Projects & Papers
Projects & Papers
Embedded Files
Papers
Papers
Mathematics Education
Mathematics Education
Gesture in the University Mathematics Classroom (2025). Submitted for publication.
[Masked Paper Title] (2025). Submitted to the 28th Conference on Research in Undergraduate Mathematics Education. Joint work with Professor Vladislav Kokushkin.
Finite Undecidability
Finite Undecidability
Finite Undecidability in NIP Fields, The Journal of Symbolic Logic, 90(2), 509-532 (2025). First published online in 2023.
Finite Undecidability in PAC and PRC Fields, Annals of Pure and Applied Logic, 175(10) 103465 (2024).
Finite Undecidability in Fields: Why, Where, and How? Conference poster (Model Theory and related topics, University of Manchester 2023).
Definability & H10
Definability & H10
On Hilbert's "Geometric'" Tenth Problem for Odd Characteristic Function Fields, Archive for Mathematical Logic, (2025).
A New Universal Definition of F_q [t] in F_q (t), arXiv1905:05745 (2019).
NLP/Category Theory
NLP/Category Theory
Applying Distributional Compositional Categorical Models of Meaning to Language Translation, EPTCS 283, pp. 28-49 (2018).
Tools for research in progress
Tools for research in progress
Model Theory & Mathematical Logic
Model Theory & Mathematical Logic
Undergraduate Mathematics Education
Undergraduate Mathematics Education
A self-curated list of favourite "big papers". Pre-2000:
Errors and misconceptions in college level theorem proving. (Selden & Selden, 1987).
The Role and Function of Proof in Mathematics. (de Villiers, 1990).
Making the transition to formal proof. (Moore, 1994).
Students' Proof Schemes: Results from Exploratory Studies. (Harel & Sowder, 1998).
Post-2000:
Doctoral students' use of examples in evaluating and proving conjectures. (Alcock & Inglis, 2008)
On Mathematicians' Different Standards When Evaluating Elementary Proofs. (Inglis et al., 2014).
Self-Explanation Training Improves Proof Comprehension. (Hodds, Alcock, & Inglis, 2014).
Mathematics Professors’ Evaluation of Students' Proofs: A Complex Teaching Practice. (Moore, 2016).
Theses
Theses
Undecidability in Some Field Theories, 2023.
This was my PhD thesis, completed at Oxford under the supervision of Professor Jochen Koenigsmann. Its main focus was to explore the concept of "finite undecidability", where a theory T is finitely undecidable if every (nonempty) finitely axiomatised subtheory of T is undecidable. (That is, given a first-order sentence A of T, no algorithm exists which correctly identifies logical consequences of A.) This property is surprisingly common in field theories!
Efforts in the Direction of Hilbert's Tenth Problem, 2018.
This was my master's thesis, completed under the supervision of Professor Damian Rössler. The thesis had three objectives: motivate the connection between the integers Z and F_q[t] from a decidability and definability standpoint, excurse through the definability results of Koenigsmann and subsequent authors in global fields, and provide a shorter and simpler universal definition of F_q[t] in F_q(t) than existed at the time.
An Analysis of Tame Topology using O-Minimality, 2017,
with accompanying poster.
This was my bachelor's thesis, completed under the supervision of Professor Andreea Nicoara. Here I explored some 'tame' properties of o-minimal structures, in comparison to the corresponding properties for semialgebraic, semianalytic, and subanalytic sets, and also proved some algebraic results using quantifier elimination in ACF and RCF.
Undergraduate Projects
Undergraduate Projects
Computer Science
Computer Science
Getting strung up & Dithering around (project upon request).
This is a report I wrote a previous summer while exploring some ideas in the intersection of Computer Science and Art. I was initially inspired by the work of Petros Vrellis, an artist who creates artwork using computer programming and algorithms. I ended up tackling three problems; recreating Vrellis' work, recreating the work of Yumi Yamashita, another artist who also designs continuous line illustrations, and Kel Cruz, an artist who makes art from squares of coloured tape. (Right; successfully generating the Mona Lisa.)
The Moving Sofa Problem is to determine the area of the largest rigid two-dimensional shape that can be manoeuvred through an L-shaped hallway of constant unit width. I completed this project during the summer of 2015 at Trinity under Prof. Mike Peardon. (Left; an example of a sofa.)
Using numerical methods to solve the gravitational n-body problem.
This was my first internship, completed at the end of my first year in 2014 at Trinity, under Prof. Mike Peardon. Here to demonstrate the leapfrog algorithm I simulated the 10-body solar system, and constructed a Barnes-Hut algorithm to deal with larger numbers of bodies. At the end, I tried my hand at animating the results in OpenGL.
Mathematics
Mathematics
Scott Sentences in Uncountable Structures.
I completed this work during the summer of 2016 at the University of Notre Dame under Prof. Julia Knight. This paper was published by the RHIT Undergraduate Math Journal.
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