Projects

Here are some research projects and articles I have done in physics and mathematics.

Honours Project: Algebraic Curves and their Genera

Supervised by Prof. John Voight

File and summary soon.

Hopf on the Bloch: From Fiber Bundles to Qubits

Talk hosted by Sydney University Mathematics Society.
The Bloch sphere is the standard picture for representing qubits, but hidden behind it is a richer geometric story: the Hopf fibration, a beautiful map from the 3-sphere to the 2-sphere with circles as fibers. In this talk, we’ll explore how the Hopf fibration provides the natural framework for understanding the Bloch sphere, and how ideas from fiber bundles clarify the geometry of quantum states. Along the way, we’ll look at some nice visualizations that make these abstract constructions tangible.

Slides | Video

Spinors Part 1 and 2

Published by The University of Sydney’s Physics Society Journal (Jeremy Issue 3 and 4 of 2025)
In a two-part article over two issues, Richard Nicotra and I set out to explain the mathematical underpinnings of the Bloch Sphere and the Hopf Fibration. In Spinors Part 1: Bloch Sphere and the Hopf Fibration, we explain the origin and formalism of the Bloch sphere using group theory, Mobius transformations, and fiber bundles. In Spinors Part 2: Rotations, Mobius Transformations, and SU(2), we go into more depth with some of the Mobius transformations that deal with rotations and how they relate to some of the group actions on spinors.

Article 1 | Article 2

Quantum Probability Measured

Published by The University of Sydney’s Physics Society Journal (Jeremy Issue 2 of 2025)
We explore how measure theory informs quantum mechanics’ fundamental formalisms. We look at how notions of probability and expectated value in quantum systems originate with functional analysis, measure and probability theory via the ‘Projection-Valued Measure’. Article

Simulating Anyons in a Lattice via Wannier Functions (2025)

Supervised by Dr Abhijeet Laxman Alase.
We model anyons in a bravais lattice using a Hamiltonian described by Kitaev. We use a mapping that allows us to express that Hamiltonian using Wannier functions.

Simulating Dark Matter in the Galactic Halo (2024)

Supervised by Dr Ciaran O’Hare.
We simulate the galactic halo and an idealized dark matter distribution to compare to real detector data.