Dr. Alex Beams (alexander_beams@sfu.ca) and Dr. Caroline Colijn (ccolijn@sfu.ca)  

Project: Data analysis and mathematical modeling to understand Influenza B

Respiratory viruses like Influenza cause annual epidemics each winter in the Northern Hemisphere. Different species and strain subtypes can be more or less common in different years, however, so not all flu seasons are exactly the same. This makes design of the seasonal influenza vaccine a challenge, because designing an appropriate vaccine requires predicting the strain composition of the upcoming season. The predominant influenza subtypes are Influenza A H1, Influenza A H3, and Influenza B. Typically, seasons dominated by H1 have lower levels of H3, and vice versa, but considerable variability remains. Influenza B is antigenically distinct from the other two, and has generally not seemed useful for predicting the relative amounts of the Influenza A subtypes. Since the COVID-19 pandemic, influenza ciruclation has appeared to return to prepandemic levels - with one notable exception: the Yamagata lineage of Influenza B. It has not been detected since 2020, and is no longer included in trivalent vaccines.

Publicly available data clearly show the dynamics of the different influenza subtypes in different epidemic seasons, but have been mostly focused on improving our understanding of and ability to predict the variation in influenza A subtype incidence. This project is focused on examining these data to better understand Influenza B. It is unclear why one of the Influenza B lineages went extinct after the pandemic, and an improved understanding of its dynamics in the prepandemic era will help solve the puzzle. A central focus of the project will be data visualization to characterize years when Influenza B was successful in the past, and we will explore the scientific literature to develop hypotheses about patterns we observe in the data. We will develop mathematical models based on our hypotheses and simulate epidemics to see what mechanisms lead to the dynamics we observe in the data.

Requirements: Students should be motivated to study the biology of influenza viruses and apply their existing knowledge of mathematics and statistics to address open questions. Familiarity with R, Python, or a comparable programming language is necessary, and facility with differential equations and the fundamentals of statistics is preferred. The project has space for two students to work together at all phases.

Dr. Nadish de Silva (nadish_de_silva@sfu.ca)

Project: Simulating and correcting quantum computers via the stabiliser formalism

Small quantum computers are currently under construction.  How will we verify that they are working correctly?  We might try to simulate their operation on an existing conventional supercomputer.  This would be slow and difficult, however, as quantum computers, by design, perform tasks beyond the abilities of conventional computers.  Thus, clever schemes have been devised to classically simulate quantum computers as efficiently as possible within limited regimes.  Studying this question also gives us insight into the poorly understood mechanisms that drive quantum computational power.

In the longer term, how will we protect highly sensitive quantum data from errors while operating on them?  As quantum data cannot be copied or directly observed, more clever schemes have been devised to enable quantum computation in the face of environmental noise.

This project will centre on the mathematics used to answer both these questions: the stabiliser formalism.  The goal will be to better understand the stabiliser formalism and to utilise it towards facilitating quantum error correction and verifying near-term quantum computers.  

The precise question tackled in the project, and the balance between theory and numerical computations, will depend on the interests and skills of the student.

Requirements: Strong background in mathematics and computer science. Coding skills in Python could be an asset but are not strictly necessary.

Dr. Ailene MacPherson (ailenem@sfu.ca)

Project: Approximate Bayesian Computation Methods for Local Adaptation

Bayesian inference is a powerful method in population biology, allowing researchers to integrate complementary datasets to understand ecological, evolutionary, and epidemiological processes shaping the natural world (Beaumont et al. 2002). When the underlying biological processes become complex, for example disease transmission in a social network, analytical methods become cumbersome and computational approximations must be used instead.  In this project you will develop, implement, and test an Approximate Bayesian Computation (ABC) inference method for inferring the evolutionary processes underlying local adaptation. Local adaptation, where populations adapt to local environmental conditions, has widespread evolutionary and ecological consequences–it is central to generating and maintaining the biological diversity we enjoy every day.  Understanding how local adaptation arises is also essential for developing robust conservation programs (Letterhos 2024).

