Courses: 2026-2027
The following courses were scheduled for the 2026-2027 academic year:
The following courses were scheduled for the 2026-2027 academic year:
Malabika Pramanik : malabika@math.ubc.ca
University of British Columbia
Basic knowledge in measure theory and complex analysis will be required (similar to Course 420/507 at UBC or equivalent)
Registration for this course is not currently available.
This is an introductory course in functional analysis, involving
Remote students will be able to interact with the instructor and with other students through several channels during the lectures.
During lectures, students will be encouraged to ask questions and participate in discussions in real time. The instructor will pause regularly to invite questions from both in-person and remote participants. Remote students may ask questions verbally through the video-conferencing platform or through the chat function, which will be monitored throughout the lecture.
In addition, problem discussions and collaborative activities will be organized in small groups that include students from different sites. These interactions will take place using breakout rooms within the video-conferencing platform, allowing remote and in-person students to work together.
Finally, students will periodically present solutions or short expositions to the class. These presentations will be delivered either from the classroom or remotely through screen sharing, ensuring that students at all locations have equal opportunities to contribute.
This course may be open to students from universities outside of the PIMS network, and those coming from industry/government.
Yaozhong Hu : yaozhong@ualberta.ca
University of Alberta
Some preparation on mathematical analysis and measure based probability theory such as STAT 571 or STAT 580 at UAlberta is not necessarily required, but will be very much helpful
Registration for this course is not currently available.
This is a one semester three credit hour course. It is about the theory and applications of stochastic differential equations driven by Brownian motions.
The stochastic differential equations have found applications in finance, signal processing, population dynamics, biology, and many other fields. It is the basis of some other applied probability areas such as filtering theory, stochastic control and stochastic differential games.
To balance the theoretical and applied aspects and to include as much audience as possible, we shall focus on the stochastic differential equations driven only by Brownian motion (white noise). We will focus on the theory and not get into specic applied area (finance, signal processing, filtering, control and so on).
We shall first briefly introduce some basic concepts and results on stochastic processes, in particular the Brownian motions. Then we will discuss stochastic integrals, Ito formula, the existence and uniqueness of stochastic differential equations, some fundamental properties of the solution. We will concern with the Markov property, Kolmogorov backward and forward equations, Feynman-Kac formula, Girsanov formula. We will also concern with the ergodic theory and other stability problems. We may also mention some results on numerical simulations, Malliavin calculus and so on.
The instructor will use zoom and other UAlberta resources such as canvas. Preprepared slides will be shared during the zoom sessions.
This course may be open to students from universities outside of the PIMS network.
Sven Bachmann : sback@math.ubc.ca
University of British Columbia
Solid foundation in linear algebra, rigorous analysis (at the level of `baby Rudin’) and elementary point set topology. Knowledge in functional analysis and measure theory is an advantage, but the necessary material will be reviewed. No physics background beyond high school physics required.
UBC MATH320 and MATH321 (or equivalent)
UBC MATH420 and MATH421 (or equivalent) are recommended but not required.
This course is available for registration under the Western Dean's Agreement but registrations must be approved by the course instructor. Please contact the instructor (using the email link to the left) including details of how you meet the course prerequisites. Next, you must complete the Western Deans' Agreement form , with the following course details:
Completed forms should be returned to your graduate advisor who will sign it and take the required steps. For students at PIMS sites, please see this list to find your graduate advisor, for other sites, please see the Western Deans' Agreement website .
The Western Deans' Agreement provides an automatic tuition fee waiver for visiting students. Graduate students paying normal required tuition fees at their home institution will not pay tuition fees to the host institution. However, students will typically be be required to pay other ancillary fees to the host institution, or explicitly request exemptions (e.g. Insurance or travel fees). Details vary by university, so please contact the graduate student advisor at your institution for help completing the form. Links to fee information and contact information for PIMS member universities is available below in the WDA section.
