Publication List


For prepublication versions, follow this link: ArXive





Polynomial Modular Frobenius Manifolds

(co-author: E.K. Morrison)




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

(co-author: Liana David)




Dubrovin's duality for F-manifolds with eventual identities

(co-author: Liana David)

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




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


To appear: The Asian Journal of Mathematics.


Differential and Functional Identities for the Elliptic Trilogarithm


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



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


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