About me

Below are the courses I have taken at the University of Cambridge. I have (abridged) notes for most of these courses, if you are interested in seeing them please let me know. Courses I have taken Part IA (First year) Analysis I Differential Equations Dynamics and Relativity Groups Numbers and Sets Probability Vectors and Matrices Vector Calculus Part IB (Second year) Analysis and Topology Complex Analysis Geometry Groups, Rings and Modules Linear Algebra Markov Chains Methods Numerical Analysis Optimisation Quantum Mechanics Statistics Variational Principles Part II (Third year) Algebraic Geometry Algebraic Topology Analysis of Functions Differential Geometry Galois Theory Linear Analysis Number Fields Probability and Measure Representation Theory Riemann Surfaces Part III (Fourth year, Masters’ level courses) Algebraic Geometry Algebraic Topology Analysis of PDEs Commutative Algebra Differential Geometry Lie Algebras and their Representations Modular Forms

I have some experience with formalising Mathematics in the Lean theorem prover. In particular, I have made pull requests to the mathematics library mathlib. In particular, I wrote a significant proportion of the library about the fundamental groupoid of a topological space.

Summer 2022 In the Summer of 2022, I did a summer research project with Prof. Anders Hansen in the Department of Applied Mathematics and Theoretical Physics about the computational issues in various optimisation problems. In particular, I looked at the hardness of approximation for computing solutions for semidefinite programming problems and for support vector machines. Summer 2023 In the Summer of 2023, I did a summer research project with Dr Alexei Kovalev in the Department of Pure Mathematics and Mathematical Statistics on hyperkahler metrics on coadjoint orbits of complex Lie groups....