Articles
A list of articles I've authored or co-authored. Where possible, I'll provide arXiv links and a pdf.
This paper is about the (un)decidability of a class of extensions of Presburger arithmetic by Hardy field functions that grow more slowly than a polynomial. The definition of a Hardy field function is technical, but they can be thought of as well-behaved functions that look like polynomials.
One nice result of this paper is that it shows the extension of Presburger arithmetic by a very general class of polynomials—namely those with non-integer coefficients or exponents—when taken to the nearest integer is, in general, undecidable.
Talks
Talks I've given with an academic flavour. This includes everything from 5-minute lightning talks to whole 60-minute sessions. Again, where possible I'll provide slides for each of these. If I mention the Compsoc
below, I'm talking about the Oxford University Computer Science and Technology Society!
Decidability of Extensions of Presburger Arithmetic by Hardy Field Functions
If it looks like a polynomial, it's problematic
The 20-minute presentation that went along with our paper of the same name. I had a lot of fun with the diagrams in this one, and trying to work the technical detail into being explainable was enlightening.
An expository talk on the Knuth-Yao algorithm (that is, how to roll a dice using only coin flips), and how it generalises to higher dimensions. Typesetting the die-agrams was particularly fun.
A talk on the Hydra game, and an excuse to talk about both well-quasi orders and ordinals. People seemed to like this one; there was a little hydra living on the common room whiteboard for a few weeks afterwards.
I've got the (set of) power(s of two definable in Semënov arithmetic)!
Results from the master's project
This was a five-minute talk for a presentation night, where I explained a neat result from my master's project: using just Presburger arithmetic and a predicate for the powers of two, you can define the powers of four, the powers of eight, and so on. I think it's a neat number-theoretic trick.
The Philosophy of Computer Science
What did computer science and philosophy students do before AI?
This was a more light-hearted talk, meant for a five-minute lightning talk session at the Compsoc. It's not rigorously academic, but the ideas in it are still interesting, and do raise actual philosophical questions.
This talk was an hour long, given as part of the Compsoc's termly talk series. The talk covers Presburger's proof of the decidability of Presburger arithmetic, as well as some of the work Jakub Konieczny and I had been doing on the subject. The talk was aimed at non-specialist CS undergraduates.
This talk was about decidability at a high level, and aimed at a general student audience. It was given at the CatzXCon (Catz eXchange Conference), which was for the St. Catherine's college (i.e. the Oxford college) community to share any research that we'd been doing. It was preceded by a talk about early twentieth century government conspiracy theories, and followed by a talk about language preservation in Inner Mongolia, so that gives you an idea of how general the talk had to be!
Given as an hour-long talk for the Compsoc's Learn to Code talk series. It's aimed mostly at getting CS undergraduates to actually typeset their problem sheets rather than handwriting everything, and so the talk walks through an example of that. I hope the talk worked.