Mathematics
Applied Mathematics
- Kinetic theory of informationally connected active particles
- Kinetic theory of dense granular gases of viscoelastic particles
- Anomalous dynamics of an infinite set of Smoluchowski-like ordinary differential equations: Numerical and Analytical study
- Mathematical Modelling of nano-actuators
- Mathematical Modelling of icy geysers on icy satellites Enceladus and Europa
- 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
- Dimensionality Reduction in Data Analysis
- Training Algorithms for Neural Networks
- Dynamics of Systems of Physical, Chemical, and Biological Kinetics
- Dynamics of Physiological Adaptation
- Financial mathematics and economics, more concretely risk modelling and optimisation under risk
- Discrete mathematics and optimisation
- Mathematics formalization and formal proofs
- Mathematical Ecology and Population Dynamics
- Dynamical systems, reaction-diffusion-advection models, optimisation, evolutionary game theory, integro-differential equations, pattern formation and chaos, disease modelling
Mathematical Ecology and 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
- Nonparametric and semi-parametric modelling for longitudinal and functional data, and applications
- Gaussian process methods for nonlinear regression
- Stochastic mortality modelling and forecasting
Pure Mathematics
- Lie Algebras and Representation Theory
- Direct Limits of Finite Dimensional Algebras, Groups, and their Representations
- Differential Geometry
- Conformal surfaces, in particular, minimal surfaces, CMC surfaces, HSL surfaces and Willmore surfaces
- Quaternionic Holomorphic Geometry
- Transformation theory
- Integrable systems
- Isoparametric manifolds
- Visualisation
- Shape recognition
- Surfaces in 3D
- 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
Dr Andrew Tonks
- Category theory, infinity groupoids
- Homological algebra, K-theory
- Homotopical algebra, operads, simplicial methods