Mathematical Physics Group
The Mathematical Physics group covers a wide range of scientific interests spanning from pure mathematics to applications and theoretical physics. The group is very active and offers several oportunities to postgraduate students. We take part in the regular geometry seminar, and organize several other research activities such as an informal seminar in Geometry and Mathematical Physics, mini-courses and reading groups.
Our Research Interests include
- Algebraic structures coming from quantum field theory and statistical mechanics, such as: Elliptic algebras and corresponding Poisson structures. Quantum and classical Yang-Baxter relations.
- Connection theory, singularities and completion of manifolds, universal connections, supermanifolds. Mathematical problems of quantum physics; quantization; cohomology in physics; bracket structures and homotopy algebras; polynomial invariants of supermatrices.
- Integrable systems. Non-commutative integrable systems and corresponding algebraic structures. 3D integrable hydrodynamic type systems. Frobenius manifolds. Algebraic techniques to construct soliton solutions. Automorphic Lie algebras. Integrable wave coupling and applications to nonlinear optics.
- Hamiltonian systems with symmetry: The dynamics and bifurcations of Hamiltonian systems with symmetry, particularly of relative equilibria. The effects of the geometry of the momentum map and its degenerations in such systems. Applications to n-body systems including point vortices.
- Stochastic differential equations and random walks models and their applications to reaction-transport phenomena, dynamo theory, mathematical biology and turbulence.
Members of staff involved
NAME | Title | EMAIL @manchester.ac.uk | PHONE | OFFICE | |
Fedotov | Sergei | Prof. | Sergei.Fedotov | 0161 30 63659 | 2.141 |
Khudaverdyan | Hovhannes | Dr | Hovhannes.Khudaverdyan | 0161 30 68975 | 1.118 |
Montaldi | James | Dr | J.Montaldi | 0161 30 63667 | 2.113 |
Parkinson | John | Dr | John.Parkinson | 0161 27 55897 | G.112 |
Voronov | Theodore | Dr | Theodore.Voronov | 0161 30 63682 | 2.109 |