PhD Mathematics - Probability and Statistics

University of Hull

Choose to study for an MSc by Thesis or PhD degree in Mathematics at Hull. Themes include pure and applied maths, probability and statistics. Join a close-knit department and be supported by renowned academics working at the forefront of mathematical research with a PhD or Masters by Research at the University of Hull. Our staff have a wide range of expertise in many different areas, from pure maths theories around low-dimensional topology and asymptotic geometric analysis, to fluid dynamics, superstring theory and astrophysics across other disciplines. We welcome research proposals in any of our specialisms and while studying towards a PhD at Hull, you’ll be fully supported by two supervisors who are able to offer expert supervision in your area. Probability and Statistics Processes on complex networks Large complex networks can be found everywhere, for example as social, information, technological and biological networks. Many of these networks share the property that they are scale free, i.e., the number of links of nodes have a power law distribution. Hubs with a very high number of links play an important role in the behaviour of the network. Processes on these networks one can think of are opinion formation in social networks, the spread of information via telecommunication and computer networks, and epidemics in society. In Hull, we use probability theory to investigate what the effect is of the scale-free nature of complex networks on processes on these networks, both in and out of equilibrium. Potential projects include investigating: Properties of complex networks and random graphs Interacting particle systems on random graphs Metastability in interacting particle systems Foundations of statistics We study the mathematical modelling and management of uncertainty, in which a central role is played by probability distributions. Questions of interest include: what and how can we learn from statistical data? How can we combine different sources of uncertain information? And how can we use such information in order to make optimal decisions in situations involving uncertainty? Potential projects include: Regression with interval data Learning from data with graphical models An axiomatic approach to likelihood decision making Statistics in Astrophysics What is the mass of the most massive object in the Universe? What is the size of the biggest cosmic void we are most likely to observe? What is the magnitude of the most energetic solar flare that could occur? We address these questions by studying the likelihood of rare, extreme events with extreme-value statistics, which has long been used in meteorology and engineering, and has recently found many applications in astrophysics. Potential projects include: Superclusters and supervoids Extreme-value in the inflationary landscape Understanding extreme solar flares.

Faculty of Science and Engineering