# School of Mathematics

## Dr Derek G Harland

Associate Professor in Geometry

Pure Mathematics

### Contact details

Room: 8.06

Tel: +44 (0)113 3435152

Email: D.G.Harland @ leeds.ac.uk

### Keywords

Topological solitons

Gauge theory

Monopoles

Instantons

Skyrmions

## Research interests

In theoretical physics and in differential geometry one often encounters the problem finding minima of an "energy functional" defined over an infinite-dimensional configuration space. Typically the configuration space might be a space of maps between manifolds, or a space of connections on and sections of a vector bundle. The study of such critical points may provide non-trivial information about the underlying manifolds and the physics involved. Two systems I am currently interested in are the Yang-Mills-Higgs, Yang-Mills and Skyrme energy functionals, whose critical points are called "monopoles", "instantons" and "skyrmions" respectively. Some of my recent work has looked at such systems on manifolds of relatively high dimension.

### Useful links

## Current postgraduate students

Joshua Cork (2014)

Ben Daniel-Thorpe (2016)

Joe Driscoll (2016)

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