Tristan Hodgson

Education

Mmath in Mathematics, University of Oxford

(2024-2028, Expected)

Current third-year research project in numerical linear algebra, supervised by Prof. Yuji Nakatsukasa, focusing on model-order reduction and randomised linear algebra for repeated least-squares problems, with applications to Kalman filtering
Modules Taken
- MT Year 3 (Current)
  - Functional Analysis 1
  - Probability, Measure and Martingales
  - Numerical Solutions of PDEs
  - Thesis (see above)
- HT Year 3
- TT Year 3
- MT Year 2
  - Linear Algebra
  - Complex Analysis
  - Probability
  - Metric Spaces
  - Differential Equations 1
- HT Year 2
  - Numerical Analysis
  - Statistics
  - Integration
  - Topology
  - Integral Transforms
- TT Year 2
  - Graph Theory
  - Number Theory
  - Calculus of Variation
- MT Year 1
  - Analysis I
  - Linear Algebra I
  - Geometry
  - Introductory Calculus
  - Probability
  - Computational Mathematics (continued in HT1)
- HT Year 1
  - Analysis II
  - Linear Algebra II
  - Groups and Group Actions (continued in TT1)
  - Multivariable Calculus
  - Dynamics
  - Computational Mathematics (continued from MT1)
- TT Year 1
  - Analysis III
  - Groups and Group Actions (continued from HT1)
  - Statistics and Data Analysis

High School

(2018-2024)

Research intern, Lancaster University STOR-i, supervised by Dr. Luke Fairley

(Github | Jul-Aug 2026)

Formulated research questions and proved results characterising optimal repair strategies in a Markov Decision Process model, including guarantees on system uptime and the structure of long-run behaviour
Reduced policy representation from O(N²) to O(N) for an extended model by proving structural results
Proposed further conjectures on optimal policy structure, proved special cases, and built computational experiments to systematically test them across the model's parameter space

Machine Learning Intern, Harper AI

(One Week, Summer 2026)

Developed a model to predict refinancing likelihood, leading to an estimated > 100% improvement in conversion rates through a new lead-prioritisation feature
Achieved 88% precision across 80,000 UK property developers with XGBoost, using SQL to reconstruct historical data without contaminating the training data through temporal leakage
Added interpretable outputs using SHAP after identifying demand in customer interviews

IT Officer, Trinity College JCR

(Oct 2025-)

Reduced annual IT spend by 94% by leading the JCR website migration from a legacy Wix setup to the University-wide Fresco platform
Restructured the website as a clearer resource for prospective and current students, coordinating requirements and approvals across College, University, and JCR stakeholders

Process & Data Systems Intern, It's Our Planet Too

(One Week, Summer 2025)

Replaced legacy spreadsheet workflows with a more maintainable and powerful operational system using Power Query, UserForms, and Pivot Tables
Simplified management of operational data through task-specific dashboards and documentation that enabled users to use and maintain the new system

Low Rank Approximation of Transformer Matrices for Decryption

GitHub

Increased inference throughput by 85% while retaining 98.5% of the original accuracy by applying SVD low-rank approximation to transformer weight matrices
Developed a greedy compression method that allocates rank by each matrix's sensitivity to truncation, achieving a 49.7% reduction in error rate compared to singular-value-based allocation
Deployed models using Docker and FastAPI on AWS EC2 and benchmarked inference throughput for compressed and uncompressed models

Performance Modelling of In-Database Sparse Matrix Multiplication

Write-up | GitHub

Derived and empirically validated a sparsity threshold predicting when in-database matrix multiplication outperforms client-side computation
Benchmarked performance across compute, bandwidth, matrix size, and sparsity, validating asymptotic runtime predictions

Real Estate Market Dashboard

GitHub

Identified regional and socio-economic housing-market divisions without using location features by segmenting government data with PCA and K-Means
Built a data pipeline and interactive dashboard for exploratory analysis of housing prices and returns across time and geography

Presentation on Algorithmic Information Theory, Kolmogorov Complexity

Slides

Independently studied literature on Kolmogorov complexity and compression-based similarity measures
Implemented a simple illustrative example (Normalized Compression Distance) to support explanation
Presented core theory, motivation, and limitations to a mixed undergraduate-faculty audience

London Stock Exchange Group, Financial Essentials

(Aug 2025)

Completed a certification program covering the foundational principles of financial markets, investment, and their economic and regulatory drivers

Duke of Edinburgh Gold Award

(Oct 2022-Jul 2024)

Adapted quickly to new challenges, learning navigation, and teamwork in unfamiliar environments
Independently planned and completed an expedition, demonstrating resilience, and self-sufficiency