# School of Mathematics

## Prof J Martin Speight

Professor of Mathematics

Pure Mathematics

### Contact details

Room: 9.11

Tel: +44 (0)113 3435169

Email: J.M.Speight @ leeds.ac.uk

### Keywords

Topological solitons

Moduli spaces

Mathematical physics

Differential geometry

Superconductivity

## Research interests

There are many systems of partial differential equations of interest in theoretical physics which possess soliton solutions (stable, smooth, localized lumps of energy). 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.

### Useful links

## Publications

**Adam C, Speight JM, Wereszczynski A** Volume of a vortex and the Bradlow bound *Physical Review D*, **95**, 2017

DOI:10.1103/PhysRevD.95.116007

View abstract

**Gillard M, Harland D, Kirk E, Maybee B, Speight M** A point particle model of lightly bound skyrmions *Nuclear Physics B*, **917**, 286-316, 2017

DOI:10.1016/j.nuclphysb.2017.01.027

View abstract

**Babaev E, Carlström J, Silaev M, Speight JM** Type-1.5 superconductivity in multicomponent systems *Physica C: Superconductivity and its Applications*, **533**, 20-35, 2017

DOI:10.1016/j.physc.2016.08.003

View abstract

**Adam C; Naya C; Speight JM; Vazquez R; Sanchez-Guillen J; Wereszczynski A ** *A unified approach to nuclei: The BPS Skyrme Model*Nuclear and Particle Physics Proceedings, 1480-1486 2016

DOI:10.1016/j.nuclphysbps.2015.09.239

View abstract

**Alqahtani LS, Speight JM** Ricci magnetic geodesic motion of vortices and lumps *Journal of Geometry and Physics*, **98**, 556-574, 2015

DOI:10.1016/j.geomphys.2015.07.008

View abstract

**Speight JM** Near BPS Skyrmions and restricted harmonic maps *Journal of Geometry and Physics*, **92**, 30-45, 2015

DOI:10.1016/j.geomphys.2015.02.001

View abstract

**Gillard M, Harland D, Speight M** Skyrmions with low binding energies *Nuclear Physics B*, **895**, 272-287, 2015

DOI:10.1016/j.nuclphysb.2015.04.005

View abstract

**Speight JM** Solitons on tori and soliton crystals *Communications in Mathematical Physics*, **332**, 355-377, 2014

DOI:10.1007/s00220-014-2104-z

View abstract

**Babaev E, Carlström J, Garaud J, Silaev M, Speight JM** Type-1.5 superconductivity in multiband systems: Magnetic response, broken symmetries and microscopic theory - A brief overview *Physica C: Superconductivity and its Applications*, **479**, 2-14, 2012

DOI:10.1016/j.physc.2012.01.002

View abstract

**Speight JM** Long range vortex interactions and type 1.5 superconductivity *AIP Conference Proceedings*, **1389**, 660-663, 2011

DOI:10.1063/1.3636817

View abstract

**Harland D, Speight M, Sutcliffe P** Hopf solitons and elastic rods *Physical Review D - Particles, Fields, Gravitation and Cosmology*, **83**, 2011

DOI:10.1103/PhysRevD.83.065008

View abstract

**Speight JM** The volume of the space of holomorphic maps from S-2 to CPk *J GEOM PHYS*, **61**, 77-84, 2011

DOI:10.1016/j.geomphys.2010.09.005

**Speight JM** Compactons and semi-compactons in the extreme baby Skyrme model *J PHYS A-MATH THEOR*, **43**, 2010

DOI:10.1088/1751-8113/43/40/405201

**Speight JM** Supercurrent coupling in the Faddeev-Skyrme model *J GEOM PHYS*, **60**, 599-610, 2010

DOI:10.1016/j.geomphys.2009.12.007

**Krusch S, Speight JM** Exact moduli space metrics for hyperbolic vortex polygons *J MATH PHYS*, **51**, 2010

DOI:10.1063/1.3277189

**Speight JM** A pure Skyrme instanton *PHYS LETT B*, **659**, 429-433, 2008

DOI:10.1016/j.physletb.2007.10.040

**Speight JM ** *Magnetic bubble refraction and quasibreathers in inhomogeneous antiferromagnets*THEOR MATH PHYS+, 1043-1055 2007

