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.