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Harry Hylock
(he/him)
Teams and roles for Harry Hylock
Graduate Tutor
Computational & Mathematical Sciences
Overview
After gradudating with a BSc (Hons) Mathematics at the University of Surrey, I joined Cardiff Univeristy as a full-time Maths PhD student.
My ongoing research here entails higher dimensional joint ordered factorisations and their relation to additive systems and cyclotomic polynomials. In addition to Number Theory, my research interests include Complex Analysis, Analytic PDEs in Fluid Dynamics and Weather Systems, and Graph/Knot Theory.
Additionally, I work at Cardiff University as a graduate tutor. This work includes assiting with tutorials for 1st year undergrad students, and running Maths Support sessions for students of all years. My duties as a graduate tutor have also extended to the Transnational Education (TNE) work the university is doing in Astana, Kazakhstan, which has involved travelling over there to help deliver a foundational mathematics module to STEM undergraduate students.
Research
PhD Research
My current research as part of my PhD has began with looking at how my supervisor (Dr Matthew Lettington) and co-supervisor's (Professor Karl Schmidt) result with m-dimensional joint ordered factorisations compare with prior results in relevent publications. Following this generalisation to match with prior literature, I approached my supervisors' result with a new method of combinatorial interpretation to see if this new pathway can offer more insights into the internal combinatorial objects at play. What followed is an investigation into how we can write c-irreducible polynomial constructions in terms of joint ordered factorisations, and subsequently how irreducible c-factorisations clump prime factors of a certain form.
The new focus with joint ordered factorisations is to see how their bijective centred sum systems can relate to m-dimensional ellipsiods, in particular how their density/cluster changes throughout the higher dimension shape.
Other Research Interests
- As part of a Summer Research Internship, I began looking to improve on current published results for upper bounds on primes (bounds of the form (1 + epsilon)n). This follows from work on Bertrand's Postulate and Ramanujan's estimates.
- Using Knot Theory to better understand the Collatz Conjecture
- Complex Analysis with regards to identities and multiplicative inverses
- Boundary Value Problems of the Monge-Ampere Equation (Optimal Transport Problem)
Teaching
Graduate Tutor (Problem Classes)
- Elementary Differential Equations (1st Year module, Cardiff University), 2026 to present
Graduate Tutor (Transnational Education; Astana, Kazakhstan)
- Mathematical Foundations (Foundation Year module, Cardiff University Kazakhstan), 2026