I study mathematics, with a focus on abstract algebra and category theory.
The following are notes that I made for seminars at the University of Sydney.
My PhD is supervised by Kevin Coulembier at the University of Sydney, and I am studying symmetric tensor categories over fields of positive characteristic. Brief summary: a symmetric tensor category is a definition in category theory which mimics the structure of the category of finite-dimensional representations of a group. In characteristic zero (i.e. working over the complex numbers), every symmetric tensor category of moderate growth has a symmetric tensor functor to the category of super vector spaces, which means it's equivalent to a category of representations of an affine super group scheme. In characteristic p for prime numbers p however (i.e. working over the algebraic closure of the finite field of order p), there are interesting examples of tensor categories which are not of this form. I am studying a family of these called the Verlinde categories which are (possibly pre-emtively) conjectured to comprise all incompressible symmetric tensor categories of moderate growth.
Here is my most recent work on the topic:
I completed a Bachelor of Science and Bachelor of Advanced Studies (Dalyell Scholars including Mathematical Sciences) at the University of Sydney from 2019 through 2022, with majors in mathematics and physics. My honours project was on Coxeter systems, in which I proved a classification of parabolic quotients of Coxeter groups up to isomorphism in Bruhat order. A preprint for that work can be found here, although note that this may not be the most up-to-date version since it is still going through the review process.