A list of courses which I have taken, or are currently taking. A * denotes a course which I did not take to exams.
University of Cambridge
First year (Part IA)
- Numbers and Sets
- Groups
- Vectors and Matrices
- Differential Equations
- Analysis I
- Probability
- Vector Calculus
- Dynamics and Relativity
Second year (Part IB)
- Analysis and Topology
- Linear Algebra
- Markov Chains
- Methods*
- Quantum Mechanics*
- Geometry
- Groups, Rings and Modules
- Complex Analysis
- Numerical Analysis
- Statistics
- Optimisation*
- Variational Principles
In the summer after second year, I did a summer project with Anders Hansen, studying the Solvability Complexity Index, and looking at the potential (non-)computability of optimisation algorithms, such as kernel machines.
Third year (Part II)
- Algebraic Topology
- Galois Theory
- Linear Analysis
- Number Theory*
- Probability and Measure
- Representation Theory*
- Algebraic Geometry
- Analysis of Functions
- Differential Geometry
- Number Fields
- Riemann Surfaces
In the summer after third year, I did a summer project with Alexei Kovalev, studying the hyperkähler structures on nilpotent orbits of $\mathrm{SL}(n, \mathbb C)$. In particular, I looked at a paper by Kobak–Swann, constructing them as hyperkähler quotients of a flat hyperkähler space1. The other method which I looked at was on papers by Kronheimer, which constructed the hyperkähler structure by considering spaces of solutions to Nahm’s equations.
Fourth year (Part III)
- Algebraic Geometry*
- Algebraic Topology
- Analysis of PDEs*
- Commutative Algebra
- Differential Geometry
- Lie Algebras and their Representations
- Abelian Varieties*
- Elliptic PDEs*
- Geometric Group Theory*
- Group Cohomology*
- Symplectic Topology
- Toric Varieties
My Part III Essay was titled Quantum Cohomology and the Seidel Representation. See more here
University of Glasgow/AGQ CDT/SMSTC
- Algebraic Geometry
- Geometric Invariant Theory (reading group, organiser)
- Gradient Flows
- Riemann Surfaces and their Associated Moduli Spaces
- Topological Quantum Field Theory
Which with more knowledge now, this is a quiver variety, and the methods which were used in this paper are used when studying quiver representations. ↩︎