School of Computing and Mathematics

As an undergraduate, I read for an MMath at the University of Oxford (Exeter College). I graduated in 2005 and moved to the University of Exeter where I studied for a PhD in algebraic number theory under the supervision of Nigel Byott. After submitting my thesis I held two short term posts in Exeter, initially as a research fellow and subsequently as a teaching fellow. I finally left Exeter in 2010 to come to Keele.

My research interests are in algebra and number theory, specifically the Galois module structure of algebraic integers. I am particularly interested in Hopf-Galois module theory, where a Hopf algebra takes the place of the Galois group. 

My PhD research concerned the Hopf-Galois module structure of tamely ramified extensions, and possible generalisations of Noether’s theorem to this setting. Since then, in addition to considering further generalisations of the results of my thesis, I have studied the application of these techniques to wildly ramified extensions. In particular, I am interested in the possibility of a Hopf-Galois analogue of Elder’s concept of Galois Scaffolding.

• "Hopf-Galois Module Structure of Tame Cp x Cp Extensions" In preparation
• "Hopf-Galois module Structure of Tame Biquadratic Extensions"
   Journal de théorie des nombres de Bordeaux  2012, vol. 24, no 1, pp. 173-199
• "Towards a generalisation of Noether's theorem to nonclassical Hopf Galois structures"
    New York J. Math. 17 (2011) 799-810
• "Hopf-Galois Module Structure of Some Tamely Ramified Extensions"
    PhD Thesis, University of Exeter, 2009
  https://eric.exeter.ac.uk/repository/handle/10036/71817

MAT-10035: Analysis
MAT-10038: Algebra I
MAT-10040: Algebra II
MAT-20021: Real Analysis
MAT-20025: Abstract Algebra
MAT-30022: Number Theory
MAT-30027: Codes and Cryptography