Department of Mathematics

Research

The research interests of the Department cut a broad swathe through both pure and applied areas of mathematics

Research covers analysis, nonlinear partial differential equations, ergodic theory, and geometry to quantum field theory, general relativity, string theory, fluid dynamics, complex systems, mathematical biology, statistics, and modelling in the life sciences. A particular emphasis is placed on research at the interface between pure and applied mathematics.

Research groups

Research in the Department is organised into a number of research groups, but there are many overlaps and links between these.

Research blog

  • diamond4dCongratulations to Timothy Burchell who passed his PhD confirmation examination today (Friday 17th February).  His confirmation report is titled “Clifford analysis and nonlinear wave equations“.  The examiners were Bin Cheng and Jan Gutowski.   His principal supervisor is Tom Bridges and his second supervisor is Claudia Wulff.

  • workshop-1Gianne Derks was an invited speaker at the Workshop on Mathematical Medicine and Mathematical Pharmacology held in the BioMaths group in the Department of Mathematics at the University of Swansea.  It was held on Thursday-Friday 2-3 February.  Her talk was on “Dimer dynamics and degenerate transversally intersecting manifolds“.  An abstract can be found here.  Click on the workshop photo to the left to see a larger version.

  • innerorbits1The paper “Fast numerics for the spin orbit equation with realistic tidal dissipation and constant eccentricity” co-authored by Michele Bartuccelli, Jonathan Deane, and Guido Gentile (Roma III and Visiting Professor at Surrey), has been accepted for publication in the journal Celestial Mechanics and Dynamical Astronomy. A link to the arXiv version is here. The paper presents an algorithm for the rapid numerical integration of a time-periodic ODE with a small dissipation term that is continuously differentiable in the velocity. Such an ODE arises as a model of spin-orbit coupling in a star/planet system, and the motivation for devising a fast algorithm for its solution comes from the desire to estimate probability of capture in various solutions, via Monte Carlo simulation: the integration times are very long, since they are interested in phenomena occurring on timescales of the order of 10 million years. The pay-off is an overall increase in speed by a factor of about 7.5 compared to standard numerical methods.