Under the supervision of Dr Dhruv Ranganathan, I completed an essay on matroids (a combinatorial object which abstracts the notion of independence) and the advanced methods from algebraic geometry required to resolve certain `log concavity' conjectures for matroids.
My work centred on a result of Huh, Katz (2011) and provided an opportunity to appreciate both the theory of matroids and toric intersection theory.
I partook in a summer research project supervised by Dr Thomas Unger which gave me experience in the area of real algebra, algebras with involution, and quadratic and hermitian form theory.
Astier and Unger defined prepositive cones, a notion of ordering on algebras with involution. I had the intention of finding the first ever example of a prepositive cone that was not maximal with respect to inclusion. When my scripts on SAGE were returning no results, my work changed direction, leading me to prove that in fact no such examples existed in the first non-trivial setting: quaternion algebras with involution.
This work has been published in Journal of Algebra and Its Applications, and is available on arXiv.
Supervised by Dr Richard Smith, I produced a Bachelor's thesis in the area of functional analysis on Lipschitz and Lipschitz-free spaces. This focused on a recent paper by Talimdjioski (2023) regarding metrics on the `middle-thirds' Cantor set for which the free space fails the approximation property.