Publication List
For prepublication
versions, follow this link: ArXive
Polynomial Modular Frobenius Manifolds
(co-author: E.K. Morrison)
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)
Dubrovin's
duality for F-manifolds with eventual identities
(co-author: Liana David)
Advances in
Mathematics 226:5 (2011) 4031-4060
DOI: 
doi: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
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
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)
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
(co-author O.D.McCarthy)
J. Phys. A 34 (2001) 2435-2442.
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