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- Dr Paul Truman
Dr Paul Truman
|Location:||MacKay Building Room 2.16|
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 algebraic number theory, specifically the Galois module structure of algebraic integers. I am particularly interested in Hopf-Galois theory, where a Hopf algebra takes the place of the Galois group.
My PhD research concerned the Hopf-Galois module structure of rings of algebraic integers in tamely ramified extensions of local or global fields, and I continue to work on this topic. I also study the structure and properties of Hopf algebras that give Hopf-Galois structures on extensions of fields, and how these properties might be useful in answering questions of integral module structure.
I maintain an archive of the talks given at the annual conference Hopf algebras and Galois module theory.
I am interested in hearing from potential PhD students in Algebraic Number Theory.
Full Publications List show
Integral Hopf-Galois structures for tame extensions. New York Journal of Mathematics, vol. 19, 647-655. full text>2013.
Hopf-Galois module structure of tame biquadratic extensions. Journal de Theorie des Nombres de Bordeaux, vol. 24(1), 173-199. full text>2012.
Towards a generalisation of Noether's theorem to nonclassical Hopf-Galois structures. New York Journal of Mathematics, vol. 17, 799-810. full text>2011.
Normality and Short Exact Sequences of Hopf-Galois Structures. Communications in Algebra. full text>
The structure of Hopf algebras giving Hopf-Galois structures on Quaternionic extensions. New York Journal of Mathematics. full text>
The Structure of Hopf Algebras Acting on Dihedral Extensions. In Advances in Algebra: Research from the Southern Regional Algebra Conference 2017. Springer. full text>
MAT-30022: Number Theory
MAT-30027: Codes and Cryptography
MAT-40008 Algebraic Number Theory