View abstract

**Speight JM, Svensson M** On the strong coupling limit of the Faddeev-Hopf model *COMMUN MATH PHYS*, **272**, 751-773, 2007

DOI:10.1007/s00220-007-0240-4

**Speight JM** Sigma models on curved space and bubble refraction in doped antiferromagnets *NONLINEARITY*, **19**, 1565-1579, 2006

DOI:10.1088/0951-7715/19/7/006

**Speight JM, Zolotaryuk Y** Kinks in dipole chains *NONLINEARITY*, **19**, 1365-1382, 2006

DOI:10.1088/0951-7715/19/6/008

**Krusch S, Speight JM** Fermionic quantization of Hopf solitons *Communications in Mathematical Physics*, **264**, 391-410, 2006

DOI:10.1007/s00220-005-1469-4

**Auckly D, Speight JM** Fermionic quantization and configuration spaces for the Skyrme and Faddeev-Hopf Models *Communications in Mathematical Physics*, **263**, 173-216, 2006

DOI:10.1007/s00220-005-1496-1

**Speight JM** Slow equivariant lump dynamics on the two-sphere *Nonlinearity*, **19**, 441-452, 2006

DOI:10.1088/0951-7715/19/2/011

**Babaev E, Speight JM** Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors *Physical Review B (Condensed Matter and Materials Physics)*, **72**, 1-4, 2005

DOI:10.1103/PhysRevB.72.180502

**Speight JM** Homotopy classification of multiply based textures *None*, **72**, 79-82, 2005

**Romao NM, Speight JM** Slow Schrodinger dynamics of gauged vortices *NONLINEARITY*, **17**, 1337-1355, 2004

DOI:10.1088/0951-7715/17/4/010

**Haskins M, Speight JM** The geodesic approximation for lump dynamics and coercivity of the Hessian for harmonic maps *J MATH PHYS*, **44**, 3470-3494, 2003

DOI:10.1063/1.1586480

**Speight JM** The L-2 geometry of spaces of harmonic maps S-2 ->S-2 and RP2 ->RP2 *J GEOM PHYS*, **47**, 343-368, 2003

**Manton N, Speight JM** Asymptotic interactions of critically coupled vortices *Communications in Mathematical Physics*, **236**, 535-555, 2003

DOI:10.1007/s00220-003-0842-4

**Speight JM** The L^2 geometry of spaces of harmonic maps $S^2 \to S^2$ and $RP^2 \to RP^2$ *Journal of Geometry and Physics*, **47**, 343-368, 2002

DOI:10.1016/S0393-0440(02)00227-9

**Haskins M, Speight JM** Breather initial profiles in chains of weakly coupled anharmonic oscillators *PHYS LETT A*, **299**, 549-557, 2002

**Speight JM, Sutcliffe PM** Discrete breathers in anisotropic ferromagnetic spin chains *J PHYS A-MATH GEN*, **34**, 10839-10858, 2001

**Speight JM** The deformed conifold as a geometry on the space of unit charge CP1 lumps *PHYS LETT B*, **511**, 295-301, 2001

**Speight JM** Instability of breathers in the topological discrete sine-Gordon system *NONLINEARITY*, **14**, 843-848, 2001

**Speight JM** A quantum Peierls-Nabarro barrier *Journal of Physics A: Mathematical and General*, **33**, 4741-4754, 2000

**Speight JM** Topological discrete kinks *Nonlinearity*, **12**, 1373-1387, 1999

**Speight JM** Breathers in the weakly coupled topological discrete sine-Gordon system *Nonlinearity*, **11**, 1651-1671, 1998

**Speight JM** Lump dynamics in the CP^{1}model on the torus *Communications in Mathematical Physics*, **194**, 513-539, 1998

**Speight JM** A discreteφ^{4}system without a Peierls-Nabarro barrier *Nonlinearity*, **10**, 1615-1625, 1997

**Speight JM, Svensson M** Some global minimizers of a symplectic Dirichlet energy *vol*, **62**, 737-745,

View abstract

**Babaev E, Jäykkä J, Speight M** Magnetic field delocalization and flux inversion in fractional vortices
in two-component superconductors *Phys. Rev. Lett*, **103**, 237002,

DOI:10.1103/PhysRevLett.103.237002

View abstract

**Babaev E, Carlstrom J, Speight M** Type-1.5 Superconducting State from an Intrinsic Proximity Effect in
Two-Band Superconductors *Phys.Rev.Lett.*, **105**, 067003,

