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## NSERC | VPR

The Undergraduate Student Research Awards (USRA) give students hands-on research experience while working on actual projects. These awards prepare students to pursue graduate studies and encourage interest in research careers.

The awards are supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and SFU's Vice-President, Research (VPR).

Full-Time USRA awards are valued at $6,000 for a minimum of 16 weeks, 35 hours per week. The faculty will supplement this amount with an aditional minimum $2,512 + 9.8% (for statutory benefits). These awards are provided to encourage undergraduate student interest in research and graduate studies.

Working on a USRA project can potentially be counted towards a co-op work term. Please contact the Science Co-op Office to learn more.

## Eligibility for USRA's

**SFU Graduate and Postdoctoral Studies USRA guidelines can be found here:**

**NSERC USRA guidelines can be found here:**

## Procedures for applying for Math USRA's...

*Please be sure to review full eligibility criteria, guidelines, and application forms on the NSERC USRA and Graduate and Postdoctoral Studies: USRA websites listed above, BEFORE beginning the application process.*

**NOTE**: While we do our best to match students up with their preferred projects/supervisors, we cannot guarantee a preferred match due to the competitive nature of the awards. Additionally, we cannot guarantee that every applicant will be matched with a project/supervisor or receive a USRA.

### NSERC Application - Step One

**Due by: Wed, 09 Feb, 2022**

- Interested and eligible students should contact the supervisor with regards to the project they would like to work on.
- Students must create an NSERC Online Account, complete the application for an Undergraduate Student Research Award Form 202: Part I, and upload scanned copies of their official or unofficial transcripts. Advising transcripts are not acceptable.
- Students must email the following documents to the Math Chair's Assistant (mcs@sfu.ca):
- Cover letter with a ranked list of at least three choices of projects

- A curriculum vitae (CV)
- A PDF of Form 202: Part I
- Copies of transcripts
- Their NSERC Online Reference number
- Two reference letters
**NOTE:**Your references should directly email their reference letters to the Math Chair's Assistant (mcs@sfu.ca) by the deadline above. We do not accept reference letters submitted by applicants.

- Cover letter with a ranked list of at least three choices of projects

### NSERC Application - Step Two

**Due by: Wed, 23 Feb, 2022**

**If you are nominated for an NSERC USRA:**

- Email your applicant’s reference number to your selected supervisor and have them complete Form 202: Part II.
- Your supervisor should send a PDF of the form for you to review and confirm that the information is correct.
- Once you have confirmed the information is correct, your supervisor should send a PDF of the form to the Math Chair's Assistant (mcs@sfu.ca).
- Lastly, your supervisor should “submit” the form online via the NSERC site and notify the Math Chair's Assistant afterwards.
**NOTE:**The SFU Graduate & Postdoctoral Studies (GPS) Office makes the final decision for awarding all USRAs. An award is not guaranteed until GPS sends out an award letter.

### VPR Application - Step One

**Due by: Wed, 09 Feb, 2022**

- Interested and eligible students should contact the supervisor with regards to the project they would like to work on.
**NOTE:**If you are an international student who is interested in applying for a VPR USRA, please consult International Student Services (intl_advising@sfu.ca) to ensure you do not violate the terms of your study permit.

- Fill out the VPR USRA Application Form (located on SFU GPS: Deadlines + Application Procedures website).
- Email the following documents to the Math Chair's Assistant (mcs@sfu.ca):
- A cover letter indicating a ranked list of at least three choices of projects

- A curriculum vitae (CV)
- A PDF of your VPR USRA Application Form
- A copy of your unofficial transcript
- Two letters of reference
**NOTE:**Your references should directly email their reference letters to the Math Chair's Assistant (mcs@sfu.ca) by the deadline above. We do not accept reference letters submitted by applicants.

- A cover letter indicating a ranked list of at least three choices of projects

### VPR Application - Step Two

**Due by: Wed, 23 Feb, 2022**

**If you are nominated for a VPR USRA:**

- Email your selected supervisor and ask them to complete Page 2 of your VPR USRA Application Form.
- Your supervisor must email the completed form as a PDF to the Math Chair’s Assistant (mcs@sfu.ca)
**NOTE**: The SFU Graduate & Postdoctoral Studies (GPS) Office makes the final decision for awarding all USRAs. An award isn’t guaranteed until GPS sends out an award letter.

## Current Research Projects

Below are the available research projects in mathematics from faculty members who are taking on qualified undergraduate students. Unless otherwise specified, each project is available to one student only.

**The Summer 2022 USRA competition is open**

**Here are the projects:**

**Dr. Cedric Chauve (cchauve@sfu.ca)**

**Project: Reconstructing ancestral gene orders: methods and experiments**

In a collaboration with German colleagues, we recently published a method for reconstructing putative gene orders of ancestral (extinct) species based on the gene order of current (extant) species. The method is optimization-based and is implemented in a Mixed Integer-Linear Program. The paper is available at https://dx.doi.org/10.1142/S0219720021400096, with a freely accessible preprint available at https://arxiv.org/abs/2108.04297.

The proposed project has two goals:

1. Applying this algorithm on a real dataset (either mammalian species, or yeast species) to assess its ability to handle real-world datasets (the results in the paper were solely based on simulated data).

2. Exploring the development of a local-search algorithm to correct likely errors in the results of the algorithm.

**Requirements**: This project is well suited for a student with (1) a keen interest in the application of mathematical and computational methods in biology, (2) an interest in acquiring data science skills and a willingness to face the hurdles linked to work with large data, (3) good programming skills (in python), (4) a good background in graph theory.

