A world-class PhD training programme which equips students with the skills and confidence to lead their discipline.
MAC-MIGS staff carry out research at the cutting-edge of their disciplines. Their research interests encompass a broad great variety of mathematical methods and models.
Thanks to this excellence and diversity, we are able to supervise high-quality PhD projects across many areas and enable our students to deliver internationally leading research.
There are also practitioners involved in chemistry (e.g. for molecular and quantum models, materials science), engineering (particle and granular models, processes, materials), informatics (machine learning, artificial intelligence), biology (systems biology, cell modelling) and physics (condensed matter, soft matter, density functional theory).
The supervisors’ main areas of expertise are indicated by the following tags:
ANAL = Analysis, BIO = Biology, COMP = Computation, DS = Data Science, FIN = Financial Modelling and Analysis, FLU = Fluid Dynamics, MAT = Materials, MD = Molecular Dynamics, MESO = Mesoscale Modelling, OPT = Optimisation, PDE = Partial Differential Equations, PHYS = Physics, QM = Quantum Mechanics, STAT = Statistical Analysis, STO = Stochastic Methods, UQ = Uncertainty Quantification.
Computer simulations to study how bacterial biofilms grow and respond to antibiotics. Part of this work involves using advanced algorithms for rare event simulation, such as forward flux sampling, of which I was a developer.
Statistical signal and image processing, with a particular interest in Bayesian inverse problems with applications to remote sensing and biomedical imaging
Mathematical optimization provides guaranteed optimal or near-optimal solutions for various classes of large-scale optimization problems. Much of my research, in collaboration with industry partners, is about improving optimization models and algorithms used in real-world applications. In particular, optimization helps improve the overall performance of the electricity system that is of critical importance to our society. My research contributes to the development of smart grids which combine a traditional electrical power system with a two-way flow of information and energy between suppliers and consumers. This combination can deliver higher integration of wind and solar power, energy savings, and increased reliability and security.
Rigorous treatments and approximations of probability models and their applications to bacterial, cancer and virus populations in particular. Topics include branching processes, game theory, spatial models, genetics. Example projects: modelling the evolution of multidrug resistance in bacteria or cancer, modelling cancer initiation, progression, metastasis formation and fitting to clinical data.
Development and analysis of numerical methods with emphasis on acoustic and electromagnetic wave propagation. Numerical methods include time-domain boundary integral methods, space-time discontinuous Galerkin methods, hp-FEM, BEM.
Hydrological extremes : floods and droughts. Fluvial, sediment transport, morphological and ecosystem modelling: issues for design uncertainty assessment.
Stochastic models of many-body systems in physics, biology and social science. Application of inferential techniques to empirical data to understand the fundamental mechanisms at play in these systems.
Theoretical guaranties for data-driven statistical inference for large-scale direct and inverse problems. Example project: adaptive statistical inference for inverse problems with unknown heterogeneous variance.
We develop state-of-the-art mathematical and computational models (e.g. molecular dynamics, hybrid/multiscale analysis and machine learning tools) and apply them to investigate open engineering problems and challenges. Including: de-icing/anti-icing aerospace surfaces, rarefied gas flows in ultra tight porous media, interfacial flows and instabilities (nano bubbles, nano droplets, nano films), water filtration through nanostructured membranes, slippery surfaces, ultra-cooling membranes, low-drag marine surfaces.
Applied analysis (calculus of variations, partial differential equations, optimal transportation theory), numerical analysis, and discrete and computational geometry, with applications in materials science and continuum mechanics.
Interface between applied probability, information theory and dynamical systems with applications to Bayesian data assimilation, Bayesian learning, stochastic control, and data-driven dimension reduction in stochastic systems. In particular, probabilistic approach to prediction and uncertainty quantification, as well as data-driven techniques for state estimation and classification problems from large sets of noisy and incomplete data; all of these based on maximising information flow from empirical data to modelled dynamics.
The focus of my research is the existence and regularity theory for nonlinear (stochastic) PDEs as well as their numerical analysis and related function spaces. In particular, I’m interested in compressible Navier-Stokes equations, models for non-Newtonian fluids and equations of p-Laplace type. A sample project is the long-time behaviour of stochastically forced fluid flows.
Statistical methodology and theory, with a focus on machine learning problems, such as classification and clustering. Much of my work is motivated by modern developments in technology, which result in new complex data structures and often require new statistical methods.
Stochastic modelling of the transmission of infectious diseases through populations, looking particularly at endemic infections and the effects of population heterogeneities. This typically involves computer simulation of a specific disease system of interest, followed by rigorous mathematical analysis of aspects suggested by the initial simulation work, and then further simulation to validate the theoretical results (eg checking that theory developed in the large-population limit gives sensible results for realistic finite population sizes).
