RESEARCH
My research interests broadly lie in the study of combinatorial and relational structures, in a blend of structural, extremal and enumerative combinatorics. My background is in the study of permutation containment and avoidance, where enumeration is the main game. However, the structural study of permutations can often be translated to other combinatorial objects, most notably graphs, where the consequences can be wide-ranging. Currently, I am especially investigating the question of well-quasi-ordering in combinatorial objects and the corresponding construction of infinite antichains, but I also have ongoing projects in permutation enumeration, structural graph theory, and graph parameters.
I submitted my PhD Thesis, entitled "Simplicity in Relational Structures and its Application to Permutation Classes", in July 2007, and successfully defended it in October 2007. My external examiner was Einar Steingrímsson (Strathclyde University), my internal Steve Linton. My PhD was written whilst in the School of Mathematics and Statistics at the University of St Andrews, was supervised by Prof Nikola Ruškuc, and was funded by EPSRC.
Research students
Grants
In
Opinion 117, Doron Zeilberger (my academic grandfather!) suggested more people should upload grant bids, so here are some older ones of mine.
- [FUNDED] EPSRC First Grant, EP/J006130/1, £91,797, 1st October 2012 -- 30th September 2013. Infinite Antichains of Combinatorial Structures.
[Proposal] [GoW]
- [FUNDED] LMS Conference Grants (Scheme 1), £560, 30th January 2013. Winter Combinatorics Meeting, held at The Open University.
[Proposal].
- [NOT FUNDED] ERC Starting Grant, 2014. [Part B2]
- [FUNDED] LMS Conference Grants (Scheme 1), £2,000, 11th--12th September 2014. Valediction to Jeremy Gray, held at Mercure Parkside Hotel, Milton Keynes.
[Proposal].
- [FUNDED] LMS Conference Grants (Scheme 1), £1,908, 15th--19th June 2015. Permutation Patterns 2015, held at De Morgan House, London.
[Proposal].
- [NOT FUNDED] EPSRC Standard Grant, 2015. [Proposal]
Conference Organisation
- Program Committee, Permutation Patterns 2019, Universität Zürich, Switzerland, 17-21 June 2019.
- Local organising committee, Winter Combinatorics Meeting, Open University, annually 2011-2016.
- Chair of Local Organising Committee, Permutation Patterns 2015, De Morgan House, London, 15-19 June 2015.
- Organising Committee, Permutation Patterns 2011, California Polytechnic University, San Luis Obispo, USA, 20-24 June 2011.
- Organising Committee, Permutation Patterns 2010, Dartmouth College, USA, 9-13 August 2010.
- Local organising committee, Techniques and Problems in Graph Theory, University of Bristol, 1-3 July 2009.
Editing
Other Activities
- Review for the LMS Newsletter of Alex's Adventures in Numberland by Alex Bellos.
[PDF]
[Newsletter]
A version also appeared in Plus Magazine. [Plus]
- Read my MathSciNet Reviews.
- Referee for: Annals of Combinatorics, Discrete Applied Mathematics, Discrete Mathematics, Electronic Journal of Combinatorics, Graphs and Combinatorics, Journal of Combinatorial Theory Series A, Journal of Combinatorics, LMS Lecture Note Series, Mathematika, Pure Mathematics and Applications.
List of Coauthors
- Michael Albert, Mike Atkinson, Aistis Atminas, David Bevan, Hojin Choi, Daniel Cocks, Shalosh B. Ekhad, Andrew Elvey Price, Michael Engen, Nicholas Georgiou, Sophie Huczynska, Vít Jelínek, Jisu Jeong, Nicholas Korpelainen, Jan Kynčl, Vadim Lozin, David Marchant, Sang-il Oum, Jay Pantone, Nik Ruškuc, Jakub Sliačan, Rebecca Smith, Juraj Stacho, Vincent Vatter, Rob Waters, Julian West.