\( i\hbar\,\partial_t \Psi = \hat{H}\Psi \) \( \sigma_{xy} = \nu\,\tfrac{e^2}{h} \) \( F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \) \( Q = p_z + k J_z \) \( Z = \int \mathcal{D}\phi\; e^{iS[\phi]/\hbar} \)
state = rk4_step(state, dt) ψ[m] = z**m * exp(-abs(z)**2 / 4) while universe.expands(): git commit -m "renormalons, finally" ωc = e * B / m
Casey Farren-Colloty ⟨C⟩ monogram
$ whoami

Casey Farren-Colloty

cas@web - try `help`
cas@web:~$
t = 0.0 s
pointer = (-, -)
charges = 0
B ⊙ ẑ  ·  uniform
cursor ⇒ point charge  ·  click ⇒ inject e⁻
boundary: periodic (torus)
integrator: exact gyration + kicks
▼ scroll
\( \nabla \times \vec{B} = \mu_0 \vec{J} \)
$ cat about.md

About Me

research projects
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arXiv preprint
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live experiments
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Courses taught
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I'm an incoming MSc in Mathematical and Theoretical Physics student at Balliol College Oxford. I am fortunate to be supported in this endeavour as a Martingale Scholar as well as a George Moore Scholar. I was previously a theoretical physics student at Trinity College Dublin. I am driven by a deep curiosity to understand both the fundamental principles that govern our universe and the - in my opinion more interesting - collective phenomena that follow. Coupled to this, I am also interested in the application of those principles and techniques to the broader human society. I find areas that offer both profound insights into nature's workings and practical applications for a sustainable future particularly engaging. Beyond research, I'm passionate about making science accessible to everyone. As Co-founder and Director of The Problem Solving Association CLG and a former Auditor of the Theoretical Physics Student Association of Ireland, I'm involved in initiatives in science communication and education. From creating physics lecture series and teaching at the Centre for Talented Youth (CTYI) to working on projects furthering democratic society through utilising physics-based techniques, I believe in sharing the problem-solving mindset of theoretical physics to address challenges across disciplines.

\( e^{i\pi} + 1 = 0 \)
$ git log --oneline research/

Research

3d9f0ac2026 - Capstone Thesis

My capstone thesis for the B.A. (Mod) in Theoretical Physics at Trinity College's School of Mathematics, supervised by Prof. Sergey Frolov: "Quantum Integrability: An Investigation of the Bethe Ansatz and its Application to the Hubbard Model". Starting from the classical foundations - Lax pairs, the classical \( r \)-matrix, and Hamiltonian reduction on coadjoint orbits - I built up to the quantum Yang-Baxter equation as the organising principle of quantum integrability, motivated through the Heisenberg spin chain and factorised scattering. The work culminates in solving the one-dimensional Hubbard model via both the coordinate and algebraic Bethe Ansatz, uncovering its hidden SO(4) symmetry and recovering the Lieb-Wu equations using graded vector spaces and Shastry's R-matrix. Along the way I studied the Calogero-Moser-Sutherland family and its duality with the quantum Hall effect, proposing a conjecture that placing the quantum Hall effect on a torus yields the elliptic Calogero-Sutherland model upon projection to the Lowest Landau Level. This is ongoing work.

📄 Find my thesis here 🗣️ Find my presentation here 🪧 Find my poster here
Quantum Integrability Bethe Ansatz Hubbard Model Mathematical Physics

b7e1c052025 - CERN Summer Student Programme

As a CERN Summer Student, I developed Malta2FastSim, a fast Monte Carlo simulation module for the MALTA monolithic active pixel sensor (DMAPS), built for the Allpix² detector simulation framework. MALTA sensors - designed for the harsh radiation environment of the HL-LHC - use small 3 µm collection electrodes and asynchronous readout. My module ported the validated physics of the standalone PyMaltaSim into native C++, preserving charge-dependent timing delays, position-dependent charge collection and DAC-based threshold modelling. Two algorithmic contributions stand out: a pixel-grouped accumulation scheme that keeps detection efficiency intact under arbitrary trajectory resolution, and a selective Highland multiple-scattering treatment that recovers realistic cluster sizes for perpendicular test-beam tracks. The MALTA work was validated against test-beam data from the MALTA telescope at the CERN SPS. Please find my report here for more info.

Silicon Detectors Monte Carlo Simulation DMAPS / CMOS Sensors C++

a1f9e072025 - Hamilton Trust Internship

A comprehensive exploration into quantum many-body physics through the Hamilton Trust Internship, focusing on the fascinating phenomena of the Quantum Hall Effect. Working alongside Daniel Barron and Matthew Blakeney, we present "An Investigation into Topology in the Quantum Hall Effect and Non-Abelian Anyons". Our collaborative research examines this remarkable manifestation of quantum mechanics in condensed matter systems, developing comprehensive understanding of topological phases and quantum many-body phenomena.

→ Explore the interactive simulations

Quantum Hall Condensed Matter Topology Anyons

7c3b2d42024 - Oxford University Internship

Selected for the prestigious Rudolf Peierls Centre for Theoretical Physics UROP, I investigated Renormalon effects in particle physics. Working under Prof. Gavin P. Salam FRS, Prof. Fabrizio Caola, Jack Oliver Helliwell, and Silvia Zanoli, I studied \( e^- e^+ \) annihilation events. My research focused on event shape observables, using the PanScales software to simulate electron positron annihilation to quark anti-quark pair events as well as corrections involving soft gluons and gluers to analyze the change in those event shapes.

📄 arXiv:2507.18696 - Anomalous scaling of linear power corrections
Particle Physics Quantum Chromodynamics Numerical Methods

f04d6a22023 - Electoral Redistricting Project

Democratic systems face a growing crisis of trust. This project tackles the challenge of fair electoral redistricting using computational methods from physics. Following a successful hackathon organized by TPSA and TCD's School of Mathematics, I developed a genetic algorithm approach to redistrict Irish electoral constituencies. This worked alongside a physics-based algorithm developed by Ruaidhrí Campion, forming a comprehensive dual approach to electoral fairness. The work continues through The Problem Solving Association CLG, aiming to restore institutional trust through transparent, algorithmic solutions. Since then a considerable amount of work has been done to refine the approach and to supplement our algorithm. You can read more about how our work is relevant to the current electoral discourse here. At present, we have released a preprint on Arixv and are finalising a submission to a journal.

📄 arXiv:2606.20637 - Constituency Optimisation Through Hamiltonian Representation Of Mandates (COTHROM): Algorithmic Redistricting of Irish Election Boundaries
Computational Physics Social Systems Algorithmic Design
$ ls ~/lab/  # exposed mechanism

Simulations & Games

Theory you can poke. Everything below runs live in the browser - real integrators, real symmetries, periodic boundary conditions. The previews are simulating right now.

\( \vec{F} = m\vec{a} \)
$ cat teaching.md

Teaching

I'm a firm believer of the importance of putting effort in to show the younger generation how interesting the world of science can be. As well as to show them that participating in this world is an achievable goal. The opportunity arose in the academic year 2023/24 to do just that and teach at the Centre for Talented Youth Ireland. Specifically, the 8-12 year old course. Here are some of the materials for these courses:

~/teaching/superhero-science

Superhero Science

Introduction to a variety of topics in science and engineering such as magnetism, genetics, and material science.

View Course Materials →
~/teaching/astronomy

Astronomy

Fundamentals of astronomy and related areas of physics. Topics included: Special / General Relativity, Stars, Galaxies, Stellar Evolution, and Rockets.

View Course Materials →