Students at universities not covered by the WDA but which are part of the Canadian Association for Graduate Studies (CAGS) may still be eligible to register for some courses under the terms of the Canadian University Graduate Transfer Agreement (CUGTA). Details of this program vary by university and registration is also typically subject to ancillary fees. Both your local and the hosting university must participate in the agreement (e.g. UBC does not participate in CAGS). Please contact the relevant graduate student advisors for more information.
The goal of MATH 512 is to introduce mathematical methods of quantum theory. No prerequisite of quantum physics is required. The course will cover some aspects of functional analysis, operator theory and the calculus of variations with short excursions into representation theory and operator algebras. The physical axioms of quantum theory will be introduced and elementary results will be discussed. We will introduce the Hilbert space formulation of quantum theory, discuss quantum dynamics and its relation to spectral properties of linear operators. We will also study the role of symmetries in quantum physics, in particular the rotation group thereby introducing the intrinsically quantum notion of spin. The course will conclude with a short study of strongly interacting systems and the role of locality in their analysis.
First day of teaching: Wed Sep 09; Last day of teaching: Monday Dec 07. University closed Sep 30, Oct 12, and Nov 11. Midterm break: Nov 09-11.
This will be a hybrid course delivered by Zoom. The instructor will lecture at a blackboard using a camera to allow remote participants to see the content. There will be course notes (hand written, possibly typed up) made available as the course progresses. Office hours will be conducted over zoom.
This course may be open to students from universities outside of the PIMS network, and those coming from industry/government.
There will be
The course grade will be given by $$ \max \left\{ 0.75G_H + 0.25G_F, 0.5G_H + 0.5G_F \right\} $$ where $G_H$ is the average grade of the assignments and $G_F$ is the grade of the final exam.
Andrei Volodin : andrei.volodin@uregina.ca
University of Regina
This is a graduate course, so there are no prerequisites. At the same time, students should know probability and statistics (especially linear regression) at an intermediate level.
This course is available for registration under the Western Dean's Agreement but registrations must be approved by the course instructor. Please contact the instructor (using the email link to the left) including details of how you meet the course prerequisites. Next, you must complete the Western Deans' Agreement form , with the following course details:
Completed forms should be returned to your graduate advisor who will sign it and take the required steps. For students at PIMS sites, please see this list to find your graduate advisor, for other sites, please see the Western Deans' Agreement website .
The Western Deans' Agreement provides an automatic tuition fee waiver for visiting students. Graduate students paying normal required tuition fees at their home institution will not pay tuition fees to the host institution. However, students will typically be be required to pay other ancillary fees to the host institution, or explicitly request exemptions (e.g. Insurance or travel fees). Details vary by university, so please contact the graduate student advisor at your institution for help completing the form. Links to fee information and contact information for PIMS member universities is available below in the WDA section.
Students at universities not covered by the WDA but which are part of the Canadian Association for Graduate Studies (CAGS) may still be eligible to register for some courses under the terms of the Canadian University Graduate Transfer Agreement (CUGTA). Details of this program vary by university and registration is also typically subject to ancillary fees. Both your local and the hosting university must participate in the agreement (e.g. UBC does not participate in CAGS). Please contact the relevant graduate student advisors for more information.
A graduate-level Econometrics Models (Time Series) class focuses on stationary and non-stationary processes, ARIMA modeling, and forecasting. The curriculum includes estimation techniques, unit root testing, and ARCH/GARCH modeling for volatility, often utilizing R software R for analysis. This course covers materials for Time series/forecasting part of SOA Validation by Educational Experience (VEE)-Applied Statistics.
This will be a hybrid course delivered by Zoom. The instructor will share the existing electronic presentation and will use a laptop (or tablet), which can be shared electronically for some special notes during lectures.
This course may be open to students from universities outside of the PIMS network, and those coming from industry/government.
Your final grade will be calculated as follows:
Clifton Cunningham : ccunning@ucalgary.ca
University of Calgary
Approval from instructor
Undergraduate algebra, number theory and analysis are sufficient background.
A course in representation theory and/or algebraic geometry would be helpful but not necessary.
Registration for this course is not currently available.
