Undergraduate students interested in pursuing a funded summer research project (USRA) in geometry/topology are welcome to contact me. Below are a couple of possible themes for such a project and some links about the application process. Please send me an email if you are interested!
What is the shape of a data set? This relatively new field of research exploits classical methods of algebraic topology to give some answers to this quesiton. Projects in this theme could focus on the mathematical methods and techniques of TDA, and/or applying these tools to real data sets. I recently co-supervised a PIMS VXML project on TDA, which can also give you an idea what this is about.
Symplectic geometry has its origins as the geometric formulation of classical mechanics, but it has since established meaningful connections with many areas of mathematics, such as algebraic geometry (toric varieties), topology, (Hamiltonian) pde's, and mathematical physics. After learning some of the basics of symplectic geoemtry, a project in this theme could dive deeper into the subject or explore some applications.
Category theory is an abstract framework that formalizes relationships and patterns between different areas of mathematics. Typically, one picks up some category theory here and there while learning advanced topics in algebra and topology; however, there are real (real!) applications of category that I would love to learn more about. These applications include: dynamical systems, epidemiology, computer science, chemistry, artificial intelligence, ... If you're interested in learning about these applications, I would love to learn with you!
Students interested in pursuing an MSc or PhD in geometry/topology are welcome to contact me about possible openings under my supervision. This page contains more information about my research.
Recent PhDs with compatible research interests are welcome to reach out to me about possible postdoc positions at U Manitoba. As a PIMS member, our department participates in the PIMS postdoc competitions, typically advertised on mathjobs in the Fall. Please note that the application process requires a nomination letter from the potential supervisor (possibly me, if you're reading this) that demonstrates research compatibility. Prospective candidates are encouraged to reach out to me well in advance of the stated deadlines to explore this further.