Bryan Kettle has a PhD in mathematics from the University of Alberta under the supervision of Dr. Nicolas Guay. Bryan’s academic research predominantly lies within quantum group theory focusing on the study of Yangians and their representation theory.

Over the duration of his PhD program, he was employed as a laboratory instructor for several courses in calculus and linear algebra. He has also given many presentations and talks covering topics from introductory to specialized subjects in mathematics.

Interests

- Algebra
- Mathematical Physics
- Representation Theory

Education

PhD in Mathematics, 2023

University of Alberta

MSc in Mathematics, 2018

University of Western Ontario

BSc (Honours) in Pure Mathematics, 2017

Memorial University of Newfoundland

Academically, I am an algebraist primarily focused on studying certain kinds of Hopf algebras known as *quantum groups*. The value of these types of objects are often realized in terms of their representations, where they yield non-trivial solutions to important consistency equations found in quantum physics and statistical mechanics.

The family of quantum groups I mainly study are Yangians, usually denoted $\operatorname{Y}(\mathfrak{g})$ for a suitable Lie algebra or Lie superalgebra $\mathfrak{g}$. At least when $\mathfrak{g}$ is a finite-dimensional complex simple Lie algebra, it is known that the finite-dimensional irreducible representations of $\operatorname{Y}(\mathfrak{g})$ yield rational solutions to the Yang-Baxter equation:

$$R_{12}(u) R_{13}(u+v) R_{23}(v) = R_{23}(v) R_{13}(u+v) R_{12}(u).$$In September of 2023, I successfully defended my PhD dissertation, titled *Orthosymplectic, Periplectic, and Twisted Super Yangians*, wherein several algebraic and representation theoretic results are proven about Yangians based on certain Lie superalgebras. One can access my PhD dissertation via the link available below.