DOI:10.1103/PhysRevLett.105.067003

View abstract

**Carlstrom J, Babaev E, Speight M** Type-1.5 superconductivity in multiband systems: the effects of
interband couplings *Phys. Rev. B*, **83**, 174509,

DOI:10.1103/PhysRevB.83.174509

View abstract

**Jäykkä J, Speight M** Easy plane baby skyrmions *Phys.Rev.D*, **82**, 125030,

DOI:10.1103/PhysRevD.82.125030

View abstract

**Harland D, Speight M, Sutcliffe P** Hopf solitons and elastic rods *Phys.Rev.D*, **83**, 065008,

DOI:10.1103/PhysRevD.83.065008

View abstract

Speight JM The ground state energy of a charged particle on a Riemann surface.

View abstract

**Jäykkä J, Speight M, Sutcliffe P** Broken Baby Skyrmions *Proc. R. Soc. A*, **468**, 1085-1104,

DOI:10.1098/rspa.2011.0543

View abstract

**Speight JM, Jäykkä J** Supercurrent coupling destabilizes knot solitons *Phys. Rev. D*, **84**, 125035,

DOI:10.1103/PhysRevD.84.125035

View abstract

**Auckly D, Kapitanski L, Speight M** Geometry and analysis in non-linear sigma models *St. Petersburg Mathematical Journal*, **18**, 1-31,

View abstract

**Speight JM** Static intervortex forces *Phys.Rev. D*, **55**, 3830-3835,

DOI:10.1103/PhysRevD.55.3830

View abstract

**Speight JM** Lump dynamics in the CP^1 model on the torus *Commun.Math.Phys.*, **194**, 513-539,

DOI:10.1007/s002200050367

View abstract

**Sadun LA, Speight JM** Geodesic incompleteness in the CP^1 model on a compact Riemann surface *Lett.Math.Phys.*, **43**, 329-334,

View abstract

**Speight JM** Low energy dynamics of a CP^1 lump on the sphere *J.Math.Phys.*, **36**, 796,

DOI:10.1063/1.531157

View abstract

**Speight JM** The kink Casimir energy in a lattice sine-Gordon model *Phys.Rev. D*, **49**, 6914-6919,

DOI:10.1103/PhysRevD.49.6914

View abstract

**Speight JM, Strachan IAB** Gravity thaws the frozen moduli of the CP^1 lump *Phys.Lett. B*, **457**, 17-22,

DOI:10.1016/S0370-2693(99)00526-2

View abstract

**Haskins M, Speight JM** Breather initial profiles in chains of weakly coupled anharmonic
oscillators *Phys. Lett. A.*, **299**, 549-557,

DOI:10.1016/S0375-9601(02)00670-9

View abstract

**Speight JM, Ward RS** Kink dynamics in a novel discrete sine-Gordon system *Nonlinearity*, **7**, 475-484,

DOI:10.1088/0951-7715/7/2/009

View abstract

**Babaev E, Carlstrom J, Garaud J, Silaev M, Speight JM** Type-1.5 superconductivity in multiband systems: magnetic response,
broken symmetries and microscopic theory. A brief overview *Physica C*, **479**, 2-14,

DOI:10.1016/j.physc.2012.01.002

View abstract

**Krusch S, Speight JM** Quantum lump dynamics on the two-sphere *Commun. Math. Phys*, **322**, 95-126,

DOI:10.1007/s00220-013-1730-1

View abstract

**Garaud J, Carlstrom J, Babaev E, Speight M** Chiral CP^2 skyrmions in three-band superconductors *Phys. Rev. B*, **87**, 014507,

DOI:10.1103/PhysRevB.87.014507

View abstract

**Harland D, Jäykkä J, Shnir Y, Speight M** Isospinning hopfions *J. Phys. A: Math. Theor.*, **46**, 225402,

DOI:10.1088/1751-8113/46/22/225402

View abstract

**Adam C, Naya C, Sanchez-Guillen J, Speight JM, Wereszczynski A** Thermodynamics of the BPS Skyrme model *Phys. Rev. D*, **90**, 045003,

DOI:10.1103/PhysRevD.90.045003

View abstract

Speight JM The adiabatic limit of wave map flow on a two torus.

View abstract

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