This course provides a gentle introduction to the Langlands program by focusing on GL(2) and classical number theoretic inputs such as modular forms, drawing on Dietmar’s book Automorphic Forms. The course will briefly discuss geometric and categorical variants of the Langlands program.
This course is available to students within the PIMS network, and at universities beyond the PIMS network.
All lectures will be available online (either purely or hybrid). The instructor will make course materials available on Discord, including references, and notes from the lectures. The course will connect students to the global Langlands community using research seminars.org. Other online value added tools include the L-functions and Modular Forms Database, which will be used extensively in the course.
Lior Silberman : lior@math.ubc.ca
University of British Columbia
The following UBC courses or equivalent are recommended
Elementary Number Theory (e.g. UBC MATH 537)
Real and Complex Analysis (e.g. UBC MATH 320 and 508 respectively)
We will use some basic ideas from ring theory and finite abelian groups, and will develop all the Fourier analysis we will use.
Registration for this course is not currently available.
We will count (that is, estimate the number of) integer and prime number solutions to equations. We will use combinatorial (“elementary”) methods, some Fourier analysis, and finally zeta-function (contour integration) techniques. Fourier analysis will be the unifying theme of the course. Possible topics include:
This course is available to students within the PIMS network, at universities beyond the PIMS network and from industry/government.
Lectures will be held in-person on the UBC campus and on Zoom. Lectures will be recorded and the videos posted to an unlisted but openly accessible YouTube playlist. There will be Zoom office hours and a Piazza discussion board.
The final grade will be based on six to eight problem sets. There will be no final exam.
Andrii Arman : Andrii.Arman@umanitoba.ca
University of Manitoba
Andriy Prymak : Andriy.Prymak@umanitoba.ca
University of Manitoba
Consent of the instructors (unofficial transcripts may be requested)
Students are expected to have a rigorous undergraduate foundation in linear algebra and vector geometry, real analysis and introductory probability
Foundational concepts specific to convex geometry will be reviewed throughout the course to ensure a common baseline
Registration for this course is not currently available.
How do our classical geometric intuitions change as dimension of the ambient space grows? This course investigates high-dimensional convexity and discrete geometry through the lens of geometric covering and illumination problems.
Highlighting the intersection of asymptotic bounds and discrete structures, the course extensively covers different variations of Borsuk’s partition question and recent surprising counterexamples. We will discuss constructions of special bodies of constant width, discretization techniques, and probabilistic models.
These tools will be applied to explore asymptotic estimates of various covering methods in convex and discrete geometry, volume bounds for bodies of constant width, and recent advances in Lebesgue’s universal covering problem. Ultimately, students will master a versatile research toolkit at the active intersection of combinatorics, geometry, and probability, preparing them to tackle modern open problems in asymptotic geometric analysis and related areas.
This course will be available to students at universities inside and beyond the PIMS network.
Lectures will be delivered live via Zoom using a 2-in-1 laptop and an on-screen writing application to ensure high-quality, real-time transmission of mathematical notation. To foster a collaborative learning environment at other PIMS network sites with multiple enrolled students, we will coordinate with those host institutions to request that dedicated seminar rooms equipped with projectors and videoconferencing hardware be booked for group participation.
Lior Silberman : lior@math.ubc.ca
University of British Columbia
In general this is an advanced course and students are expected to be able to catch up on any necessary background material. There are no formal pre-requisutes, but the following courses or equivalent are suggested
Basic classical mechanics (e.g. UBC PHYS 216).
Elementary ODE (e.g. UBC MATH 215).
Rigorous real analysis and linear algebra (e.g. UBC MATH 320)
Linear algebra (UBC MATH 131) will be an advantage.
Registration for this course is not currently available.
This is a course in formal mechanics from a mathematical point of view, developing in parallel the mathematical machinery and physical ideas. Some of the material will be developed in the problem sets. The graduate side of the course will make a higher emphasis on manifolds and may involve more advanced mathematics
This course is available to students within the PIMS network, at universities beyond the PIMS network and from industry/government.
Lectures will be held in-person on the UBC campus and on Zoom. Lectures will be recorded and the videos posted to an unlisted but openly accessible YouTube playlist. There will be Zoom office hours and a Piazza discussion board.
