University of Ottawa Colloquium in Mathematics and Statistics
Welcome to the University of Ottawa Colloquium in Mathematics and Statistics (UOCMS). This series brings together researchers from diverse institutions to present lectures on current developments in mathematics and statistics.
Upcoming Lectures
Winter 2026
Time: Wednesdays, 4:00–5:00 pm
Location: University of Ottawa, STEM building, room 664 (unless otherwise specified)
Speaker: Christiane Rousseau, Université de Montréal
Date: February 11, 2026
Title: The Equivalence Problem in Analytic Dynamics
Abstract: A central problem in local dynamics is the equivalence problem: when are two analytic systems locally equivalent under an analytic change of coordinates? In the neighbourhood of a singular point, representatives of equivalence classes could be given by normal forms. But, most often, the changes of coordinates to normal form diverge. Why? What does it mean? Unfolding the singularities reveals the geometric obstructions to the convergence to normal form. In this talk, we discuss a class of singularities and their unfoldings for which we can provide moduli spaces for the equivalence problems. We explain the common geometric features of these singularities, and how the study of the unfolding of these singularities allows understanding both the singularities themselves, and the obstructions to the existence of analytic changes of coordinates to normal form.
Speaker: Jonathan Yu-Meng Li, Telfer School of Management
Date: February 18, 2026
Past Lectures
Fall 2025 - Special Lectures in Analysis and Numerical Methods
Speaker: David Jekel, University of Copenhagen
Date: Wednesday, December 17, 2025, 3:00-4:00 pm
Room: STEM 664
Title: Contractibility of the Unitary Group of von Neumann Algebras
Abstract: This talk addresses the topological properties of infinite-dimensional objects coming from functional analysis. Kuiper in the 1960s proved that the group of unitary operators on an infinite-dimensional Hilbert space is a contractible space, meaning it can be continuously deformed to a point. We consider the analogous question of contractibility of the unitary groups of von Neumann algebras, which are certain algebras of operators on a Hilbert space. The last unsolved case was that of “finite” von Neumann algebras (those which satisfy that \(xy = 1\) implies \(yx = 1\) similar to finite-dimensional matrix algebras). We solve this case by a fundamentally different technique than the other cases, inspired by random matrix theory. We construct a homotopy by first smoothing out the spectral measure of the unitaries using free convolution, then applying functional calculus to push the mass toward 1.
Speaker: Conor McCoid, McMaster University
Date: Monday, December 15, 2025, 3:00-4:00 pm
Room: STEM 664
Title: Advances in Schwarz Methods
Abstract: Schwarz methods partition numerical domains to take advantage of parallelization in computing, while also acting as preconditioners. The domains may be partitioned physically into distinct regions, by field into distinct behaviours, and/or algebraically into distinct degrees of freedom. Schwarz methods tend to produce only linear convergence rates, and so should be combined with fast solvers such as Newton’s method or Krylov subspace methods. In this talk I explore two such approaches and new techniques to ensure accuracy, efficiency, and robustness. The first approach combines Newton and Schwarz in the context of a brittle fracture model, where I’ve added new backtracking to stabilize the Newton iterations. The second is a novel combination of Schwarz with Krylov subspace techniques.
