Professor Nigel Byott | Mathematics and Statistics

Prof Nigel Byott

Professor of Pure Mathematics

N.P.Byott@exeter.ac.uk

(Streatham) 3982

01392 723982

Overview

Career

After undergraduate study in Cambridge, and taking "Part III" of the Mathematics Tripos there, I was a PhD student in Manchester, where my thesis was on "Cleft Extensions of Hopf Orders". I was G.H.Hardy Junior Research Fellow at New College, Oxford for two years before coming to Exeter in 1991 as Lecturer in Pure Mathematics.

Research

My research is at the interface of algebraic number theory and abstract algebra.

My main area of research is Hopf-Galois theory (which generalises classical Galois Theory), and its connections certain algebraic structures related to skew braces which arise in connection with the Yang-Baxter Equation in theoretical physics. I also work on various aspects Galois module structure in tamely or wildly ramified extensions of local and global fields, including the determination of realisable classes for tame extensions, and the occurrence of Hopf orders as associated orders of rings of integers.

PhD Supervision:

I may be available to supervise PhD projects related to Hopf-Galois theory, skew braces, integral Galois module theory. Please contact me for further information.

Teaching.

Over the years I have taught a number of topics within Pure Mathematics (Mathematical Structures, Topology & Metric Spaces, Real Analysis, Galois Theory, Number Theory, ..), and also Mathematics: History and Culture, and Mathematical Theory of Option Pricing.

Other Responsibilities

I am currently .co-Director of Education & Student Experience in the Department of Mathematics & Statistics. I have previously held various other administrative roles, including Academic Lead for the Number Theory, Geometry and Algebra groupdmissions Officer and Assessment Officer.

I am also Exeter representative for the London Mathematical Society, and was for 10 years a member of the LMS Editorial Advisory Board.

Publications

_{Copyright Notice: Any articles made available for download are for personal use only. Any other use requires prior permission of the author and the copyright holder.}

| 2024 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2009 | 2008 | 2007 | 2006 | 2005 | 2004 | 2002 | 2000 | 1999 | 1998 | 1997 | 1996 | 1995 | 1994 | 1993 | 1992 | 1991 |

2024

Byott NP, Ferri F. (2024) On the number of quaternion and dihedral braces and Hopf--Galois structures. [PDF]
Byott NP. (2024) On insoluble transitive subgroups in the holomorph of a finite soluble group, Journal of Algebra, volume 638, pages 1-31, DOI:10.1016/j.jalgebra.2023.10.001. [PDF]

2022

Byott NP. (2022) On Insoluble Transitive Subgroups in the Holomorph of a Finite Soluble Group. [PDF]

2021

Byott NP, Martin-Lyons I. (2021) Hopf-Galois Structures on Non-Normal Extensions of Degree Related to Sophie Germain Primes, DOI:10.48550/arxiv.2102.05759.

2020

Alabdali AA, Byott NP. (2020) Hopf-Galois Structures of Squarefree Degree, Journal of Algebra, volume 559, pages 58-86, DOI:10.1016/j.jalgebra.2020.04.019. [PDF]

2019

Alabdali AA, Byott NP. (2019) Hopf-Galois Structures of Squarefree Degree, DOI:10.48550/arxiv.1910.07811.
Alabdali AA, Byott NP. (2019) Skew Braces of Squarefree Order, DOI:10.48550/arxiv.1910.07814.

2018

Byott N, Smoktunowicz A, Vendramin L. (2018) On skew braces (with an appendix by N. Byott and L. Vendramin), Journal of Combinatorial Algebra, volume 2, no. 1, pages 47-86, DOI:10.4171/JCA/2-1-3.
Byott NP, Childs LN, Elder GG. (2018) Scaffolds and Generalized Integral Galois Module Structure, Annales de l'Institut Fourier. [PDF]

2017

Alabdali AA, Byott NP. (2017) Counting Hopf-Galois Structures on Cyclic Field Extensions of Squarefree Degree, DOI:10.48550/arxiv.1703.09636.