Slim Ibrahim : ibrahims@uvic.ca
University of Victoria
Background of Partial Differential Equations and Functional Analysis
Registration for this course is not currently available.
This course introduces the mathematical analysis of anisotropic fluid flows, focusing on the Boussinesq system and its hydrostatic limit leading to the primitive equations. Emphasis is placed on the role of scaling, geometry, and stratification in deriving reduced models, as well as on well-posedness, instability mechanisms, and singularity formation. Connections with the Euler and Navier–Stokes equations are highlighted, along with recent advances and open problems in inviscid regimes.
Many fluid systems arising in physics, engineering, and biology exhibit strong anisotropy due to geometry, stratification, or external forces. A prominent example is the Boussinesq approximation, which models buoyancy-driven flows and provides a unifying framework for studying stratified fluids. This system is closely related, both structurally and analytically, to the Navier–Stokes and Euler equations, and serves as a bridge between classical fluid mechanics and a wide range of applications.
In regimes where one spatial direction is significantly smaller than the others, such as thin domains or flows with strong vertical stratification, a hydrostatic balance often emerges. Under this approximation, the governing equations reduce to the so-called primitive equations. While originally developed in geophysical contexts, these reduced models also arise in other settings, including flows in thin layers and certain biological systems, such as blood flow in narrow vessels.
This course develops the mathematical analysis of the Boussinesq system and its hydrostatic limit within a broad fluid dynamics framework. We begin with the derivation of the models from fundamental conservation laws, highlighting the role of scaling, anisotropy, and geometry in the emergence of simplified equations. We then introduce the appropriate functional setting for studying well-posedness, emphasizing connections with classical results for the Euler and Navier-Stokes equations.
The course will cover local and global existence results, as well as mechanisms leading to ill-posedness in the non-hydrostatic case, where a maximal unstable eigenvalue related to a long-wave instability in a long periodic channel can be exhibited. Particular attention will also be given to the formation and stability of singularities, the effects of anisotropy and confinement, and the role of external forces such as rotation. We will also discuss recent advances in the rigorous justification of the hydrostatic approximation and the mathematical challenges that arise in inviscid regimes.
This course is available to students at PIMS member universities.
The instructor will deliver the lectures from a fully equipped classroom (e.g., Hickman Building 110) that provides cameras, microphones, and integrated audiovisual support. The cameras will be directed toward the blackboards to ensure clear visibility of the material, while remote participants will be displayed on a screen in the room. This setup allows remote students to follow the lectures in real time and to actively participate by asking questions and interacting during the session.
Ben Ashby : bashby@sfu.ca
Simon Fraser University
Good undergraduate knowledge of systems of ODEs (preferably upper-level)
linear algebra (lower-division)
probability (lower-division)
and discrete mathematics (lower-division)
Some experience of coding (e.g., MATLAB, Python, R) would also be beneficial but is not strictly necessary.
One of MATH 360, MATH 348, MATH 468, MATH 469, or similar.
Registration for this course is not currently available.
This course introduces the mathematical foundations of evolutionary theory, with an emphasis on linking ecological processes with genetics and trait dynamics across scales. Students will learn to formulate and analyse models of evolution using tools from dynamical systems (primarily ODEs), probability, and discrete mathematics. Topics will include:
Throughout, the course emphasises analytical, graphical, and computational techniques that are widely used across applied mathematics to study nonlinear systems. By the end of the course, students will be able to construct, analyse, and critically evaluate mathematical models, and will develop transferable skills for tackling complex problems in biology and other fields.
This course is available to students within the PIMS network, and at universities beyond the PIMS network.
Lectures will be delivered in person and over Zoom, with recordings posted to Youtube. Lecture notes will be delivered using a tablet with pre-prepared slides/notes for students to fill in.
Brian Marcus : marcus@math.ubc.ca
University of British Columbia
Measure theory
Functional Analysis
Linear Algebra (including Jordan form)
Probability Theory
Registration for this course is not currently available.
