Here are some of my projects.
Rigid branchwise-real tree orders
My current research looks at the rigidity phenomenon in branchwise-real tree orders (partial order trees in which all branches are isomorphic to a real interval). I have shown that such trees can exists satisfying strong uniformity properties. Trees are grown iteratively in stages, and a key technique is the construction (in ZFC) of a family of colourings of (0,infty) which is 'sufficiently generic', using these colourings to determine how to proceed with the construction. I recently gave a talk on this project at the Leeds Models and Sets seminar. Click here to see the slides for the talk. A paper detailing the results is in preparation.
On the continuous gradability of the cut-point orders of R-trees
As part of my PhD research project, I investigated the classification of the cut-point orders of R-trees (metric space trees in which every point can branch). This research resulted in a paper, published in the journal Topology and its Applications. A preprint is available on the ArXiv.
Polyhedral semantics for intermediate logicsMy thesis for the Master of Logic at the Institute for Logic, Language and Computation (ILLC), University of Amsterdam is titled 'Polyhedral Completeness in Intermediate and Modal Logics'. Based on joint work with Nick Bezhanishvili, David Gabelaia and Vincenzo Marra, in this thesis I investigate a newly defined semantics for logic which uses polyhedra. It involves an interesting interplay between logic, geometry and combinatorics. We are in the process of preparing two papers containing our results. A preprint is available on the ArXiv. A copy of the thesis is available on the ILLC website.
Corruption is an experimental computer game whose universe is the code for the game itself, and which is slowly being corrupted. The player must try to fight the progress of corruption by deleting troublesome pieces of code, while taking care not to destroy their own capacity to exist.
Tunelines is a project by musician Helen Adam to collect toponymic tunes: songs named after places. I built the website tunelines.com using Python and Django, which features a responsive design and a dynamic, searchable database of tunes.
TikZ is a system for drawing graphics in LaTeX. Over the years I have produced many figures using it. Each time I learn a new technique, I add the corresponding code to a large indexed document. Here is a copy of the document. Also, find the code on GitHub.
During my A Levels, I created the website alevelnotes.com, on which I put the notes I made as I was revising for the exams. It has become quite popular, and now recieves millions of visitors per year.
Non-mathematical content by mathematical means
As a research project for the Master of Logic in Amsterdam, I investigated, from a philosophical perspective, the use of mathematical techniques in arguments in the philosophy of mathematics. The project was supervised by Luca Incurvati and Anna Bellomo, and resulted in a paper, which is available on PhilArchive.
Principles of reflection in higher-order logic
In my final year dissertation for my undergraduate degree, I investigated so-called 'reflection principles' in the context of higher-order set theory. The finished work may be found here.