Derek Harland

Associate Professor in Mathematics

University of Leeds

d.g.harland@leeds.ac.uk

About me

I have been a member of the geometry group in the School of Mathematics at the University of Leeds since 2013. Before that I was a lecturer at Loughborough, and had spells as post-doc in Durham and Hannover. I completed my PhD in Durham in 2008 under the supervision of Richard Ward.

Research

I am broadly interested in geometry and mathematical physics.

A lot of my research focuses on topological solitons. These can roughly be understood as solutions in classical field theories or geometric variational problems which behave like particles. The number of particles is typically equal to an integer-valued topological invariant of the underlying fields.

Monopoles are quintessential examples of topological solitons. Some of my recent work has analysed the structures that arise when collections of monopoles coalesce, and the formation of so-called magnetic bags. I have also been thinking about the distribution of magnetic charge in monopoles and how this is encoded in the integrable systems machinery that was developed to construct monopoles. In ongoing work I am analysing harmonic forms on monopole moduli spaces and how this relates to their asymptotic geometry. I am also looking at ways of constructing chains of monopoles with a high degree of symmetry using relations with Hitchin's equations.

The Skyrme model is an effective model of quantum chromo-dynamics in which atomic nuclei emerge as solitons. I have been thinking about how to tune the model to better reflect data from experimental nuclear physics, and to this end have been developing a lightly bound Skyrme model. I have also been trying to extract electromagnetic properties of nucleons by properly coupling the model to a gauge field.

Instantons are gauge-theoretic solitons that exist in dimension four and higher. I have been developing a theory of instantons on manifolds that admit real Killing spinors, including nearly Kaehler six-manifolds (which are closely linked with G2-geometry). Important problems include the construction and counting of such instantons; one of my recent results is that the only known instanton on the six-sphere is rigid (so new instantons cannot be obtained by deforming it).

Frequent collaborators

I am grateful to all of the following people for fruitful research collaborations:

Richard Ward, Seckin Kurkcuoglu, Olaf Lechtenfeld, Alexander Popov, Tatiana Ivanova, Christoph Nölle, Paul Sutcliffe, Martin Speight, David Foster, Christian Saemann, Sam Palmer, Mark Everitt, Tim Spiller, Yasha Shnir, Juha Jaykka, Mike Gillard, Stefano Bolognesi, Benoit Charbonneau, Daniel Nogradi, Eugenie Hunsicker.

PhD students

I am looking to recruit PhD students; if you would like to study for a PhD here at Leeds please contact me.

I currently supervise three PhD students: Joshua Cork, Joseph Driscoll, and (jointly with Martin Speight) Ben Daniel-Thorpe.

Links

Photos from the Leeds maths walks.

The forthcoming LEEDS conference.