2016

Byott N. (2016) GALOIS THEORIES (Cambridge Studies in Advanced Mathematics 72), Bulletin of the London Mathematical Society, volume 34, no. 3, pages 376-378, DOI:10.1112/s0024609302221141.
Byott NP, Lin C, Zhang Y. (2016) On the mixing properties of piecewise expanding maps under composition with permutations, II: Maps of non-constant orientation, Stochastics and Dynamics, volume 16, no. 03, pages 1660013-1660013, DOI:10.1142/s0219493716600133. [PDF]

2015

Byott NP. (2015) Solubility criteria for Hopf-Galois structures, New York Journal of Mathematics, volume 21, pages 883-903.

2014

Byott NP. (2014) Solubility Criteria for Hopf-Galois Structures, DOI:10.48550/arxiv.1412.5923.
Byott NP, Lin C, Zhang Y. (2014) On the mixing properties of piecewise expanding maps under composition with permutations, II: Maps of non-constant orientation, DOI:10.48550/arxiv.1405.0481.

2013

Byott NP, Elder GG. (2013) Sufficient Conditions for Large Galois Scaffolds, DOI:10.48550/arxiv.1308.2092.
Byott NP, Childs LN, Elder GG. (2013) Scaffolds and Generalized Integral Galois Module Structure, DOI:10.48550/arxiv.1308.2088.
Byott NP. (2013) Nilpotent and abelian Hopf-Galois structures on field extensions, Journal of Algebra, volume 381, pages 131-139, DOI:10.1016/j.jalgebra.2013.02.008.
Byott NP, Holland M, Zhang Y. (2013) On the mixing properties of piecewise expanding maps under composition with permutations, Discrete and Continuous Dynamical Systems- Series A, volume 33, no. 8, pages 3365-3390, DOI:10.3934/dcds.2013.33.3365.
Byott NP, Sodaigui B. (2013) Realizable Galois module classes over the group ring for non abelian extensions, Annales de l'institut Fourier, volume 63, no. 1, pages 303-371.
Byott NP, Elder GG. (2013) Galois scaffolds and Galois module structure in extensions of characteristic p local fields of degree ^p2, Journal of Number Theory, volume 133, no. 11, pages 3598-3610, DOI:10.1016/j.jnt.2013.04.021.

2012

Byott NP. (2012) Nilpotent and abelian Hopf-Galois structures on field extensions, DOI:10.48550/arxiv.1210.1693.
Byott NP, Holland M, Zhang Y. (2012) On the mixing properties of piecewise expanding maps under composition with permutations, DOI:10.48550/arxiv.1203.5145.
Byott NP, Childs LN. (2012) Fixed-point free pairs of homomorphisms and nonabelian Hopf-Galois structure, The New York Journal of Mathematics, volume 18, pages 707-731.

2011

Byott NP, Elder GG. (2011) Galois scaffolds and Galois module structure in extensions of characteristic $p$ local fields of degree $p^2$, DOI:10.48550/arxiv.1106.3577.
Byott NP. (2011) A Valuation Criterion for Normal Basis Generators of Hopf-Galois Extensions in Characteristic p, Journal de theorie des nombres de bordeaux, volume 23, no. 1, pages 59-70.
Byott NP, Carter JE, Greither C, Johnston H. (2011) On the restricted Hilbert-Speiser and Leopoldt properties, Illinois Journal of Mathematics, volume 55, no. 2, pages 623-639.

2009

Byott NP, Elder GG. (2009) Integral Galois Module Structure for Elementary Abelian Extensions with a Galois Scaffold, DOI:10.48550/arxiv.0908.4562.
Byott NP. (2009) A Valuation Criterion for Normal Basis Generators of Hopf-Galois Extensions in Characteristic p, DOI:10.48550/arxiv.0905.3085.
Byott NP, Elder GG. (2009) On the necessity of new ramification breaks, Journal of Number Theory, volume 129, no. 1, pages 84-101, DOI:10.1016/j.jnt.2008.07.011.

