Professor Martin Speight

Professor Martin Speight

Profile

I'm a mathematical physicist specialising in applications of differential geometry to elementary particle physics and condensed matter systems.

Responsibilities

  • Head of Department of Pure Mathematics

Research interests

There are many systems of partial differential equations of interest in theoretical physics which possess soliton solutions. These are smooth, knot-like lumps of energy which are stable against all deformations. Their applications span the length scale, from models of elementary particles, through condensed matter and biophysics to cosmology. Their study is a fascinating challenge involving geometry, topology, analysis and computer simulation.

Often the space of static soliton solutions forms a smooth manifold, called the moduli space, which can be equipped with a natural Riemannian metric. This is true, for example, of the Yang-Mills-Higgs, abelian Higgs and nonlinear sigma models, whose solitons are called respectively monopoles, vortices and lumps. Following a conjecture of N.S. Manton, it is believed that slow soliton dynamics in such systems is well approximated by geodesic motion in the corresponding moduli space. This leads one to study the Riemannian geometry of soliton moduli spaces and exploit this geometry to understand slow soliton dynamics. My own research concentrates on solitons in 2+1 dimensions, in particular, the completeness, volume and curvature properties of moduli spaces of vortices and lumps.

Qualifications

  • B.Sc. Physics, Imperial College, London
  • Ph.D. Mathematics, University of Durham

Professional memberships

  • London Mathematical Society

Student education

I teach mathematics.

Research groups and institutes

  • Pure Mathematics

Current postgraduate research students

<h4>Postgraduate research opportunities</h4> <p>We welcome enquiries from motivated and qualified applicants from all around the world who are interested in PhD study. Our <a href="https://physicalsciences.leeds.ac.uk/research-opportunities">research opportunities</a> allow you to search for projects and scholarships.</p>