Bryan Kettle has a PhD in mathematics from the University of Alberta, where he studied 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
- Data Science
- 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

My academic research 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 can yield non-trivial solutions to important consistency equations for quantum integrable systems found in statistical mechanics.

The family of quantum groups I mainly studied are known as *Yangians*, usually denoted
$\operatorname{Y}(\mathfrak{g})$ for a suitable Lie algebra or Lie superalgebra
$\mathfrak{g}$. 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.