Projects

A Visual Studio Code extension that shows a live MathJax overlay as soon as the caret enters a LaTeX equation in .tex, Markdown, MDX, or Jupyter notebooks. There is no compile step: macros from .sty/.cls, align/tabular, and screenshot OCR all stay on the local machine. Published on the Visual Studio Marketplace as silkmath.silk-math-preview.

This is my final-year pure mathematics project on Diophantine approximation. The project is centred on the question of how well real numbers can be approximated by rationals, and develops a structured account of continued fractions, Liouville's theorem, Thue's theorem, and their connections with Pell equations, binary homogeneous polynomials, and Dirichlet's Unit Theorem. The project strengthened my ability to organise mathematical literature, write rigorous proofs, and build a coherent logical narrative across number theory and algebra. It also motivates my current interest in transferring proof-based mathematical training toward formalised mathematics, theorem proving, proof assistants, and mechanised reasoning.

This project investigates the timetable feasibility of a proposed redesign of the honours Mathematics curriculum at the University of Edinburgh. Using Google OR-Tools, I helped develop a large-scale CP-SAT model that captures course scheduling, student choice structures, fixed outside-school timetables for joint-degree students, student-level clash feasibility, and timetable-quality rules. A key modelling idea is student-type aggregation: instead of modelling every student individually, students with the same programme structure and external timetable are grouped together to reduce model size while preserving the essential combinatorial structure of the problem. While the project is applied in setting, it strengthened my interest in formal modelling, computational guarantees, and the gap between practical constraint systems and rigorous correctness or verification questions.

This summer research project focuses on expressivity in graph neural networks. Starting from limitations of standard message-passing GNNs such as oversmoothing and oversquashing, the project explores whether random-walk-based approaches can provide richer representations and more flexible graph modelling. My work included reviewing standard GNN architectures, studying existing random-walk-based methods, and investigating theoretically motivated random-walk schemes, with possible extensions to hypergraphs. Although I am not primarily pursuing applied AI, this project gave me useful exposure to graph theory, representation learning, and the importance of theoretical structure in machine learning models.

In this project, I led a team in building a statistical model for winter peak electricity demand in Great Britain using historical data from 1991 to 2014. The model uses a multi-factor linear regression framework that incorporates renewable generation, seasonal effects, and weekday structure. I also built an automated model-selection workflow based on five-fold cross-validation together with AIC/BIC comparisons. The project demonstrates experience in reproducible modelling, validation, and communicating quantitative results, although my current research interests are more theory- and verification-oriented.

This project studies the operational performance of a ride-sharing system through a data-driven discrete-event simulation. Together with a teammate, I built a model that captures rider arrivals, driver availability, distance-based matching, trip execution, cancellations, revenue, and costs. We examined whether the project parameters were statistically consistent with observed data, re-estimated key parameters using maximum likelihood methods, and analysed trade-offs between service quality, driver earnings, profitability, and system balance.

This project considers a multi-project workforce allocation problem for a consulting firm. I used Xpress to formulate and solve a linear/integer optimisation model across projects, locations, and consultant levels, while respecting role restrictions, travel costs, bench policies, remote-work limits, outsourcing options, and disruption scenarios. The project developed my experience in mathematical programming and structured computational experimentation, but I now mainly present it as evidence of formal modelling ability rather than as my primary research direction.

This project develops a Simul8 discrete-event simulation of a multi-stage laptop manufacturing system. We carried out input analysis on interarrival times and processing-time datasets, using AIC, BIC, KS testing, and maximum likelihood estimation to select probability models. The simulation incorporated blocking, rework, inventory control, component matching, and order-level synchronisation. The project developed my skills in input modelling, system diagnosis, experimental simulation, and operational interpretation.