# Lead supervisors for the Centre for Doctoral Training in Statistical Applied Mathematics

We are academic staff from the Department of Mathematical Sciences who may be available to supervise your PhD project as your lead supervisor.

Get in touch with us about PhD projects.

- Mathematical biology
- Infectious disease epidemiology and evolution
- Ecological modelling
- Statistical geometry
- Spatial analysis
- Survival analysis and statistical methods in epidemiology
- Methods for handling missing data in statistical analyses
- Causal inference methods for randomised trials
- Biostatistical and epidemiological applications
- Mathematical modelling to explore medical and biological problems
- Infectious disease dynamics
- Differential equations and Individual-based modelling
- Inverse problems (in particular, tomography)
- Sparse regularisation and optimisation (in particular, wavelet and shearlets)
- Machine learning and deep learning in imaging
- Industrial applied maths especially problems involving electricity, food or telecommunications.
- Numerical weather forecasting and data assimilation.
- Non smooth dynamical systems, friction, impact and chaos.
- Scale-interaction phenomena via asymptotic analysis of PDE
- Operator theory and functional models
- Applied calculus of variations
- Probability and applications in Mathematical Finance
- Stochastic optimal control
- Martingale optimal transport
- Dynamical systems (pattern formation, reaction-diffusion problems, bifurcation theory)
- Networks and dynamics
- Fluid mechanics (nonlinear phenomena, asymptotic methods)
- Analysis of nonlinear partial differential equations
- Blow-up patterns in nonlinear evolution problems
- Singular limits in variational problems with loss of compactness
- Generalised Linear Models: Modelling, Approximate Methods, Value of Information
- Spatial and Spatial-Temporal Geostatistics: Modelling, Sampling Design
- Time Series: Modelling, Sequential Analysis
- Numerical linear algebra and scientific computing
- Approximation and reduction of multivariate functions and tensors
- Probabilistic and quantum modelling
- Inverse problems (e.g. models, algorithms)
- Large-scale, randomized optimization (e.g. convergence guarantees, rates)
- Applications (e.g. imaging, machine learning, deep learning
- Asymptotic analysis and perturbation methods
- Industrial and applied mathematical modelling
- Complex fluids with memory, high order nonlinear evolutionary PDEs and free boundary problems
- Functional data analysis
- Shape Statistics
- Applications of Statistics
- Harmonic Analysis (commutative and non-commutative)
- Lie groups, homogeneous domains, representation theory
- Pseudo-differential operators and Partial Differential Equations
- Inverse problems and regularization
- Image restoration and reconstruction
- Numerical linear algebra, Krylov subspace methods
- Analysis and solvers for high frequency wave problems
- PDEs with random input data and UQ
- PDE eigenvalue problems and reactor stability
- Sequential Monte Carlo and Markov Chain Monte Carlo methods
- Martingales and Markov processes
- Computational methods in population genetics
- Models arising from statistical physics, with an emphasis on understanding critical phenomena
- Abelian sandpile model of self-organised criticality
- Behaviour of random walks on fractal graphs
- Complex stochastic models
- Markov Chain Monte Carlo samplers
- Adaptive and group sequential clinical trials
- Reinforced random walks, self-interacting processes
- Random walks in random environment, or in dynamical environment
- Reinforcement learning
- Dynamical systems and partial differential equations (modelling, analysis and numerical analysis)
- Data analysis and mathematical approaches to machine learning
- Applications in biology, climate science, engineering and industry
- Self-similar processes, Lévy processes and their applications
- Spatial branching, fragmentation and coalescing processes
- Stochastic (numerical) modelling
- Branching processes
- Pólya's urns and stochastic approximation
- Random networks
- Averaging and Homogenisation for PDEs
- Infinite-dimensional dynamics: PDEs and lattice ODEs
- Many particle dynamics
- Geophysical fluid mechanics and conservation laws
- Nonlinear waves and free-surface problems
- Mathematical biology
- Scientific computing, HPC and novel architectures
- Fast solvers for partial differential equations in atmospheric fluid dynamics
- Algorithms and software for stochastic differential equations and molecular dynamics
- Partial differential equations and nonlinear analysis
- Concentration phenomena in nonlinear elliptic equations
- Blow-up in nonlinear parabolic equations
- Wavelets and lifting schemes
- Time series, image and network analysis
- Bayesian Computation
- Model reduction
- Control theory
- Analysis
- Stochastic analysis with applications in biology
- Random networks
- Stochastic processes in random environment
- Probabilistic models motivated by population genetics
- Spatial branching processes with interactions
- Applications of probability theory to partial differential equations
- Pure and applied probability
- Stochastic Geometry
- Random graphs, percolation and interacting particle systems
- Clustering algorithm
- Application of inverse problems techniques
- Neural Networks
- Inverse problems and compressed sensing
- Machine learning and optimisation
- Infinite dimensional regularisation
- Numerical methods for geophysical fluid problems
- Natural Disasters
- Automated computational adaptive algorithms
- Probability
- Branching processes: branching Brownian motion, branching random walks
- Random graphs, random environments
- Graphs and networks
- Applied stochastic processes
- Emergent phenomena
- Extreme value theory
- Methods for spatial and spatio-temporal data
- Bayesian computation
- Statistical analysis of networks and graphical models
- High dimensional inference
- Optimization Methods
- Analysis, Partial differential equations, and Applied mathematics
- Modelling of biological systems and Numerics
- Geometric analysis
- Scalable Bayesian methods (including Markov chain Monte Carlo algorithms).
- Particle filtering and sequential Monte Carlo algorithms.
- Bayesian neural networks.
- Stochastic PDEs and their applications
- Langevin equations
- Numerical methods for strong and weak approximation
- Bayesian networks and uses of conditional independence
- Bayes linear methods
- Analysis of collections of (second-order) exchangeable sequences
- Design and analysis of numerical methods for PDEs
- Geometric numerical integration
- Optimal design of quantum systems (NMR, laser, quantum gates)
- Variational problems
- Applied analysis, Partial differential equations
- Nonlinear elasticity, fluid mechanics
- Methods for spatial and spatio-temporal data
- Computation for Bayesian methods
- Applications in the public health and the social sciences
- Propagation of acoustic and electromagnetic waves
- Transform methods for linear and nonlinear integrable PDEs
- Problems at the interface between analysis and numerical analysis of PDEs
- Asymptotic analysis and perturbation theory
- Industrial and applied mathematical modelling
- Fluid dynamics and free-surface flows
- Stochastic partial differential equations
- Rough path theory and regularity structures
- Statistical mechanics
- Nonlinear partial differential equations
- Free boundary problems in fluid mechanics
- Local and global bifurcation theory
- Using mathematical models to explore problems in healthcare
- Non-invasive drug monitoring and infectious disease control
- Behaviours of network systems
- Mathematical modelling of biological systems in which stochasticity plays an important role
- Efficient stochastic modelling and simulation methodologies
- A range of biological application areas: (e.g. cell migration, embryogenesis, Collective animal behaviour, parasite dynamics, pattern formation)
- Unsupervised and semi-supervised learning on graphs
- Spectral graph theory
- Randomised algorithms and Markov chains