Speaker: Loïc Cappanera, University of Houston
Date: Friday, December 12, 2025, 3:00-4:00 pm
Room: STEM 664
Title: Numerical Methods for Incompressible Flows with Variable Density: Analysis and Applications
Abstract: Incompressible multiphase flows, meaning flows involving fluids with variable density and viscosity, arise in many natural phenomena such as the interactions between the Earth mantle’s layers or between the ocean and atmosphere. Such flows also play an important role in engineering applications such as the production of aluminum or the storage of energy using liquid metal batteries. Thus, the development of efficient and robust numerical methods to approximate incompressible multiphase flows is crucial to bring a better understanding of the above problems. In this context, we will first highlight the main challenges one faces when solving the incompressible Navier-Stokes equations that governs the dynamics of such flows. After describing some of the classic methods used to approximate these equations when the density is constant, we will introduce two novel discretization for problems where the density is variable. We assume that fluids are immiscible and that the dynamical viscosity is a function of the density. Thus, the viscosity also becomes a space-time dependent variable. The proposed methods both use a level set technique to track the interface between the fluids and to reconstruct the fluid’s density and viscosity. Both methods also uses the momentum, equal to the density times the velocity, and the pressure as primary unknowns. This particular choice, commonly used in compressible fluid mechanics, allows us to derive formulations that yield time-independent stiffness matrices and that are suitable for spectral and pseudo-spectral methods. The two proposed methods differ on how the incompressibility constraint is enforced. One method uses a pressure correction projection method while the other uses an artificial compressibility technique. We will first analyze the stability and convergence properties of both our methods. Then, we will investigate numerically their robustness and accuracy on various setups involving either manufactured solutions, rotating flows or magneto-convection. We will conclude with a short outlook on future promising research directions.
Speaker: Tattwamasi Amrutan, Institute of Mathematics of the Polish Academy of Sciences
Date: Wednesday, December 10, 3:00-4:00 pm
Room: STEM 364
Title: A Unified Perspective on Rigidity: From Groups to \(C^*\)-Algebras
Abstract: We will study the “Rigidity phenomena” which lie at the heart of modern group theory and dynamics. Beginning with Margulis’s Normal Subgroup Theorem, we will see that fixed-point structures survive surprising enlargements of the objects under study—from subgroups to invariant random subgroups, and beyond. In this talk, I will present a unified perspective on rigidity by passing through three increasingly flexible categories: deterministic fixed points, probabilistic fixed points, and finally operator-algebraic fixed points inside group \(C^*\)-algebras and von Neumann algebras. I will describe new results establishing non-commutative analogues of “Intermediate Factor Theorems” and a characterization of invariant subalgebras for free groups. Finally, I will also discuss the emergence of strict comparison in the reduced group \(C^*\)-algebra of \(F_2\).
Fall 2025
Time: Thursdays, 1:00–2:00 pm
Location: University of Ottawa, STEM building, room 664 (unless otherwise specified)
Speaker: Anush Tserunyan, McGill University
Date: December 4, 2025
Title: A Pointwise Approach to Pointwise Ergodic Theorems
Abstract: Pointwise ergodic theorems link the global behaviour of a dynamical system to the local, often combinatorial, statistics observed along individual orbits. They are powerful tools in ergodic theory, probability, number theory, and beyond. I will present a general yet elementary method for proving such theorems, inspired by ideas from descriptive set theory. This approach yields new kinds of pointwise ergodic theorems; I will describe several examples arising from joint work with Jenna Zomback.
Speaker: Mark Reesor, Wilfrid Laurier University
Date: November 20, 2025
Title: Approximating the Money-Weighted Rate of Return
Abstract: We develop a closed-form approximation to the so-called money-weighted rate of return (MWRR), in the context of a stylized retirement savings account. The approximation is general in the sense that (i) it allows for contributions of varying sizes made at irregularly-spaced times (including both discrete and continuous contributions), (ii) it allows the composition of the underlying portfolio (as manifested through the mean and standard deviation of its instantaneous return) to vary through time and (iii) it does not make any specific assumptions on the stochastic dynamics of the underlying portfolio return. The approximation facilitates insights into a complicated object, which in turn allows us to explain and/or resolve findings elsewhere in the literature. This is joint work with A. Metzler, M. Lau and D. Polegato.
Speaker: Bruno Feunou Kamkui, Bank of Canada
Date: November 13, 2025
Title: Generalized Autoregressive Positive-Valued Processes
Abstract: We introduce generalized autoregressive positive-valued (GARP) processes, a class of autoregressive and moving-average processes that extends the class of existing autoregressive positive-valued (ARP) processes in one important dimension: each conditional moment dynamic is driven by a different and identifiable moving average of the variable of interest. The article provides ergodicity conditions for GARP processes and derives closed-form conditional and unconditional moments. The article also presents estimation and inference methods, illustrated by an application to European option pricing where the daily realized variance follows a GARP dynamic. Our results show that using GARP processes reduces pricing errors by substantially more than using ARP processes.