This highly interdisciplinary USRA project will combine elements of mathematics, statistics, computer science, and biology to address a scientific question of practical relevance to conservation. The student will be introduced to the fundamentals of Bayesian inference, mathematical statistics, and the population biology background.  They will design and implement an ABC approach in python, compare this method against an existing analytical sub-case, test the performance of their method more generally, and summarize and disseminate their methods and results.  The student will be encouraged to develop and present their work at one of two possible local scientific meetings in Fall 2025.

Up to 2 students are invited to work on this project.

Requirements: Previous experience with python programming and Math 348, 360, 468 or 469.

Dr. David Muraki (muraki@sfu.ca)  

Project: Mathematics of the Weather

Students are invited to join a research effort that uses computational models to understand the fluid mechanics of the weather.  There are active projects that investigate a variety of atmospheric phenomena.

One current area of interest involves projects connected with the question, "What is the shape of a cloud"?  We have developed a new mathematical model for the motion of cloud edges --- one that has already confirmed the behaviour of "lenticular" clouds caused by airflow over mountains, and somewhat rare phenomenon known as a "holepunch" cloud (search for images!).  Many of the beautiful observed cloudscapes display a distinctive pattern that are generally believed to be formed by atmospheric instability.

Other areas of research involve the study of larger-scale weather flows, and the evolution of midlatitude storms.  Most of the projects involve the use of a research-quality numerical forecast model.

Requirements: Students should be independently motivated undergraduates in the third or fourth year of their degree.  Some background in a differential equations is essential, as is proficiency in a computational environment such as Matlab/Python. Participants should have a natural curiosity for the workings of the Earth's atmosphere.

Dr. Nilima Nigam (nna29@sfu.ca)

Project: Eigenvalues and resonances

Important physical systems are described by systems of partial differential equations (PDE). The eigenvalues, eigenfunctions and resonances of these systems have beautiful mathematical properties, and deep physical relevance.

This summer, we'll be looking at the eigenvalues and resonances for Maxwell's equations. We'll study questions of spectral optimization: what shapes optimize the kth eigenvalue? The approach will be a blend of analytical and computational. Students should be prepared to read background material, work together on proving conjectures, and also design/run computational experiments using existing software libraries.

Requirements: At least one PDE class (Math 314/418), at least 1 computing class (MACM 316/416). Familiarity with linear analysis would be great, but is not required

Dr. Jessica Stockdale (jessica_stockdale@sfu.ca)

Project: Mathematical modelling of the 1918 Flu pandemic in British Columbia

Modelling of historical disease data can help us understand how outbreaks progressed in the past, but also generate useful insights for combating infectious disease in the present. The 1918 influenza pandemic shared many parallels with the COVID-19 pandemic, despite being 100 years apart.

In this project, we will analyse newly-digitized data from the 1918 pandemic here in British Columbia. By fitting mathematical models to the data, we will explore how the outbreak spread, what bought it under control, and try to uncover whether flu surveillance was effective in detecting cases. The student will develop compartmental models (e.g., SIR) of transmission, explore computational methods for fitting these to data, and ultimately dive into the history of the flu pandemic in BC to interpret their findings in context.

This project would be ideal for a student with interests in applying mathematical and/or statistical methods in public health.

Requirements: Requires some programming skills (suggested R or Python) and experience with either mathematical modelling (systems of ODEs) or stochastic models/statistical inference. Completion of any of MATH 348, 360, 468 or 469 would be a bonus.

Dr. Paul Tupper (pft3@sfu.ca)

Project: Improving Clustering Algorithms with Diversities

Clustering is the task of assigning a large number of unlabeled data points to a small number of classes. Typically, the data are points in a vector space and a metric is defined on the vector space, leading to a distance matrix for the data. When clustering, the metric is used to break up the data into a number of groups. But using just the metric may throw out a lot of information about the placement of the points in the space.

Diversities are an extension of the idea of a metric space, where not just pairs of points but all finite subsets of points are assigned a value. The diameter of a set of points in a metric space is a diversity, but there are many other natural examples. In this project the student will investigate using the perspective of diversities to devise new clustering algorithms, investigating what works well computationally on large data sets.

Up to 2 students are invited to work on this project.

Requirements: Basic programming skills. Strong background in mathematics.