Professor of Mathematical Physics,
University of Glasgow
2018-2023: Head of School, School of Mathematics and Statistics, University of Glasgow
2015-2017: President, Edinburgh Mathematical Society
and ex-officio member of the UK’s
Council for the Mathematical Sciences
2015-2018: Member of the UK’s Engineering and Physical Sciences Research Council (EPSRC) Strategic Advisory Team for the Mathematical Sciences
2003-present: Member of the EPSRC peer review college
2006-2010: Associate Dean (Postgraduate) and Head of the Faculty
2008-2009: Convenor of the University’s Heads of Graduate Schools Forum
Editorial Advisor, Bulletin, Journal and Transactions of the London Mathematical Society
Former Editor-in-Chief, Glasgow Mathematical Journal
I am always interested in hearing from students who might wish to undertake a PhD under my supervision. Please feel free to contact me directly. Possible topics include:
- construction and properties of Frobenius manifolds;
- bi-Hamiltonian structures;
- deformations of integrability;
- qDT invariants and deformations of hyperKahler geometry.
Leo Kaminski (jointly supervised with Prof Misha Feigin)
|Georgios Antoniou (jointly supervised with Prof Misha Feigin)
||Frobenius structures, Coxeter discriminants, and supersymmetric mechanics
||Deformations, Extensions and Symmetries of Solutions to the WDVV equations
||Modular Frobenius manifolds
||Geometric structures on the tangent space of Hamiltonian evolution equations
||Frobenius manifolds: caustic submanifolds and discriminant almost duality
||Deformations of equations of hydrodynamic type
||Dispersionless Integrable Systems of KdV type
All my recent preprints and publications appear on ArXiv - the list below is automatically updated from there. For the published version, click on the DOI link at the end of each entry - this will take you to the published version but you will need library access to read them. Older papers are listed below.
Another source of information is my ORCID account.
How to count curves: from nineteenth century problems to twenty-first century Solutions,
Phil. Trans. R. Soc. Lond. A 361 (2003) 2633-2648.
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
Unitized Jordan algebras and dispersionless KdV equations
J. Phys. A 34 (2001) 2435-2442.
Degenerate bi-Hamiltonian structures
Teoreticheskaya i Matematicheskaya Fizika
(republished in Theoretical and Mathematical Physics 122:2 (2000) 247-255)
On the integrability of a third-order Monge-Ampere type Equation,
Physics Letters A 210 (1996) 267-272
Kahler-Einstein metrics with SU(2) action,
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
Some 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
My research interests are in integrable systems and mathematical physics. In particular I am interested in Frobenius manifolds and their applications. Such objects lie at the intersection of many areas of mathematics, from Topological Quantum Field Theories (TQFT’s), to quantum cohomology, singularity theory and mathematical physics.
Specific areas of interest are: extended-affine orbit spaces and associated Frobenius manifolds, symmetries of Frobenius manifolds and related structures; bi-Hamiltonian geometry and the deformation of dispersionless integrable systems. An informal introduction to the theory may be found here: What is a Frobenius Manifold
More recently I have become interested in Donaldson-Thomas invariants and hyperKahler geometry, and quantum DT invariants and integrable deformations of hyperKahler geometry.
The background image shows the zero set corresponding to a certain point in the versal deformation space of the E₆ elliptic singularity. This deformation space may be endowed with the structure of a Frobenius manifold.
I am a member of the Integrable Systems and Mathematical Physics research group within the School, and the Core Structures group.