I am the organizer of the Weekly Colloquium in Mathematics and Statistics, partially funded by Centre de Recherches Mathématiques, Tutte Institute for Mathematics and Computing, and Department of Mathematics and Statistics (uOttawa). The talks are on Wednesday 4:00 p.m.-5:00 p.m. in STEM 664. Below is the list of talks (Oct. 2023-April 2024):

Mayer Alvo (University of Ottawa, Sept. 20) --- Colloquium 
Title: Model Fitting Using Partial Rankings or How to Bet on a Horse Race
Abstract: The importance of models for complete ranking data is well established in the literature. Partial rankings on the other hand arise naturally when the set of objects to be ranked is relatively large. Partial rankings give rise to classes of compatible order preserving complete rankings. In this article, we define an exponential model for complete rankings and calibrate it based on a random sample of partial rankings data. We appeal to the EM algorithm.  The approach is illustrated in some simulations and in real data.

Akshay Ramachandran (CWI, Amsterdam, Sept. 27) --- Colloquium 
Title: A Tale of Two Subspaces
Abstract: Optimization problems with orthogonality constraints arise in many fields in science and engineering. For example, optimization over subspaces in physics and signal processing, and over rotations in computational geometry.
The key step in solving these problems often boils down to understanding the relation between two subspaces. It turns out that this question has a surprisingly elegant answer given by the CS decomposition from numerical linear algebra. In this talk, we will discuss the CS decomposition in the context of the geodesic geometry of subspaces. This perspective further gives unifying framework for understanding the various numerical algorithms used to solve problems with orthogonality constraints. As our main illustration, we study the problem of computing eigenspaces of a matrix, giving a rigorous convergence analysis of the well-known power method and its subspace generalization.
If time permits, we also present some new results on tractable algorithms for constrained optimization over rotation matrices. This is joint work with Kevin Shu and Alex Wang.

Frank Hilker (Osnabrück University, Oct. 4) --- Colloquium 
Title: Mathematical models of a social-ecological system: coupling lake pollution dynamics and human behavior
Abstract: From global warming over land-use change to pollution, the world is facing many environmental problems. While the causes are mostly well-known from a natural sciences point of view, the challenge is the implementation of possible solutions. Societal demands, human behavior, and economic aspects not only impact the environmental state, but are reversely affected by the environment. Mathematical models can be helpful in better understanding mutual feedbacks in coupled human-environment systems. In this talk, I will introduce a system of two nonlinear differential equations, one describing lake water pollution and the other one describing human behavior of discharging pollutants. The latter uses approaches from evolutionary game theory. Stability analysis reveals up to four coexisting attractors as well as limit cycle oscillations. Numerical bifurcation analysis suggests the existence of Bogdanov-Takens and saddle-node homoclinic bifurcations. Due to the diversity of dynamical regimes and counterintuitive equilibria, policy interventions that may be useful one context need not be useful in another. Thus, it seems impossible to derive a general rule of thumb for how to achieve a desirable state. Nevertheless, knowing the dynamics of a system in question can help comparing management strategies and preventing undesired consequences. (Joint work with Anthony Sun.)

Emanuele Caputo (University of Jyväskylä, Oct. 11) --- Colloquium 
Title: Metric measure spaces satisfying the Poincaré inequality: analysis and geometry
Abstract: In this presentation, I do an introduction of analysis on metric measure spaces. These objects are complete and separable metric spaces endowed with a locally finite nonnegative measure. In the class of such objects for which the measure is doubling, we study the ones that satisfy the Poincaré inequality, and some significant examples will be given. To define such objects and in particular Poincaré inequality, I will give a brief introduction on how we can compute the ‘differential' of a function in such a setting. I will explain why this class is relevant from the point of view of analysis and how it can be characterized in a geometric way (in terms of properties of curves and surfaces). In the last part of the talk, I will present an ongoing characterization in a joint work with N. Cavallucci (EPFL) in terms of properties of surfaces that separate points.

Alistair Savage (University of Ottawa, Oct. 18) --- Colloquium 
Title: Two-dimensional algebra
Abstract: Group theory and ring theory involve algebraic manipulations that are, in some sense, one-dimensional. For example, you write a product of several elements in a line and then perform replacements or simplifications that correspond to various properties (associativity, commutativity, etc.) or to relations that hold in your group/ring. However, it is often useful to perform operations in two dimensions. So, instead of having a single multiplication that is written horizontally, we have two multiplications: one written horizontally and one written vertically. In this talk we will explain how this idea arises very naturally in many areas of mathematics. The corresponding structure even has a fancy name; it’s called a monoidal category.

Brian Wetton (University of British Columbia, Oct. 25), -CRM-uOttawa Colloquium
Title: Numerical methods for geometric motion
Abstract: We consider the evolution of curves and curve networks in 2D. We describe it as geometric motion if the evolution only depends on the shape of the curve. There are applications in material science (the evolution of microstructure in materials), biochemistry, and image processing. An overview and comparison of several mathematical formulations of the geometric evolution of curves is given, including tracking and level sets, and their numerical approximation. Two new gradient flow models are derived and their numerical implementation in a general computational framework is described.

