NSERC Undergraduate Student Research Awards (USRA)

2021 USRA Projects in CMS

1. The student will prepare a report on the potential effectiveness of rapid tests in the COVID pandemic.

2. The student will do a brief literature search for background on the following: situations where rapid tests have been used against COVID (in Canada and elsewhere in the world)

3. The student will construct a numerical simulation to determine whether:

    (a) If rapid tests were used to identify and isolate contagious individuals, would this curtail the COVID pandemic?

          i. How low would the false negative rate have to be in order that rapid testing could contain the pandemic?

          ii. How often would rapid testing have to occur in order for to contain the pandemic?

          iii. How high would the rate of noncompliance have to be (people who failed to isolate themselves although they received a positive test result) in order that rapid testing would not succeed in stopping the pandemic?

    (b) If at-home rapid tests became available, and people tested themselves regularly for COVID at home, how frequently would individuals have to test themselves in order to bring the pandemic under control? (Once a day? Three times a week?)

The simulation could take the form of a SIR model.

Reference: Michael Mina, Roy Parker and Daniel B. Larremore, Rethinking COVID-19 Test Sensitivity: A Strategy for Containment. N. Engl. J. Med. 2020; 383:el20 DOI:10.1056/NEJMp2025631

Supervisor: Professor Lisa Jeffrey

2019 USRA Projects in CMS

Hamiltonian Systems

1. The student will learn about Hamiltonian group actions (for example using the book "Symmetry in Mechanics: A Gentle, Modern Introduction" by Stephanie Frank Singer).

2. Based on this background, the student will investigate what could be the image of the moment map for a Hamiltonian circle action on a manifold of dimension two (and why it is only possible to have a Hamiltonian circle action on a simply connected orientable 2-manifold). A moment map is a function whose Hamiltonian flow generates a circle action. The student will investigate what happens if the 2-manifold is noncompact.

3. The student will also investigate the image of the moment map for a Hamiltonian torus action on a symplectic manifold of dimension higher than two.

4. The student will consider what happens if the dimension of the torus is less than half the dimension of the manifold.

Supervisor: Professor Lisa Jeffrey

2018 USRA Projects in CMS

UTeach: A Community Curated Peer Instruction Resource Repository for CS Education

CS education, particularly the secondary and early post-secondary level often requires educators to spend a great deal of time designing and developing curricula and materials. Improving access to high quality materials is a key step in improving access to CS education, particularly for students from underrepresented communities. This project seeks to develop and evaluate methods of sharing educational materials and developing a community of practice among CS educators.
 

Assessment of the predictive power of pedagogical elements on outcomes in computer science

With increasing enrolment in CS programs, it is becoming increasingly important to evaluate students early in their educational careers in order to accurately predict their probability of success in a program. It is also important from a pedagogical point of view that we develop and use modes of assessment that accurately reflect not only what a student has learned, but also how well they will be able to apply their knowledge in future. This project aims to evaluate the ability of various factors to predict future success in computer science degrees.
 

Knots Invariants

The student will explore questions in knot theory (starting with the textbook by W.B.R. Lickorish). One fundamental question is defining invariants of knots using Chern-Simons gauge theory (as in Witten's fundamental 1989 paper "Quantum Field Theory and the Jones Polynomial". Witten defines the Jones polynomial as a path integral (over a space of connections on a three-manifold such as the three-sphere, which is the same as three-dimensional space with an extra point added at infinity). It is basic to understand what kinds of knot invariants can be defined in this way. The student will spend the first few weeks learning background material (from Lickorish's book and the book "The Geometry and Physics of Knots" by Michael Atiyah). The latter part of the project will be spent on defining and calculating knot invariants as integrals.