Lecture slides
Speaker: Jeremy Quastel, University of Toronto
Date: November 6, 2025
Title: The Kardar–Parisi–Zhang Fixed Point
Abstract: We will survey some of the mathematics that has come out of the study of one dimensional random growth models, in particular the surprising connection to integrable partial differential equations. The talk is intended for a very broad audience and no background is assumed.
Speaker: Florian Dumpert, Federal Statistical Office of Germany
Date: October 30, 2025
Location: Exceptionally, this colloquium will take place in STEM 464.
Title: Reflections Regarding the Procedure and Methodology of Statistical Data Editing
Abstract: Statistical data editing in statistical production is, on the one hand, an essential part of the quality assurance of incoming data (and thus, subsequently, of the products of official statistics). On the other hand, however, it is also a comparatively complex and time-consuming step. Naturally, attempts are therefore regularly made to increase the efficiency of editing. (Which is also - by the way - entirely in keeping with the concept of quality.) German official statistics are currently undergoing a paradigm shift. Whereas in the past, data was often first accepted and then checked for plausibility, in future only (more or less) clean data is to be accepted. Selective editing and automated processing of the majority of cases, including the use of Machine Learning, are then the next step – a procedure that is nothing new in the world of official statistics. The presentation will nevertheless address these points and take a closer look at some of them. In particular, a procedure for automated editing will be presented in more detail and the question of when a replacement of incorrect values can be described as ‘good’ or ‘successful’ will be examined.
Lecture slides
Speaker: Alejandro Adem, University of British Columbia
Date: October 23, 2025
Title: Topology and Symmetries
Abstract: In this lecture we will discuss how methods from algebraic topology can be applied to shed light on fundamental questions related to finite group actions. We will start with basic invariants such as the Euler characteristic and explore classical applications such as topological space forms as well as more recent work about actions on 4-dimensional manifolds (joint with I. Hambleton). This will be illustrated with a variety of examples, as well as some open problems.
Speaker: Giusy Mazzone, Queen’s University
Date: October 16, 2025
Title: On the Mathematical Analysis of Fluid–Solid Interaction Problems
Abstract: I will present several models describing the interactions between viscous incompressible fluids and solids, which may be either rigid or deformable. The governing equations for these interactions consist of the Navier–Stokes equations coupled with either the Euler equations for rigid body dynamics or the Navier equations of linearized elasticity. A common feature of these problems is that the governing equations have a dissipative—conservative (parabolic—hyperbolic) structure: while the fluid introduces dissipation in the mechanical energy of the coupled system, the solid contributes to the same energy with a conservative (more generally, non-decreasing) component. From a mathematical perspective, this interplay poses significant challenges when establishing the existence and stability of solutions to the governing equations. I will provide an overview of my contributions to the analysis of these problems for various mechanical systems involving fluid–solid interactions.
Speaker: Jen Hom, Georgia Institute of Technology
Title: 3-Manifolds, Groups, and Heegaard Floer Homology
Date: October 2, 2025
Location: Exceptionally, this colloquium will take place in STEM 464.
Abstract: We will consider various ways to build 3-manifolds. Under the operation of connected sum, the set of 3-manifolds forms a monoid, and modulo an appropriate equivalence relation, this monoid becomes a group. What is the structure of this group? What families of three-manifolds generate (or don’t generate) this group? We give some answers to these questions using Heegaard Floer homology. This is joint work with (various subsets of) I. Dai, K. Hendricks, M. Stoffregen, L. Truong, and I. Zemke.