Douglas Stinson (University of Waterloo, Nov. 22) 
CRM-uOttawa Colloquium
Title: A compendium of difference families
Abstract: We discuss a variety of external difference families (EDFs), including strong and circular variants. The study of these combinatorial objects is motivated by applications to robust and nonmalleable threshold schemes. However, they are also of intrinsic interest, apart from applications. In this talk, we mainly discuss mathematical aspects, especially existence and nonexistence, of various types of EDFs. Two of the interesting construction techniques involve using graceful labellings to construct circular EDFs, and using classical results on cyclotomic numbers to obtain close approximations to (nonexistent) strong circular EDFs.
Ben Webster (University of Waterloo, Jan. 24) 
CRM-uOttawa Colloquium
Title: Representation theory and a little bit of quantum field theory
Abstract: One of the central foci of representation theory in the 20th century was the representation theory of Lie algebras, starting with finite dimensional algebras and expanding to a rich, but still mysterious infinite dimensional theory.  In this century, we realized that this was only one special case of a bigger theory, with new sources of interesting non-commutative algebras whose representations we’d like to study such as Cherednik algebras.  In mathematical terms, we could connect these to symplectic resolutions of singularities, but more intriguing explanation is that they arise 3-d quantum field theories.   I’ll try to provide an overview about what’s known about this topic, and what we’re still confused about.

Suzane Pumpluen (University of Nottingham, Feb. 7) 
CRM-uOttawa Colloquium
Title:  Nonassociative algebras, applications to coding theory, and how I got there...
Abstract: It is well known that the complex numbers can be constructed from the real numbers: 
they can be viewed as pairs of real numbers, together with a suitable multiplication.
We will look at this construction and play with it a bit. What happens if we use the same 
multiplication, or a similar one, and instead multiply pairs of complex numbers?
In the process we introduce the concept of algebras, which are vector spaces with some 
multiplication on them that allows two elements in the vector space to be "multiplied" 
with each other. We will meet quaternion algebras, cyclic algebras, and generalisations of them.
Some of these algebras are employed to build codes used for wireless digital data transmission,
e.g. in mobile phones, laptops or portable TVs, or in other areas of coding theory. 
We will explain how some of these codes work. I will also tell you a bit about how I ended up
studying these particular nonassociative algebras, and their applications, over the last 10 years.

Sue Ann Campbell (University of Waterloo, Feb. 28)  and 
CRM-uOttawa Colloquium
Title: Time Delays, Hopf Bifurcation and Synchronization
Abstract: We consider networks of oscillator nodes with time delayed, global circulant
coupling.  We first study the existence of Hopf bifurcations induced by
coupling time delay, and then apply equivariant Hopf bifurcation theory to
determine how these bifurcations lead to different patterns of phase-locked
oscillations.  We apply the theory to a variety of systems inspired by biological
neural networks to show how Hopf bifurcations can determine the synchronization
state of the network. Finally we show how interaction between two Hopf bifurcations
corresponding to different oscillation patterns can induce complex torus solutions
in the network.

Federico Salmoiraghi (Queen's University, March 6) ---- Colloquium
Title: Foliations, contact structures and Anosov flows in dimension 3
Abstract: Anosov flows are an important class of dynamical systems due to their ergodic and geometric properties. Even though they represent examples of chaotic dynamics, they enjoy the remarkable property of being stable under small perturbations. In this talk, I will explain how, perhaps surprisingly, Anosov flows are related to both integrable plane fields (foliations) and totally non-integrable plane fields (contact structures). The latter represents a less-studied approach that has the potential to make new connections to other branches of mathematics, such as symplectic geometry and Hamiltonian dynamics. Along the way, I will discuss some applications and examples.
Nancy Reid (University of Toronto, March 8)  and 
CRM-uOttawa Distinguished Women in Mathematics Colloquium
Title: Theoretical statistics in practice
Abstract: The theoretical foundations of statistical science distinguish the subject from 
the many fields of research in which statistical thinking is a key intellectual 
component.  In this talk I will emphasize the ongoing importance and relevance of 
theoretical advances and theoretical thinking through some illustrative examples 
from the scientific literature.

Monica Nevins (University of Ottawa, March 20) ---- Colloquium
Title: Why p-adic numbers are better than real for representation theory
Abstract: The p-adic numbers, discovered over a century ago, unveil aspects of number theory that the real numbers alone can’t.  In this talk, we give an elementary introduction to p-adic fields and their fractal geometry, and then to some representation theory.  We apply this to the (complex!) representation theory of the p-adic group SL(2) and describe a surprising conclusion: that close to the identity, all representations are a sum of finitely many rather simple building blocks arising from nilpotent orbits in the Lie algebra.

Leon Glass (McGill University, April 3)  
CRM Colloquium
Title: Mathematical aspects of cardiac arrhythmias
Abstract: Heart function depends on a few basic processes. Specialized cardiac cells act as pacemakers sending out excitation waves about once per second. As these waves travel through the heart they lead to contraction of the cardiac muscle, pumping blood to the body. Following a wave, there is a refractory period during which a new excitation of the cardiac tissue cannot occur. If two waves originating from different pacemakers collide, they annihilate. Quantitative descriptions of these processes may depend on such factors as recent activity and medications. That's it.. Cardiac arrhythmias may arise in many ways. Abnormal pacemakers can arise and compete with the normal pacemaker. Heterogeneity of cardiac tissue can lead to blocked or abnormal conduction.  Excitation can travel in reentrant loops leading to the frequency being set by the time an excitation takes to circulate rather than the period of a pacemaker. Although many detailed mathematical models have been proposed for these processes, I will describe a more geometric approach leading to testable predictions. The mathematics uses concepts from qualitative theory of differential equations, bifurcations in difference and differential equations, number theory, cellular automata. I will mention applications to arrhythmias in which there are palpitations, extra heart beats, irregular heart rhythms (atrial fibrillation), fast heart rhythms (tachycardias).