About Me

I am currently a PhD student at Keele University, working under the supervision of Dr. Paul Truman. I did my MMath at the University of Exeter, my master's dissertation was on Finite Abelian Extensions of the Rational Numbers and was supervised by Dr. Henri Johnston. During my time at Exeter I undertook an undergraduate research project, supervised by Prof. Nigel Byott and funded by an LMS Undergraduate Research Bursary, counting Hopf-Galois structures on separable extensions of particular degree.

For the 2022/23 academic year, was also a Teaching Fellow at Keele. I lead the second year module Exploring Algebra and Analysis (MAT-20035) the third year module Number Theory and Cryptography (MAT-30038), as well as assisting in tutorials for the foundation year.

Research Interests

Broadly, I am interested in algebra with a group theoretic flavour. My current work is on the novel algebraic structure of the skew bracoid, which is a generalisation of the skew brace corresponding to Hopf-Galois structures on separable but not necessarily normal extensions of fields. As with the skew brace, the skew bracoid is also connected to the study of solutions to the Yang-Baxter equation. I am most excited when structural information can be passed through these various correspondences.

Keywords: Algebra, Group Theory, Hopf-Galois Theory, Yang-Baxter Equation, Skew Brace, Skew Bracoid.

Contact

Email me at i.d.martin-lyons@keele.ac.uk. Mi faswn i'n hapus iawn i glywed ohonoch chi yn Gymraeg.