Mathematical analysis of free boundary problems involving continuum mechanics models (Euler equations, Navier-Stokes equations, nonlinear elastodynamics): Well-posedness, finite-time singularity formation. Example project: singularity formation and propagation in free boundary problems.
Applied probability, including modelling of random systems, and analytic techniques in probability (eg, for proving limit theorems). Example projects: random graphs and networks; optimal coupling and rates of convergence to stationarity for Markov chains.
I am an industrial mathematician specialising in energy systems analysis, and good practice in the use of modelling in public policy. Example project: coordination of electric vehicle charging.
Fundamental questions (existence, uniqueness and properties) of elliptic and parabolic PDEs.
I do research at the interface of applied mathematics and stochastic analysis. My current applications involve time-consistent optimal control under evolving streams of information and analysis/development of a stochastic model for charging of electric batteries. The former includes applications in data science and so-called machine learning while the former has a strong component of both modeling and probabilistic numerical analysis.
Numerical analysis of time dependent PDEs and integral equations, including those describing wave propagation and scattering.
Parameter estimation for subsurface flow problems, UQ, Carbon Caputre, ML.
Stochastic modelling of systems `out of equilibrium’ including biophysical processes. The research entails finding analytical solutions of mathematical models and performing stochastic simulations of complex systems. Example projects: nonequilibrium stationary states; modelling of intracellular. processes
My area of research is logistics and combinatorial optimization, applications where some optimal decisions must be taken from among a finite (but very large) set of potential decisions which cannot be computed in a reasonable amount of time. Examples of these applications that I am working now or I have worked in the past are: warehouse location problems, vehicle routing problems, aircraft cockpit architecture, and matching problems (junior doctor allocation, kidney exchange).
Modelling and simulation of hydrocarbon recovery from carbonate and fractured reservoirs, geothermal energy and CO2 storage.
PDEs and their numerical analysis in the engineering and biological sciences, recently also swarm robotics. In particular nonlocal operators, error analysis of finite and boundary elements, variational analysis of nonlinear PDEs, computational mechanics. Example project: Space-time adaptive discretisation of wave equations.
Modelling, rigorous analysis and numerical simulation for complex, multiscale systems in areas such as quantum chemistry, molecular dynamics and statistical mechanics. I have a strong history of interdisciplinary research with chemists, engineers and physicists.
The theory and numerical analysis of PDEs and stochastic PDEs with applications in stochastic control and nonlinear filtering and in mathematical models arising in physics, engineering and economics.
My research interests include: Uncertainty Quantification, Stochastic Differential Equation, Numerical methods for SDEs and PDEs, Multilevel Monte Carlo, Particle systems, Crowd modelling, Mean-field theory, Sparse Grids, Combination techniques, Multi-index techniques, Inverse problems, risk measures and adaptive sampling.
Optimization methods for linear and quadratic programming. Sparse numerical linear algebra for high performance large scale computational optimization. Industrial applications: feed formulation, genomics, telecommunications, petrochemicals, data science and finance.
Numerical analysis, stochastic computation, network science and applications in machine learning, digital human behaviour, urban analytics, crime and life sciences.
Formal modelling and logic-based model checking for dynamic properties of stochastic concurrent systems. Approximations and efficient analysis techniques for the underlying Continuous Time Markov Chains. Example project: fluid approximations of heterogeneous populations of Markovian agents.
I am interested in how large data sets can circumvent the problem of a priori model selection related to stochastic control problems. More broadly I am interested in the fact that mathematical models actively direct social systems, rather than be passive describers of physical systems, and the ethical implications of this. Example project: stochastic control that does not require the specification of the diffusion but infers necessary functions from large data sets.
a. geometric analysis (curvature flows, convexity estimates, analysis of singularities, L^p Minkowski problem), free boundary boundary problems and minimal surfaces (existence, min-max method, classification of global profiles) b. Calabi-Jorgens-Pogorelov type theorems for the Monge-Ampere type equations, exploring the structure of global convex solutions arising win the reflector-antennae and optimal mass transport problems.
Chemical and quantum dynamics, including nonadiabatic dynamics in chemistry and physics and deep learning for potential energy surfaces in chemical dynamics.
Mathematical modelling, and both approximate solution and analysis of the resulting equations, of industrial problems and societal issues. Example projects: flash sintering–mathematically modelling the interaction of the electric current and changing temperature during electrical fusing of ceramic powders; homeless modelling: The aim is to better model changing homeless levels, accounting for causes such as drug dependency and relation to crime.
