Opportunities for math and computer science students

There are two research projects happening this summer:

1) The distribution of disease within a honey bee farm can tell us a lot of
information about where a disease started, and how to best treat it. This summer, we’ll be continuing work on a robust simulator to study
different disease/pathogen patterns for informing treatment strategies of BeeCSI, a Genome Canada project for honey bee
conservation.

2) How effective are masks and lockdowns? Since it is difficult to determine the effectiveness of a preventative measure by
measuring the very thing you are trying to prevent, we will use historical seasonal flu data (1999 – 2023) (that we will generate) coupled
with identified periods of mask mandates and lockdowns across Canada to look at the effects of masking and lockdown on influenza. This
can give us an idea of the effectiveness of these non-pharmaceutical interventions in a general sense.

My research uses category theory, which allows one to transfer ideas and results betweendifferent areas of mathematics. My recent
research has shown in particular how we can transfer some of the ideas of differential geometry (the study of smooth surfaces) to
algebraic geometry (the study of the common zeroes of some set of polynomials). The research project (either summer research, or
honours, or possibly both) would involve learning some of the details of this theory, then applying it to understand what vector
fields and connections look like in various algebraic geometry examples.

Required background is strong performance (A- or better) in at least one of Math 3111 (Real Analysis), Math 3221 (Advanced linear
algebra), Math 3211 (Modern Algebra I), or Math 4221 (Modern Algebra II), and preferably more than one of these courses.

We investigate opacity, an information-flow privacy property, in a setting where two competing agents or adversaries aim to hide
their secrets and expose the secrets of the other agent. We want to incorporate quantitative aspects to this problem, where
secrets now have an associated cost, and agents can choose to leak less-costly secrets if it means that they gain better access to their
adversary's secrets.
This project is an extension of (Sharpe, Ricker and Marchand, 2022) and is appropriate for up to two students, one of whom preferably has experience with game theory and automata theory.

Quantum entanglement refers to the ability for small particles to interact with each other in very strange and unintuitive ways that can't be explained by classical physics.

My research focuses on exploring the mathematical properties of quantum entanglement, typically using tools from linear algebra and matrix analysis.
I have a project in mind for mathematics students with a particular interest in linear algebra. I would like to explore the extent to
which the eigenvalues of a quantum state (for us: a symmetric matrix) determine how much entanglement it has. More broadly, the goal is to determine how a state's eigenvalues determine how "useful" it is (i.e., how good it is as a resource in protocols like quantum
teleportation).
Students should have a strong understanding of linear algebra (at least Math 2221, though Math 3221 would be an asset). Complex
Variables (Math 3161) would also be an asset. No physics background is required.

Deep learning models are powerful, and have become a key part of computer vision in the lab and in practice. Unfortunately, many of
these models require vast quantities of data and extremely powerful computers to train from scratch. A variety of approaches have
been taken to this; one of the most commonly seen is adapting a pre-trained model to a new problem by tuning it to a new (and often much smaller) dataset, but this is not entirely satisfactory, especially if we there are no models available that solve closely related
problems.

I am currently working on methods for combining deep learning models with statistical reasoning and “classical” machine
learning methods to build smaller models that can be trained with less data, but retain the ability of deep learning models to construct
powerful features for a specific problem. I am especially interested in applying these models to processing complex documents like web
pages; my work has important applications to web accessibility, among other areas. I hope to several students this summer. Ideally, students will have background in Python programming, statistics, or artificial intelligence, but you don't need experience in all of them! I am also interested in supervising an ISRG student, and I'll be happy to work with you on an application.