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The theory of integrable systems studies differential equations which are, in a sense, exactly solvable and possess regular behaviour. Such systems play a fundamental role in mathematical physics providing an approximation to various models of applied interest. Dating back to Newton, Euler and Jacobi, the theory of integrable systems plays nowadays a unifying role in mathematics bringing together algebra, geometry and analysis.
The research of the group includes both classical and quantum integrable
systems in relation with representation theory and special functions, as
well as algebraic, differential and symplectic geometry.
The geometry and mathematical physics research group holds seminars in the mathematical physics seminar series. |
Academic staff
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| Dr Alexey Bolsinov |
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Integrable tops, bi-Hamiltonian systems and compatible Poisson structures; integrable geodesic flows on Lie groups and homogeneous spaces, magnetic geodesic flows, symmetries and reduction; obstructions to integrability; symplectic and topological invariants for Lagrangian foliations; singularities of the momentum mapping, their invariants and algorithmic classification; projective equivalence in Riemannian geometry. |
| Dr Gavin Brown |
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Algebraic geometry, especially higher dimensional birational geometry and applications of computer algebra to algebraic geometry. |
| Proffessor Jenya Ferapontov |
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Classical differential geometry (web geometry, projective differential geometry, Lie sphere geometry, theory of congruences, conformal structures, geometric aspects of PDEs); Integrable systems (equations of hydrodynamic type, hyperbolic systems of conservation laws, multi-dimensional dispersionless integrable systems, Hamiltonian formalism, symmetry methods). |
| Dr Martin Hallnas |
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Integrable systems and special functions. In particular, in the context of exactly solvable Schrodinger- and analytic difference operators; symmetric functions; and multivariable generalisations of hypergeometric functions. |
| Dr Derek Harland |
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Topological solitons, including monopoles, skyrmions, instantons (in 4 dimensions and higher), calorons, and hopfions. Applications of these to differential geometry, string theory, high energy physics, and nuclear physics. |
| Dr Marta Mazzocco |
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Non–linear differential equations describing monodromy preserving deformations of linear systems (isomonodromic deformation equations). Quantization of Teichmuller spaces and Frobenius manifold theory. |
| Dr Vladimir Novikov |
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Classification of integrable nonlinear partial differential equations and differential-difference equations. Integrability tests: symmetry approach, perturbative symmetry approach in the symbolic representation. Integrable models of mathematical physics. |
| Professor Sasha Veselov |
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Classical and quantum integrable systems in relation with geometry and representation theory; solvable Schroedinger equations, special functions and Huygens' principle. |
Visiting Fellows
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| Dr Ian Marshall |
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Poisson structures of integrable systems and Poisson Lie groups. |
| Dr Antonio Moro |
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Multidimensional dispersionless systems and dispersive corrections: hydrodynamic reductions, quasi-classical DBar-dressing method, symmetry constraints. Nonlocal nonlinear optics: singular solutions of the 2D-eikonal equation, optical vortices, integrable nonlocal perturbations for Cole-Cole media. |
Research students
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| Stuart Andrew |
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Complex monodromy and quantum integrability. |
| David Dowell |
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| William Haese-Hill |
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Integrability and special functions. |
| Adrian Hemery |
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Spectral theory and integrability. |
| Anton Izosimov |
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Integrable Hamiltonian systems and singularity theory. |
| Graham Kemp |
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Geometry of 3D manifolds and quantum integrability. |
| Ilitsa Roustemoglou |
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Integrable systems in 2+1 dimensions: hydrodynamic reductions, dispersive
deformations, symmetries, solutions. |
| Veronika Schreiber |
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Special geometric configurations and integrability. |
| Nikola Stoilov |
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Integrable Hamiltonian systems of hydrodynamic type in 2+1 dimensions, dispersive deformations. |
| Dragomir Tsonev |
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Geodesically equivalent pseudo-Riemannian metrics, Berger subalgebras and special holonomy groups. |
| Pumei Zhang |
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Integrability, bi-Hamiltonian systems, compatible Poisson brackets, Lie groups and Lie algebras, Lie pencils. |
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