Symbolic Dynamics is a part of the theory of dynamical systems, with strong connections to ergodic theory and information theory. This course will develop the fundamentals of symbolic dynamics, with a focus on classification problems for shifts of finite type and sofic shifts and applications of symbolic dynamics to modelling smooth dynamical systems. The course textbooks will be: An Introduction to Symbolic Dynamics and Coding, Second Edition, 2021, by Douglas Lind and Brian Marcus and Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms by Rufus Bowen (with updates and corrections by Jean-Rene Chazottes, 2017)
The instructor will write on overhead projectors which will be shared via zoom. Lecture notes will be posted on the course website.
This course is available to students within the PIMS network, universities beyond the PIMS network and from industry/government.
Anotida Madzvamuse : am823@math.ubc.ca
University of British Columbia
Ordinary differential equations
Numerical methods (Numerical Analysis I and II)
Partial differential equations
Matrix theory
Linear systems
Registration for this course is not currently available.
The purpose of this graduate course is to equip graduate students with cutting-edge techniques in data-driven mathematical and computational modelling, analysis and simulations of semi-linear parabolic partial differential equations (PDEs) of reaction-diffusion type. It will cover diverse areas in data-driven modelling using PDEs in biology. I will cover approaches on formulating models from data using first principles, mathematical analysis of reaction-diffusion systems such as linear stability analysis, basic concepts on bifurcation analysis and numerical bifurcation analysis. The second part will focus on numerical methods for PDEs including finite difference methods, and finite elements. This part will also deal with time-stepping schemes and nonlinear solvers for nonlinear PDEs. If time allows, we will look at applications of reaction diffusion theory to cell motility and pattern formation. To support theoretical modelling and numerical analysis, numerical algorithms will be developed and implemented in MATLAB as well as in open finite element source software packages such as FeNiCs, deal.ii and others. Students will be allowed to use packages of their choice as appropriate. Expertise and skills sets to be acquired through this course
We will use zoom for each lecture. Course notes will be distributed in advance and lecture notes will be distributed after each lecture.
This course may be open to students from universities outside of the PIMS network.
Ben Williams : tbjw@math.ubc.ca
University of British Columbia
A solid background in finitely generated abelian groups, and good knowledge of point-set topology or of metric spaces. Knowledge of fundamental groups and covering spaces is helpful but not essential.
Registration for this course is not currently available.
This is a course in algebraic topology. It introduces singular homology and cohomology, their definitions and some methods of calculation. It culminates with Poincaré duality. Applications are provided along the way.
Remote access for this course will be provided via zoom. The instructor intends to lecture from handwritten notes on a tablet. Lecture notes will be provided after the lectures have been delivered.
This course is open to students in the PIMS network.
Assessment will be via homework, midterm and final exam.
Rebecca Tyson : rebecca.tyson@ubc.ca
University of British Columbia - Okanagan
Registration for this course is not currently available.
In this course we are learning to build and analyse nonlinear partial differential equation models. The focus of the course will be models of ecological systems, but the techniques learned apply broadly across application areas. We learn a wide variety of analytic, graphic, and simplification techniques which elucidate the behaviour of these mathematical models, whether or not a closed-form solution is available. By the end of the class, the students will be able to competently read and follow a research paper presenting and analysing a differential equation model from a wide variety of application areas. One of the exciting aspects of Math 459/559, is the relevance of this course to understanding real-world models, such as models of diseases like COVID-19. We will therefore spend some time learning about disease models, and understanding the mathematical basis of concepts that have been talked about regularly in the media: The reproductive number, flattening the curve, epidemic wave, peak size, and final size. We will also discuss the effect of spatial movement on disease progression in the population. Broadly, the topics that we cover are ecological applications of travelling waves, disease models, and pattern formation in reaction-diffusion and reaction-diffusion-chemotaxis models.
TBA
This course is available to students within the PIMS network.
Lectures will be livestreamed via zoom. The lecturer will be writing on a whiteboard interspersed with pdf presentations. Lecture notes will be posted on Canvas. Office hours will be offered in hybrid format.
This course may be open to students from universities outside of the PIMS network.