Mathematical Physics

Fractal patterns

About us

When investigating physical phenomena, considerable insight can often be gained using modern mathematical techniques commonly associated with general relativity and string theory.

We make extensive use of analytical techniques and practical theories, rather than large-scale computation, to explore the world around us and interdisciplinarity permeates our work. Our broad research programme reflects our extensive range of interests. It connects the theoretical investigation of matter in extreme conditions (such as the ultra-powerful laser fields of the Extreme Light Infrastructure (ELI), or the strong-field environment of a magnetar) with ubiquitous fluid-structure interactions of utmost importance to the oil industry (such as the vortex-induced vibration of marine risers). Some of the most mathematical aspects of our work include novel regularisation-free techniques for analysing quantum (Casimir) stresses and the development of new methods for investigating electromagnetic transport in spatially dispersive media such as metamaterials.

We maintain close connections with several external institutions through our membership of ALPHA-X consortium and our association of the Cockcroft Institute of Accelerator Science and Technology at Daresbury, UK.

Key Research

  • Radiation reaction, high-field electrodynamics and wave-particle interaction in ultra-intense plasmas and beams
  • Casimir forces in media and spatial dispersion in photonic structures
  • Continuum mechanics of Cosserat media and vortex-induced motion

Postgraduate Training

The Mathematical Physics Group offers informal lectures dedicated to postgraduate students. Examples of topics covered in recent years include coordinate-free approaches to non-linear field theory and advanced techniques in quantum theory. The questions are chosen based on the needs of the postgraduate students in the Mathematical Physics Group, and they are also encouraged to consider the opportunities provided by the other research groups. For example, in recent years, mathematical physics students have also attended lectures delivered by the Experimental Particle Physics group and lectures at the Cockcroft Institute (see the Accelerator Physics group for more details).

Furthermore, mathematical physics students are encouraged to participate in international summer schools and student conferences aligned with their broader interests, as well as the particular area of their PhD research.

In common with all Lancaster postgraduate students, mathematical physics students have access to a wide range of other general and transferable-skills training courses through the university and faculty.