PhD Course
This is normally a three year course. The majority of the first year is taken up with a small research project and dissertation together with lecture courses. The latter can range from the full set of lecture courses taken by M.Sc. students to none at all, depending on experience and background. The rest of the course is taken up with research for the main thesis project.
Candidates are required to hold a first or upper second class Honours degree from a British University, or equivalent. However, if you already hold an M.Sc. degree with substantial research content you may be able to bypass the first year of the course and take the degree in two years. The course can start in September, January, April or July, but September is strongly recommended for the 3 year PhD course.
Opportunities exist for research in a range of different topics. Potential thesis topics might include:
Evolutionary game theory (supervisors: Galla and/or McKane)
Evolutionary game theory models the dynamics of populations of players who are subject to competitive interaction and selection pressure. Models of such processes can be studied with tools from nonlinear physics and from statistical mechanics. The proposed PhD project would focus on the analysis of stochastic effects in finite populations of agents. The methods to be used will include analytical techniques (nonlinear dynamics, stochastic processes) as well as numerical simulations.
Chaos and noise in game dynamical learning (supervisor: Galla)
In this project you will study learning algorithms in the context of game theoretic interaction. Such processes are of interest in behavioural economics, where laboratory experiments of repeated interaction between human players are carried out. Modelling these experiments mathematically is a significant challenge, in the proposed project you would be looking at the convergence of learning of games with a large number of strategies, and at potentially chaotic behaviour, which prevents players from learning Nash equilibria. Learning algorithms are also of relevance in computer science and contacts with the machine learning group exist. Techniques to be used include the path-integral analysis of high-dimensional disordered systems, methods from nonlinear physics (chaotic attractors), and extensive computer simulations.Microstructure of financial markets (supervisor: Galla)
Understanding structure of financial markets and the `ecology' of different types of traders is a key challenge in modern finance, and at the heart of constructing resilient markets. Ongoing work in the group is concerned with the analysis of high-frequency trading data, with a focus in particular on market impact. In parallel we are interested in modelling financial markets by simple agent-based systems, and to simulate (and where possible to characterize analytically) the outcome of the interplay of heterogeneous agents. Projects in this general area of `econophysics' are available.Statistical mechanics and pattern formation in models of social dynamics (supervisor: McKane)
In the group there is currently a lot of interest in modelling social processes, for example opinion dynamics, segregation and migration. We approach these questions with stylized mathematical models of interacting individuals, and study the statistical physics of these models. For example we are interested in pattern formation and coarsening, jamming transitions, non-equilibrium transport and the effects of noise. Projects in this area typically have analytical components, based on the theory of stochastic processes, and they will require extensive computer simulations as well.Individual-based models of ecological systems (supervisor: McKane)
There are two main ways in which biologists formulate models in ecology: as differential equations or as computer simulations of the dynamics of individuals. Very rarely are the dynamics of individuals studied mathematically, probably because the dynamics is stochastic (random) and the techniques required for their study are not so familiar to theoretical biologists. They are, however, extensively used by theoretical physicists. Over the last few years members of the group have analysed individual-based models using these techniques, principally in models of epidemics, but also in other systems. This project would extend this work and apply it to other areas, including multilevel systems and cellular processes.
More detailed information about our research interests can be found on the home pages of the appropriate Ph.D. supervisors, see people
MSc Courses
This is a postgraduate course in theoretical physics consisting of both lecture courses and a research project. The level is suitable for British students who have completed their first degree. It will also be attractive to students at a similar level from European Countries, who wish to visit this country for a year as part of their programme of study. For non-European students the course provides an opportunity to study theoretical physics at an advanced level in a European environment.
Opportunities exist for research in all the areas mentioned above.
How to Apply
For further information, application forms for admission and copies of our postgraduate prospectus, please look at the school's web pages, or the University's postgraduate `How to apply' pages. You can also contact the Postgraduate Admissions Officer in Physics and Astronomy.
For further information about possibilities in the group, please contact Dr Tobias Galla.