My name is Catherine, but I'm more commonly known as Katie. I am currently a third year PhD Student at University of East Anglia, working under supervison of Professor Robert Gray.
My current interests are mainly in combinatorial algebra. My thesis explores many different decision problems in groups and inverse monoids.
Before joining UEA, I attended University of St Andrews where I obtained a First Class Masters of Mathematics (MMath). My final year project, which I worked on under the supervision of Prof Nik Ruškuc, was titled "The Theory of Subdirect Products". I also completed two summer research internships and a research assistantship, working with Prof Nik Ruškuc and Dr Ashley Clayton, which led to two publications.
Clayton, A., Reilly, C., & Ruškuc, N. (2025). A characterisation of semigroups with only countably many subdirect products with Z. Bulletin of the Australian Mathematical Society, 111(2), 314-323. https://doi.org/10.1017/S0004972724000613
Clayton, A., Reilly, C., & Ruškuc, N. (2025). On the number of subdirect products involving semigroups of integers and natural numbers. Journal of Algebra and Its Applications, Article 2650137. Advance online publication. https://doi.org/10.1142/S0219498826501379
Rational Subsets of Groups (UEA EMP Research Day, 14th January 2026)
Decidability Problem in Two-Generator One-Relator Groups and Inverse Monoids (North British Semigroups and Applications Network meeting, University of St Andrews, 12th-13th June 2025)
Some Decidability Results for One-relator Inverse Monoids with Two Generators (Conference in Theoretical and Computational Algebra, Èvora, Portugal, 29th June - 4th July 2025)
One-Relator Inverse Monoids With Decidable Word Problem Are Algorithmically Unclassifiable (York Semigroups Seminar, University of York, 12th November 2025)
Decidability: Exploring the limits of logic and computation (UEA PhD Seminar, University of East Anglia, 26th November 2025)
As a PhD student at UEA, I have taught a variety of courses at different levels. I have worked as an Associate Tutor (AT) on the modules:
MTHF5035A Cryptography
MTHA5003A Complex Functions & Linear Algebra
MTHA4007B Computation and Modelling
MTHB3001A Basic Mathematics 1
MTHB3006B Further Mathematics For Scientists
I am currently Postgraduate Research (PGR) Representative in the UEA School of Engineering, Mathematics and Physics. This involves attending, and representing all PGR students, at regular school meetings and arranging social events for PGR students in the Faculty of Science.
I was a local organiser for the Model Theory in the UK meeting held at University of East Anglia in June 2025. https://motuknetwork.github.io
UEA website: https://research-portal.uea.ac.uk/en/persons/catherine-reilly
Orcid profile: https://orcid.org/0009-0001-5079-2136