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

**Project:** **Classical simulation of quantum computation via stabiliser methods**

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. Beyond their anticipated practical use, the study of classical simulations of quantum computation gives us insight into the poorly understood mechanisms that drive quantum computational power.

This project will centre on studying the most widely utilised schemes: those based on the *stabiliser formalism*. The goal will be to better understand the rich lattice-theoretic geometry underlying the stabiliser formalism and to utilise it towards advancing state-of-the-art techniques for verifying near-term quantum computers.

**Requirements**: Strong background in mathematics and computer science. Coding skills in Python could be an asset but are not strictly necessary. The project is intended for 1 student. However, up to 2 students may be accepted in the case of multiple exceptional candidates.

**Dr. Razvan Fetecau (****van@sfu.ca****) & Dr. Steve Ruuth (****sruuth@sfu.ca****)**

**Project**: **Numerical methods for partial differential equations on surfaces**

The project aims to investigate numerically and analytically certain partial differential equations (PDEs) set up on surfaces. The class of PDEs that we will consider include the p-Laplacian operator, with the infinity Laplacian as a special case (as p tends to infinity). Such operators and PDEs have applications in image processing and game theory.

The student will review relevant existing literature, will implement various numerical methods to simulate these PDE's on simple surfaces such as a sphere or a cylinder, and will investigate numerically (and possibly analytically) these methods.

**Requirements:** Students are expected to have taken and performed well (with grades in the A range) in MACM 316 and MATH 314. Having taken MACM 416 and MATH 418 are great assets. Students need to be proficient with scientific computing using Matlab.

**Dr. Nathan Ilten (****nilten@sfu.ca****)**

**Project: Problems arising in combinatorial algebraic geometry**

Algebraic geometry, at its most fundamental level, is the study of solution sets of systems of polynomial equations. These solution sets, called varieties, are often very challenging to understand. This project will involve studying problems in algebraic geometry using tools from combinatorics. Specific problems could include the study of degenerations to toric varieties, and properties of cluster varieties.

**Requirements**: Interested students should have a strong background in linear algebra (e.g. Math 240) and rings and ideals (e.g. Math 340), with added background in commutative algebra/algebraic geometry a plus. Up to 2 students are invited to join this project.

**Dr. Ailene MacPherson (****ailenem@sfu.ca****)**

**Project: Modelling Coevolutionary Dynamics in C. Elegan**

Interactions between hosts and parasites are ubiquitous in the natural world and coevolution between species is hypothesized to be an important driver of biological diversification. If and how coevolution generates diversity depends on the dynamics of the genetic “arsenal” of the host and parasite. Do natural systems exhibit genetic “arms races” of ever escalating genetic complexity or a perpetual “trench warfare” of genetic gain and loss? In this project you will develop and fit mathematical models that facilitate the analysis and interpretation of results from a laboratory study of coevolution between the worm *C. elegans* and its bacterial parasite *B. thuringiensis*. The development of mathematical models to complement and support laboratory experiments has the potential to elevate the capabilities of both theoretical and empirical approaches and crack open age-old mysteries in evolutionary biology.

**Requirements: **Previous experience with probability theory and/or dynamical systems and ODEs recommended.

**Dr. David Muraki (****muraki@sfu.ca****) & Dr. JF Williams (****jfwillia@sfu.ca****)**

**Project: Computation of Fluid Models for Atmospheric Science**

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!).

**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. Participants should have a natural curiosity for the workings of the Earth's atmosphere.

**Dr. Alexander Rutherford (arruther@sfu.ca) and Dr. Tamon Stephen (tamon@sfu.ca)**

**Project: Projecting COVID-19 Admissions to Hospitals and Intensive Care Units**

The COVID-19 pandemic is placing considerable strain on the healthcare system. Extensive public health measures, including closures of schools, workplaces, and places of business have been implemented to reduce infections and prevent overwhelming the hospital system. Public health officials agree that COVID-19 is here to stay and may soon become endemic in the population, requiring new management approaches for the healthcare system. This project will develop a machine learning model to project admissions to hospitals and intensive care units from COVID-19 testing data. This model will be integrated with a simulation model of the British Columbia critical care system to create an integrated decision support tool for the British Columbia Centre for Disease Control.

**Requirements: **This project is well-suited to a student interested in data science and operations research. A course in machine learning or operations research would be beneficial. Programming experience in Python or R is required.

**Dr. JF Williams (****jfwillia@sfu.ca****)**

**Project: Optimal control of induction heaters for soil remediation**

From old gas stations through to former oil fields this country has many locations filled with contaminated soil. It is often impossible to remove the soil so sites are left unused for decades while non-aqueous petroleum contaminants degrade or diffuse away. Another option is to remediate the soil in situ. One method for doing this involves burying heaters and essentially baking the hydrocarbons out and capturing them at the surface.

These remediation projects can take months to perform and cost well over a million dollars in electricity costs alone. This project will develop algorithms to control heaters used to remediate contaminated soil to minimize both the time taken and electricity needed.

The successful student will work with existing models both for the operation of the heater and also for the temperature profile in the soil. The goal will be to develop and test optimal control strategies.

**Requirements:** Any students who have taken MATH 260/310 and at least two of MATH 309, MATH 314 (or PHYS 384), MATH 418 or MACM 316 are encouraged to apply.