**Student projects**

### Student projects

I am available to supervise undergraduate and MSc projects in theoretical physics. Information on the corresponding project modules is available through the maths intranet (login required). The possible topics below are not necessarily an exhaustive list. Interested students are welcome to chat with me about these or other possibilities.

**Lattice Monte Carlo**

Replacing continuous space and time by a finite lattice of discrete points enables numerical predictions of the properties of statistical systems (and related quantum field theories, without requiring prior knowledge of quantum field theory). This project will use this approach to investigate a simple lattice field theory, numerically analyzing phase transitions, non-trivial soliton solutions, or other phenomena. Computer programming is likely to be a significant component of this work, and can be learned in the course of the project.

**Quantum simulation**

An important application of quantum computing is to simulate quantum systems that are not amenable to classical lattice Monte Carlo analyses. After learning the basics of qubits and quantum gate operations, this project will explore recent proposals for quantum simulation using existing or near-future quantum devices.

**Dark matter**

The first stage of this project will be a survey of the evidence for dark matter and the experiments underway to constrain or reveal its fundamental nature. With this background, the second stage will choose a particular dark matter proposal and delve more deeply into its features and ways it has been or may be tested.

**Analysis techniques for time-series data**

Time-series data are important in many different areas of mathematical sciences, from gene expression to finance to Monte Carlo calculations. This project will involve becoming conversant with numerical techniques to analyze time series, and applying those techniques to real or synthetic data of interest.

**Non-linear dynamics and chaos**

This project will survey tools and techniques used to analyze chaotic dynamics in non-linear systems, most likely focusing on numerical methods. These techniques will then be applied to analyze some simple problems in any of the many areas of science where chaotic dynamics are important.

**CPT and Lorentz invariance**

The related symmetries of Lorentz invariance and CPT (charge--parity--time) invariance are among the cornerstones of modern physics. This project will focus on learning about the observations and experiments that provide the most stringent tests of these important fundamental symmetries of nature.

**Fitting noisy and correlated data** (This is designed as a six-week project for MSc students taking MATH549, which could lead in to an MSc dissertation conducted over the second semester and following summer.)

It is a common task in many mathematical sciences to fit noisy and correlated data to simple mathematical models. For this project you will write programs to carry out such fitting, and apply them to analyze existing data from lattice field theory computations. You will begin with over-simplified approaches, and observe how the results change for more sophisticated analyses, with the final degree of sophistication determined by the time available.

Last modified 11 May 2021