Research Interests

I am interested in aspects of transformation monoids and permutation groups. I am currently researching the structure of endomorphism monoids of certain semigroups.

If we let S be some semigroup and End(S) be its endomorphism monoid then we can define End₂ (S) as the endomorphism monoid of End(S). We then define End_i(S) as End(End_i-1(S) for all natural numbers i. This sequence is called the endomorphism tower of S. I am currently looking at patterns that arise in these endomorphism towers for different S.

Research Output

Talk: The Endomorphism Tower Problem - Presented at the 40th NBSAN

Paper (preprint): The Endomorhism Tower of a Finite Symmetric Group

Teaching and Departmental Activities

I am a Graduate Teaching Assistant in the Department of Mathematics at the University of York. I have taught on the following modules:

- Groups, Rings and Fields

- Introduction to Pure Mathematics

- Mathematical Programming and Skills

Additionally, I am currently the PGR Rep for the equality, diversity, and inclusivity committee in the mathematics department and am serving as a PGR Mentor for the Summer Research students in the departments of Mathematics and Computer Science.

Hobbies

Any spare time I have is often given over to archery. I am currently:

- An ArcheryGB Session Coach

- Team Captain and coach for the University of York Archery Club

- A general committee member of the Yorkshire Archery Association

- A volunteer coach for the British Transplant Games