Speaker: Sumiya Baasandorj, University of Ottawa
Title: Regularity for a Class of (Non)Variational Problems with (Non)Standard Growth
Date: September 25, 2025
Abstract: Regularity issues in (non)variational problems with (non)standard growth have been a central topic of analysis, witnessing tremendous development over the past century. Regularity techniques ultimately aim to show that suitable weak or distributional solutions are, in fact, classical solutions. In this talk, I will present some recent regularity results for a class of variational functionals with nonstandard growth conditions, namely the so-called Orlicz double phase functional. This will involve revisiting the fundamental contributions of De Giorgi and Nash and connecting them with recent advances in nonuniformly elliptic problems. Furthermore, I will try to give an overview of the regularity theory for nonvariational elliptic problems, such as the Monge–Amp`ere equation, and discuss its connections to optimal transport theory.
Lecture slides
Speaker: Emanuele Naldi, University of Genoa
Title: Inexact Jordan–Kinderlehrer–Otto and Proximal-Gradient Algorithms in the Wasserstein Space: Links and Differences from the Hilbert Case
Date: September 18, 2025
Abstract: In this talk, we explore the asymptotic convergence properties of inexact Jordan–Kinderlehrer–Otto (JKO) scheme and proximal-gradient algorithm in the Wasserstein space. While the classical JKO scheme assumes exact minimization at each step, practical implementations rely on approximate solutions due to computational constraints. We analyze two types of inexactness: errors in Wasserstein distance and errors in functional evaluations. We establish rigorous convergence guarantees under controlled error conditions. Beyond the inexact setting, we also extend the convergence results by considering varying stepsizes. Our analysis expands previous approaches, providing new insights into discrete Wasserstein gradient flows. We finish the talk with a comparison to the Hilbert space setting, where the proximity operator is nonexpansive, a property that plays a central role in many classical convergence results. In the Wasserstein setting, the nonexpansivity of the proximity operator generally fails, even for geodesically convex functionals. We discuss the class of functions for which this property still holds and highlight potential directions for future research.
Lecture slides
Speaker: Susanne Pumplün, University of Nottingham
Title: On Skew Constacyclic Codes and their Surprising Connection to Nonassociative Algebra
Date: September 11, 2025
Abstract: Cyclic, constacyclic and skew constacyclic codes are some of the most important and most investigated classes of linear codes (some are now also being used to build quantum error-correcting codes). Their cyclic structure allows us to characterize them using polynomials or skew polynomials, and to describe them as ideals in an algebra. More precisely, each codeword corresponds to a (skew) polynomial in a suitable chosen ideal of its ambient algebra. This ambient algebra may, however, be not associative. This is not well known, as all approaches so far only worked with associative ambient algebras or divert to ambient submodules. In the first part of the talk we will thus set up a cohesive theory that includes the nonassociative case. In the second part, we will address the problem how to classify skew constacyclic codes using the isomorphisms of their ambient algebras. We propose a new definition of equivalence that will result in tighter code classifications than previously presented ones, and will help to de-duplicate codes with the same performance paramenters. We prove with combinatorial methods that the notions of isometry and equivalence defined by Ou-azzou et al. (2025) coincide when the ambient algebras are not associative.
Lecture slides
Speaker: Francesca Bartolucci, Delft University of Technology
Title: Representation Equivalent Neural Operators: A Framework for Alias-Free Operator Learning
Date: September 4, 2025
Abstract: Recently, operator learning, or learning mappings between infinite-dimensional function spaces, has garnered significant attention, notably in relation to learning partial differential equations from data. Conceptually clear when outlined on paper, neural operators require discretization in the transition to computer implementations. This step can compromise their integrity, often causing them to deviate from the underlying operators. This research offers a fresh take on neural operators with a Representation equivalent Neural Operators (ReNO) framework designed to address these issues. At its core is the concept of operator aliasing, which measures inconsistency between neural operators and their discrete representations. More generally, this framework not only sheds light on existing challenges but, given its constructive and broad nature, also potentially offers tools for developing new neural operators. This is a joint work with Rima Alaifari, Emmanuel de Bézenac, Siddhartha Mishra, Roberto Molinaro and Bogdan Raonić.
Lecture slides