My research lies in the area of mathematical logic, specifically model theory. As a PhD student under the supervision of Dugald Macpherson I was a member of the Leeds Logic Group, which is one of the research groups in the Department of Pure Mathematics at the University of Leeds.
- Model theory of multidimensional asymptotic classes, PhD thesis, University of Leeds, 2016.
Published online | Mathematics Genealogy Project
- A report on the Fourth British Postgraduate Model Theory Conference in the Newsletter of the London Mathematical Society, No. 434, March 2014, pp. 14–15.
I was the chairman of the organising committee for this conference.
(Work written before February 2015 is under the surname Wood, which is my birth name.)
- Multidimensional exact classes and Lie coordinatisation, Model theory of finite and pseudofinite structures,
University of Leeds, 29th July 2016. Abstract
- Model theory: Your new favourite area of maths, Warwick Mathematics and Philosophy, 17th March 2016. Abstract
- Exact classes and smooth approximation, Midlands Logic Seminar, 17th March 2016. Abstract | Slides
- Asymptotic classes and Lie coordinatisation, 7th meeting of the Lancashire–Yorkshire Model Theory Seminar (LYMoTS), UCLan (Preston), 5th December 2015. Abstract | Slides
- The Axiom of Choice, or: One Principle, Many Things, Leeds Pure Mathematics Postgraduate Seminar,
19th November 2015. Abstract
- Interpretations: semantic and syntactic, Leeds Postgraduate Model Theory Seminar, 18th February 2015. Abstract
- Ultrafilters and ultraproducts, Leeds Pure Mathematics Postgraduate Seminar, 12th February 2015. Abstract
- R-macs, Leeds Model Theory Seminar, 28th October 2014. Abstract
- Asymptotic classes, British Logic Colloquium PhD Day 2014, UCLan (Preston), 2nd September 2014.
Abstract | Slides
- Indiscernibles, Leeds Postgraduate Model Theory Seminar, 19th November 2012. Abstract
Mathematics and the philosophy of mathematics
- A poster about asymptotic classes, 2014.
I presented this at Angus Macintyre's retirement conference at ICMS in Edinburgh.
- With Lovkush Agarwal and Ricardo Bello Aguirre: Lecture notes of a graduate course given by Anand Pillay on stable groups, 2013.
In order to get credits for the course, Lovkush, Ricardo and I typed up the notes. We did approximately a chapter each. I did the first chapter. The notes are a little rough around the edges.
- My MA dissertation Changing Spaces: Can synthetic differential geometry offer an autonomous foundation for mathematics?, 2010.
I wrote this under the supervision of Richard Pettigrew at the University of Bristol.
- An essay about the effect of Gödel's incompleteness theorems on Hilbert's programme, 2010.
I wrote this for a module about the philosophy of mathematics taught by Øystein Linnebo as part of my MA at the University of Bristol.
Erratum: The description of Robinson arithmetic (Q) given on page 9 is incorrect: The axioms of Q are characterised as being much stronger than they actually are.
- My MMath final-year project Finite set theory, arithmetic, and interpretations between them, 2009.
I wrote this under the supervision of Adam Epstein at the University of Warwick.
General warning: I wrote this a little hurriedly and consequently there are some typos and unfortunately even some mathematical mistakes. The statements of the theorems are (I think!) all correct, but some of the "proofs", especially towards the end, should be read with caution.
- A tongue-in-cheek parody of the famous "To be, or not to be..." soliloquy from Hamlet on the topic of the axiom of choice, 2008/2015.
- An essay about relational quantum mechanics, 2010.
I wrote this for a module taught by James Ladyman about the philosophy of physics as part of my MA at the University of Bristol.
Erratum: On pages 6 and 7 superpositions of classical states are incorrectly characterised as mixed states.
- An essay about Darwinian natural selection and the historical lack of knowledge of the mechanism of inheritance, 2010.
I wrote this for a module taught by Andrew Pyle about the history of science as part of my MA at the University of Bristol. It was the bicentenary of Darwin's birth, which is why we chose to study his work in particular.