to understand and predict evolutionary change. I will then highlight an important shortcoming of such approaches and consider an alternative that attempts to overcome the problem. This alternative encompasses what I refer to as "open-ended" evolution. I will then present a proof, using this approach, that certain evolutionary questions are inherently unanswerable unless the process of evolution has specific properties. The cause of this limitation on evolutionary theory is shown to be fundamentally the same as that underlying the Halting Problem from computability theory and Gödel’s Incompleteness Theorem.

CAIMS-MPrime Industrial Mathematics Prize:
André Fortin (Laval)
High accuracy solutions to industrial problems

Les partenaires industriels ont souvent de très hautes attentes vis-à-vis desméthodes numériques: précision, efficacité, robustesse et, si possible, faible coût de calcul, et ce pour des problèmes souvent très complexes. Au cours des dernières années, nous avons opté au GIREF pour une utilisation intensive des discrétisations quadratiques (en espace et en temps) pour une vaste gamme d'applications. Il s'agit là d'un bon compromis entre l'utilisation de solutions linéaires (prétendûment à faible coût) et des approximations de plus haut degré qui demande plus de régularité de la
solution. Toujours dans le but d'améliorer la précision, nous avons aussi développé des stratégies d'adaptation de maillages anisotropes permettant d'obtenir des maillages optimaux pour des discrétisations de degré élevé. Cela exige aussi le développement de méthodes itératives ne perdant rien de leur robustesse même sur des maillages très anisotropes. Dans cet exposé, nous présenterons un survol de ces différentes méthodes ainsi que quelques applications industrielles.

Industrial partners often have very high expectations concerning numerical modeling: accuracy, efficiency, robustness and, whenever possible, low computation costs and this, for very complex problems. In the last few years, we have concentrated our efforts at GIREF on the development of quadratic discretizations (in both space and time) for a large variety of applications. This is a good compromise between linear solutions (wrongly believed as low cost solutions) and higher order finite element approximations requiring higher solution regularity. To further enhance the accuracy of our solutions, we have also developed an adaptive remeshing strategy that can be applied to high order discretizations and leads to optimal meshes in a sense that will be explained. This also led to the development of iterative methods that maintain their convergence properties on very anisotropic meshes. In this presentation, we will briefly describe some of these methods and present a few industrial applications.

CAIMS-PIMS Early Career Award in Applied Mathematics:
Theodore Kolokolnikov (Dalhousie)
Localized Patterns and their dynamics in Reaction-Diffusion systems.

Localized patterns are prevalent in nature. Some examples include
animal skin patterns, vegetation patches, hot-spots in crime, insect
swarms, laser pulses in optical cavities and many others. While these
examples are very diverse, many share a common underlying cause.
Mathematically, localized patterns involve solutions to PDE's that
that exhibit sharp spatial gradients and include spikes or
autosolitons, transition layers, stripes and so on. They typically
have very complex dynamics such as self-replication, coarsening,
oscillations, wave propagation, drift, and spatio-temporal chaos. In
this talk we will give an overview of some of the mathematics behind
the analysis of localized patterns and their dynamics. We will also
give some more recent results in this field.