Colloquium



I am the organizer of the Weekly Colloquium in Mathematics and Statistics, partially funded by Centre de Recherches Mathématiques 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: TBA
Abstract: TBA

Suzane Pumpluen (University of Nottingham, Feb. 14) 
CRM-uOttawa Colloquium
Title: TBA
Abstract: TBA

Sue Ann Campbell (University of Waterloo, Feb. 28) 
CRM-uOttawa Colloquium
Title: TBA
Abstract: TBA
Nancy Reid (University of Toronto, March 6) 
CRM-uOttawa Colloquium
Title: TBA
Abstract: TBA

Leon Glass (McGill University, April 3) --- Colloquium
Title: TBA
Abstract: TBA