Before applying for a PhD/MPhil programme, use the links below to learn more about the specific areas of expertise in which our staff supervise PhD/MPhil candidates and identify one or two members of staff whose interests cover the area you would like to work in:
What if my research interests do not match the staff interests listed?
It is important that the area you want to work in is broadly compatible with our research interests - otherwise we may not be able to accept your application.
However, please do not feel we will not be interested if there is not an exact match. It is sometimes possible to be flexible, so please contact us.
Pure Mathematics
Particular interests in the pure mathematics group include:
- Dynamical Systems and Aperiodic Orders
- Representations and Cohomology of Algebras and Groups, including Algebraic Groups and Quantum Groups
- Polynomial Functors and Functor Homology
- Unstable and Stable Homotopy Theory
- Classifying and Moduli Spaces
- K-Theory, Lie Theory, Surface Theory, and Conformal Geometry
- Derived Categories, Operads and Operadic Algebras with Links and Applications to Other Areas of Mathematics such as Algebraic Geometry, Commutative and Noncommutative Geometry, Mathematical Physics, and Combinatorics
Learn more about the Pure Mathematics group >
| Dr Alexander Baranov |
- Lie Algebras and Representation Theory
- Asymptotic Phenomena in Lie Algebras, Finite and Algebraic Groups, and their Representations
- Direct Limits of Finite Dimensional Algebras and Groups
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| Dr Alex Clark |
- Path Algebras Associated to Tilings
- Linking of Minimal Sets of Flows
- Affine Maps of Compact Abelian Groups
- Solenoids
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| Dr Frank Neumann |
- Algebraic Topology and Homotopy Theory, Cohomology of Finite Loop Spaces, and Generalized Homogeneous Spaces
- Algebraic Invariant Theory
- Applications of Homotopy Theory to Algebraic Geometry and Arithmetic Geometry, Etale Homotopy, and Cohomology of Stacks
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| Dr Katrin Leschke |
- Differential Geometry
- Study of Surfaces into 3-Space using Quaternionic Holomorphic Maps has immediate connections to Classical Complex-Analytic Geometry, Visualization, and Conformal Field Theory
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| Dr Nicole Snashall |
- Representation Theory of Finite Dimensional Algebras, in particular Homological Algebra
- Hochschild and Cyclic Cohomology Theories and Varieties of Modules
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| Dr Teimuraz Pirashvili |
- Homological and Homotopical Algebra
- Algebraic Theories, especially Functor Homology, Polynomial Functors, Topological Hochschild Homology, Structured Ring Spectra, Triangulated Categories, Secondary Invariants
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| Prof. John Hunton |
- Algebraic Topology and Applications of K-Theoretic and Homological Techniques to Symbolic Dynamics, Mathematical Physics, and Algebraic Systems
- Quasi Periodic Patterns
- Algebraic and Coalgebraic Structures Reflecting Geometric, Topological, and Group Theoretic Phenomena
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Applied Mathematics
Research in the Applied Mathematics group can be broadly grouped in the following topics:
- Numerical Analysis and Scientific Computing
- Applied Dynamics and Computation
- Fluid Modelling
- Mathematical Biology
- Mathematical Risk Theory and Finance
Learn more about the Applied Mathematics group >
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Dr Emmanuil Georgulis
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- Design, Error Analysis, and Adaptivity of Numerical Methods for Partial Differential Equations, in particular:
- Finite Element Methods
- Discontinuous Galerkin Finite Element Methods
- A-Priori and A-Posteriori Error Bounds
- Polynomial Approximation Theory
- Function Spaces
- Regularity Theory of Partial Differential Equations
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Dr Ruslan Davidchack
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- Detection of Unstable Periodic Orbits in Nonlinear Dynamical Systems
- Generating Partitions, Homoclinic Tangencies, and Symbolic Dynamics in Non-Hyperbolic Systems
- Free Energy Computation Methods with Application to Solid-Liquid Interfaces
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Dr Stephen Garrett
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- Stability Theory in Fluid Mechanics, including Local and Global Analyses Applied to the Boundary Layers on Rotating Bodies
- Financial Mathematics, including Interest-Rate Models
- Actuarial Mathematics, including Stochastic Mortality/ Morbidity Models
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Dr Sergei Petrovskii
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- Mathematical Population Dynamics, in particular:
- Mechanisms of Spatiotemporal Self-Organisation in a System of Interacting Species
- Pattern Formation and Chaos
- Biological Invasion
- Population Waves
- Coupling between Biological and Environmental Processes
- Self-Organised Plankton Patterns in Turbulent Environment
- Biologically Relevant Diffusion-Reaction Systems
- Application of Nonlinear Partial Differential Equations in Biology and Ecology
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Prof. Alexander Gorban
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- Functional Analysis
- Architecture of Neurocomputers and Training Algorithms for Neural Networks
- Dynamics of Systems of Physical, Chemical, and Biological Kinetics
- Human Adaptation of Hard Living Conditions
- Methods and Technologies of Collective Thinking
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Prof. Jeremy Levesley
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- Theoretical Aspects of Approximation by Interpolation and Quasi-Interpolation of Manifolds using Polynomials and Radial Basis Functions
- Solutions of Partial Differential Equations using Radial Functions and the Lattice Boltzmann Method
- Fast solutions of Interpolation Equations
- Practical Approximation of Physical Data
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Dr Andrew Morozov
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- Mathematical Ecology and Population Dynamics
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Prof. Michael Tretyakov
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- Theory of Numerical Integration of Stochastic Differential Equations
- Development of Numerical Methods for Nonlinear Partial Differential Equations
- Stochastic Dynamics
- Computational Financial Mathematics
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Prof. Andrey Lazarev
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- Graph Cohomology and NoncomMutative Geometry
- Homotopy Theory of Algebras over Operads and Modular Operads
- Deformation Theory of Algebraic and Geometric Structures
- Moduli Spaces and Topological Field Theories
- Operads and Formal Frobenius Manifolds
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Prof. Sergei Levendorskii
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- Pricing of Financial Options of Various Kinds, mainly Barrier Options and American Options on Stocks, Indices, and Exchange Rates
- Real Options
- Interest rate Derivatives
- Estimation of Time-Irreversible Processes
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