Research
I am a logician by training. My own work is in computable structure theory and model theory; with student teams I work on how to evaluate machine reasoning, on quantum annealing, and on tools for teaching computation.
Areas
- Computable structure theoryHow much computational power does it take to find an isomorphism between two copies of a countable structure, and how complex must a sentence be to describe the structure completely? My thesis studied degrees of categoricity and the isomorphism problem; current work with M. Mirabi studies the Scott complexity of trees of finite rank.
- Vaught’s conjectureA countable complete theory has either countably many or continuum many countable models, up to isomorphism, or so the conjecture says. I first worked on it in my MSc thesis through cylindric algebra; a 2026 preprint studies the structure of minimal counterexamples. It does not settle the conjecture.
- Evaluating machine reasoningBenchmarks whose answer keys come from running a verified toolchain, not from someone’s judgement: for example, asking language models to act as interpreters for programs in a student-built language, where every correct answer is produced by execution. The pilot is complete; scaling it up is next.
- Quantum annealingFormulations of graph isomorphism as quadratic optimization problems, which I derived and a student team tested on D-Wave’s Advantage2, and an honest look at how much of the work classical pruning does before the annealer starts.
- Computing educationTools for teaching Turing machines, and how students use generative AI in computing courses.
Publications
Peer-reviewed
- How Far Does Classical Pruning Carry Quantum-Annealed Graph Isomorphisms? An Advantage2 Case Study
- Investigating the Impact of Student Usage of Generative AI Tools in Computing Courses
- On Modern Tooling for Teaching Turing Machines
- Varphi: A Description Language for Turing MachinesVarphi documentation
- Degrees of Categoricity of Trees and the Isomorphism Problem
- Degrees of Categoricity Above Limit Ordinals
- On the Multi-modal Logic of Substitutions
Under review and preprints
- Scott Complexity of Trees of Finite Rank via Degrees of CategoricityarXiv:2606.27151
- ω1-Anchored Labels in Minimal Counterexamples to Vaught’s Conjecture: A Per-Witness Trichotomy and an Unconditional Stationary DichotomyarXiv:2608.15044
Background
- PhD, Pure Mathematics, University of Waterloo, 2019
- Postdoctoral Fellow, Toronto Metropolitan University, 2020–2021
- MSc, Mathematical Logic, and BSc (Hons), Mathematics, Cairo University