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 populationlevel 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 commonlyused iterative methods.
This
talk is based on joint work with my PhD cosupervisors XiaoWen
Chang and Chris Paige of McGill University, as well as Serge Gratton
and Pavel Jiranek of CERFACS.
2012

Brendan Pass, University of Alberta
Multimarginal optimal transportation
The
multimarginal 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
semiRiemannian 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 "openended"
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.
CAIMSMPrime
Industrial Mathematics Prize:
André Fortin (Laval)
High
accuracy solutions to industrial problems
Les
partenaires industriels ont souvent de très hautes attentes
visàvis 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.
CAIMSPIMS
Early Career Award in Applied Mathematics:
Theodore Kolokolnikov (Dalhousie)
Localized Patterns and their dynamics in ReactionDiffusion systems.
Localized
patterns are prevalent in nature. Some examples include
animal skin patterns, vegetation patches, hotspots 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 selfreplication, coarsening,
oscillations, wave propagation, drift, and spatiotemporal 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.
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