2008

Byott NP. (2008) On the integral Galois module structure of cyclic extensions of p-adic fields, Quarterly Journal of Mathematics, volume 59, no. 2, pages 149-162, DOI:10.1093/qmath/ham037.
Trovati M, Ashwin P, Byott NP. (2008) Packings induced by piecewise isometries cannot contain the Arbelos, Discrete and Continuous Dynamical Systems, volume 22, no. 3, pages 791-806.

2007

Byott NP, Elder GG. (2007) On the necessity of new ramification breaks, DOI:10.48550/arxiv.0704.3951.
Byott NP. (2007) Hopf-Galois structures on almost cyclic field extensions of 2-power degree, Journal of Algebra, volume 318, no. 1, pages 351-371, DOI:10.1016/j.jalgebra.2007.04.010.
Byott NP, Elder GG. (2007) A valuation criterion for normal bases in elementary abelian extensions, Bulletin of the London Mathematical Society, volume 39, no. 5, pages 705-708, DOI:10.1112/blms/bdm036.

2006

Byott NP, Elder GG. (2006) A valuation criterion for normal bases in elementary abelian extensions, DOI:10.48550/arxiv.math/0605011.
Byott NP, Greither C, Sodaigui B. (2006) Classes realisables d'extensions non abeliennes, Journal fur die reine und angewandte Mathematik (Crelles Journal), volume 2006, no. 601, pages 1-27, DOI:10.1515/CRELLE.2006.093.

2005

Sodaigui, B.. (2005) Realizable Galois module classes for tetrahedral extensions, Compositio Mathematica, volume 141, no. 3, pages 573-582.
Byott NP, Sodaïgui B. (2005) Galois module structure for dihedral extensions of degree 8: Realizable classes over the group ring, Journal of Number Theory, volume 112, no. 1, pages 1-19, DOI:10.1016/j.jnt.2005.01.003.
Byott NP, Elder GG. (2005) New ramification breaks and additive Galois module structure, Journal de theorie des nombres de Bordeaux, volume 17, no. 1, pages 87-107.

2004

Byott NP. (2004) Hopf-Galois structures on field extensions with simple Galois groups, Bulletin of the London Mathematical Society, volume 36, no. 1, pages 23-29, DOI:10.1112/S0024609303002595.
Byott NP. (2004) Hopf-Galois structures on Galois field extensions of degree pq, Journal of Pure and Applied Algebra, volume 188, no. 1-3, pages 45-57, DOI:10.1016/j.jpaa.2003.10.010.
Byott, N.P.. (2004) Monogenic Hopf orders and associated orders of valuation rings, Journal of Algebra, volume 275, no. 2, pages 575-599.

2002

Byott NP. (2002) Integral Hopf-Galois structures on degree p2 extensions of p-adic fields, Journal of Algebra, volume 248, no. 1, pages 334-365, DOI:10.1006/jabr.2001.9053.
Byott NP, Elder GG. (2002) Biquadratic extensions with one break, Canadian Mathematical Bulletin, volume 45, no. 2, pages 168-179, DOI:10.4153/CMB-2002-020-3.

2000

Byott NP. (2000) Picard invariants of Galois algebras over dual Larson Hopf orders, Proceedings of the London Mathematical Society, volume 80, no. 1, pages 1-30, DOI:10.1112/S0024611500012417.
Byott NP. (2000) Galois module structure and Kummer theory for Lubin-Tate formal groups, Algebraic Number Theory and Diophantine Analysis, Graz, 30th Aug - 5th Sep 1998.

1999

Byott NP. (1999) Integral Galois module structure of some Lubin-Tate extensions, Journal of Number Theory, volume 77, no. 2, pages 252-273, DOI:10.1006/jnth.1999.2385.
Byott NP, Chapman RJ. (1999) Power sums over finite subspaces of a field, FINITE FIELDS TH APP, volume 5, no. 3, pages 254-265.

