Publication List

 

For prepublication versions, follow this link: ArXive

 

 

 

 

Polynomial Modular Frobenius Manifolds

(co-author: E.K. Morrison)

arXiv:1110.4021

DOI :dx.doi.org/10.1016/j.physd.2011.12.006

 

Symmetries of F-manifolds with eventual identities and special families of connections 

(co-author: Liana David)

arxiv:1103.2045

 

 

Dubrovin's duality for F-manifolds with eventual identities

(co-author: Liana David)

Advances in Mathematics 226:5 (2011) 4031-4060

DOI: http://www.sciencedirect.com/scidirimg/clear.gifdoi:10.1016/j.aim.2010.11.006

 

 

Modular Frobenius manifolds and their invariant flows

(co-author: E.K.Morrison)

International Mathematics Research Notices (2010)

article ID rnm236, 26 pages, doi:10.1093/imrn/rnq236

Online version

 

Simple Elliptic Singularities: a note on their $G$-function

arXiv:1004.2140

To appear: The Asian Journal of Mathematics.

 

Differential and Functional Identities for the Elliptic Trilogarithm

arXiv:0903.2425

SIGMA 5 (2009), 031, 12 pages

DOI: doi:10.3842/SIGMA.2009.031

 

Weyl groups and elliptic solutions of the WDVV equations

Advances in Mathematics, 224:5 (2010), 1801-1838

DOI: http://dx.doi.org/10.1016/j.aim.2010.01.013

 

Logarithmic deformations of the rational superpotential/Landau-Ginzburg construction of

solutions of the WDVV equation

(co-author: J.T.Ferguson)

Communications in Mathematical Physics 280:1, (2008), 1-25

http://dx.doi.org/10.1007/s00220-008-0464-y

 

Multidimensional integrable systems and deformations of Lie algebra homomorphisms
(co-authors: Maciej Dunajski and James D.E. Grant)

J. Math. Phys. 48, 093502 (2007)

DOI:  doi:10.1063/1.2777008

 

A note on the relationship between rational and trigonometric solutions of the WDVV equations

(co-author: A. Riley)

J. Nonlinear Mathematical Physics 14(1)  (2007) 82-94

DOI:  doi:10.2991/jnmp.2007.14.1.7

 

Duality for Jacobi group orbit spaces and elliptic solutions of the WDVV equations

(co-author: A. Riley)

Lett. Math. Phys. 77 (2006) 221-234

 

Conformally flat pencils of metrics, Frobenius structures and a modified Saito construction

(co-author: L.David)

J. Geom. Phys. 56 (2006) 1561-1575

 

Compatible metrics on a manifold and non-local bi-Hamiltonian structures

(co-author: L.David), 

Int. Math. Research Notices (2004) 66 3533-3557

 

On the isomonodromic tau-function for the Hurwitz spaces of branched coverings of genus zero and one

(co-author: A.Kokotov),

 Maths. Res. Letters. Math. Res. Lett., (2005) 857-875

 

Frobenius submanifolds: natural submanifolds and induced bi-Hamiltonian Structures,

Differential Geometry and its Applications 20 (2004) 67-99

 

Deformations of the Monge/Riemann hierarchy and approximately integrable systems

J. Math. Phys. 44 (2003) 251-262.

 

How to count curves: from nineteenth century problems to twenty-first century Solutions

Phil. Trans. R. Soc. Lond. A 361 (2003) 2633-2648.

 

Symmetries and Solutions of Getzler's Equation for Coxeter and Extended Affine Weyl Frobenius manifolds

Int. Math. Research Notices (2003) 19 1035-1051.

 

Einstein metrics on tangent bundles of spheres

(co-author: A.S.Dancer)

Class. Quan. Grav. 19 (2002) 4663-4670

 

Deformations of dispersionless KdV hierarchies

Lett. Math. Phys. 58 (2001) 129-140.

 

Frobenius manifolds and the biHamiltonian structure on discriminant hypersurfaces

In Integrable Systems, Topology and Physics

Amer.Math.Soc. Contemporary Mathematics series 309 (2002) 251-265

 

Frobenius submanifolds

J. Geom. Phys. 38 (2001) 285-307.

 

Unitized Jordan algebras and dispersionless KdV equations

(co-author O.D.McCarthy)

J. Phys. A 34 (2001) 2435-2442.

 

Jordan manifolds and dispersionless KdV equations

J. Nonlinear Math. Phys. 34 (2001) 495-510

 

Degenerate bi-Hamiltonian structures

Teoreticheskaya i Matematicheskaya Fizika

(republished in Theoretical and Mathematical Physics 122:2 (2000) 247-255)

 

Gravity thaws the frozen moduli of CP^1 solitons.

(co-author M. Speight)

Phys. Lett. B 457 (1999) 17-22

 

Hypercomplex Integrable Systems

(co-author J.D.E. Grant)

Nonlinearity 12 (1999) 1247-1261

 

Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations

Journal of Mathematical Physics 40 (1999) 5058-5079

 

The Geometry of Multidimensional Integrable Systems

Journal of Geometry and Physics 21 (1997) 255-278

 

The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies

(co-author: D.B.Fairlie)

Inverse Problems 12 (1996) 885-908

 

The dispersive self-dual Einstein equations and the Toda Lattice

J. Phys. A 29 (1996) 6117-6124

 

On the integrability of a third-order Monge-Amp\'ere type Equation

Physics Letters A 210 (1996) 267-272

 

The Hamiltonian structure of the dispersionless Toda equation

(co-author: D.B.Fairlie)

Physica D 90 (1996) 1-8

 

The Moyal bracket and the dispersionless limit of the KP hierarchy

J.Phys. A  28 (1995) 1967-1975

 

On the symmetry structure of anti-self-dual Einstein hierarchy

Journal of Mathematical Physics 36 (1995) 3566-3573

 

Kahler-Einstein metrics with SU(2) action

(co-author: A.S.Dancer)

Math. Proc. Camb. Phil. Soc. 115 (1994) 513-525

 

Moduli Space Metrics for Axially Symmetric Instantons

Proc. Roy. Soc. A 446 (1994) 479-497

 

Hierarchy of Conserved Currents for Self-Dual Einstein Spaces

Classical and Quantum Gravity 10 (1993) 1417-1423

 

Integrable Hierarchies in (2+1)-Dimensions and their Twistor Description

Journal of Mathematical Physics 34 (1993) 243-259

 

Wave Solutions of a (2+1)-Dimensional generalisation of the Non-Linear Schrodinger Equation

Inverse Problems 8 (1992) L21-L27

 

The Moyal Algebra and Deformations of the Self-Dual Einstein Equations

Physics Letters B 283 (1992) 63-66

 

A New Family of Integrable Models in (2+1)-Dimensions Associated with Hermitian Symmetric Spaces

Journal of Mathematical Physics 33 (1992) 2477-2482

 

Low-Velocity Scattering of Vortices in a modified Abelian Higgs Model

Journal of Mathematical Physics 33 (1992) 102-110

 

Self-Dual Gauge Fields and the Non-Linear Schrodinger Equation

Physics Letters A 154 (1991) 123-126