1998

Byott NP. (1998) Tame Realisable Classes over Hopf Orders, Journal of Algebra, volume 201, no. 1, pages 284-316, DOI:10.1006/jabr.1997.7247.

1997

Byott NP. (1997) Galois structure of ideals in wildly ramified abelian p-extensions, Journal de theorie des nombres de Bordeaux, volume 9, no. 1, pages 201-219.
Byott NP. (1997) Associated orders of certain extensions arising from Lubin-Tate formal groups, Journal de theorie des nombres de Bordeaux, volume 9, no. 2, pages 449-462.
Byott NP. (1997) Two constructions with galois objects, Communications in Algebra, volume 25, no. 11, pages 3513-3520, DOI:10.1080/00927879708826066.

1996

Byott NP, Lettl G. (1996) Relative Galois module structure of integers in abelian extensions, Journal de theorie des nombres de Bordeaux, volume 8, no. 1, pages 125-141.
Byott NP. (1996) Uniqueness of Hopf galois structure for separable field extensions, Communications in Algebra, volume 24, no. 10, pages 3217-3228, DOI:10.1080/00927879608825743.
Byott NP. (1996) Uniqueness of Hopf Galois structure for separable field extensions (vol 24, pg 3217, 1996), COMMUN ALGEBRA, volume 24, no. 11, pages 3705-3705.

1995

Byott NP. (1995) Tame and galois extensions with respect to hopf orders, Mathematische Zeitschrift, volume 220, no. 1, pages 495-522, DOI:10.1007/BF02572628.
BYOTT NP. (1995) TAME AND GALOIS EXTENSIONS WITH RESPECT TO HOPF ORDERS, MATHEMATISCHE ZEITSCHRIFT, volume 220, no. 4, pages 495-522, DOI:10.1007/BF02572628. [PDF]
Byott NP. (1995) Hopf orders and a generalization of a theorem of L. R. McCulloh, Journal of Algebra, volume 177, no. 2, pages 409-433, DOI:10.1006/jabr.1995.1305.
Byott NP. (1995) Local Galois module structure and Hopf orders, PROCEEDINGS OF THE 2ND GAUSS SYMPOSIUM - CONFERENCE A: MATHEMATICS AND THEORETICAL PHYSICS, pages 249-255. [PDF]

1994

BYOTT NP. (1994) SOME SELF-DUAL LOCAL-RINGS OF INTEGERS NOT FREE OVER THEIR ASSOCIATED ORDERS (VOL 110, PG 5, 1991), MATH PROC CAMBRIDGE, volume 116, pages 569-569.

1993

Byott NP. (1993) Cleft Extensions of Hopf Algebras, Journal of Algebra, volume 157, no. 2, pages 405-429, DOI:10.1006/jabr.1993.1107.
BYOTT NP. (1993) CLEFT EXTENSIONS OF HOPF-ALGEBRAS .2, PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, volume 67, pages 277-304. [PDF]

1992

BYOTT NP. (1992) TOROIDAL BLOCK DECOMPOSITIONS FOR HOPF ORDERS IN GROUP-ALGEBRAS, PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, volume 65, pages 449-473. [PDF]

1991

Byott N. (1991) On Galois isomorphisms between ideals in extensions of local fields, Manuscripta Mathematica, volume 73, no. 1, pages 289-311, DOI:10.1007/bf02567642. [PDF]
Byott NP. (1991) On Galois isomorphisms between ideals in local fields, Manuscripta Mathematica, volume 73, no. 3, pages 289-311.
BYOTT NP. (1991) SOME SELF-DUAL LOCAL-RINGS OF INTEGERS NOT FREE OVER THEIR ASSOCIATED ORDERS, MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, volume 110, pages 5-10, DOI:10.1017/S0305004100070067. [PDF]