Sampling algorithms and their application in various areas, e.g. molecular modelling and data analytics and am developing large software packages (MIST and TATi) which are moving towards the general release. Currently, I am engaging with an engineering firm in Bristol on a data analytics for wind turbine assessment. I am interested in designing and training elementary structures for geometrically constrained inference in physical models. Neural nets can learn maps, but to be relevant for applications, physical law should be encoded in their DNA.
Developing Gaussian and other stochastic Bayesian process models for environmental and ecological phenomena, including spatial inhomogeneity and complex observation processes. This is tightly coupled with approximate computational methods, eliminating costly MCMC wherever possible. Example project: modelling sea surface temperatures and their observation biases.
Turbulence and large-scale structure formation in electrically conducting flows, parallel shear flows, boundary layers and thin fluid layers. Low-dimensional modelling of multi-scale non-linear dynamical systems. Applications of functional analysis in fluid dynamics.
Applied computational mathematics, numerical analysis, modelling, simulation and stochastically forced systems. Example projects: stochastic wave equation and marine reserves; numerical methods for neural fields with noise.
Geophysical fluid dynamics, focussing on ocean dynamics and mesoscale turbulence. Numerical methods, including the finite element method, with applications in numerical ocean modelling. Partial differential equation constrained optimisation, including adjoint based methods, with geoscientific applications.
Nonlinear PDEs, computational spectral theory, geometric integration, stochastic differential equations, PDEs with nonlocal nonlinearities. Example project: the solution of PDEs with nonlocal nonlinearities.
I study condensed matter using expensive Density Functional Theory. I want to extend the size of the systems I can study without losing accuracy using novel machine learning techniques. Example project: accelerated large-system structure prediction via machine learning.
Computer-aided drug design and biophysical chemistry with a focus on all aspects of molecular simulations of biological molecules (algorithms, software development, application studies and integration with experiments).
Bayesian inference given data in models represented by simulators, where simulations are expensive. Data-driven modeling of high-dimensional probability distributions, useful for data cleaning, anomaly detection, recognition, forecasting, etc.
Formal series solutions of ODEs/PDEs are often divergent, and the exponentially small terms are needed to obtain a full understanding. Example projects: Transseries and the higher-order Stokes phenomenon; Transition region expansions for turning points.
Discrete particle modelling and data analysis, applied to a wide range of industrial processes including milling, mixing, granulation, silo flow, high speed ballast railtrack etc.
Biological networks; nonlinear dynamics; optimisation; stochastic dynamics; dynamic optimisation; optimal control; network theory; systems biology; synthetic biology; control theory; data science.
My research interests are in using Monte Carlo and optimization methods for statistical problems motivated by applications. I have started my research career in applied probability, which was useful in analysing Markov Chain Monte Carlo and Sequential Monte Carlo methods, as well as the efficiency of optimization methods for stochastic functions. One area of application of such methods Is in the field of inverse problems, in particular chaotic dynamical systems that can be modelled by PDEs and ODEs. In recent years, there have been spectacular advances in optimization methods that scale to much larger problems than previously possible, by clever use of sparsity. I am keen to use them to attack challenging statistical problems.
Modelling and computational methods for inverse problems/PDE-constrained optimisation/control problems, for problems of scientific and engineering interest. Applications are optimal transport techniques include fluid dynamics and imaging, chemical and biological systems, and medical imaging.
Analysis of nonlinear PDEs, particularly of fluid dynamics, including uniqueness of solutions of geophysical fluid dynamics and numerical schemes for small dispersion limits of PDEs.
Mathematical theory, methods and algorithms to solve large-scale inverse problems related to mathematical and computational imaging, such as medical imaging and astronomical imaging problems. I am particularly interested in new Bayesian analysis and computation approaches, and in developing deep connections between modern Bayesian, variational, and Machine Learning approaches to data science. Example projects: efficient Bayesian computation in high-dimensional bilinear inverse problems; combining infinite-dimensional Markov chain Monte Carlo and Deep Learning techniques for imaging inverse problems.
I work at the interfaces between mathematics, (stochastic) systems biology, neuroscience, and (veterinary) medicine. My approach relies on a combination of analysis and numerical simulation; specific techniques include (geometric) singular perturbation theory, geometric desingularisation (“blow-up”), and asymptotic analysis, as well as low-rank approximation and coarse-graining.
Nonlinear partial differential equations, homogenisation (deterministic and stochastic), multiscale numerical methods, from discrete to continuum, bifurcation analysis & pattern formation. Multiscale modelling of biological systems and analysis and numerical simulations of mathematical models. Applications include transport processes in and mechanical properties of biofilms, biological tissues, cellular signalling processes, plant root and shoot growth, interactions between plant roots and soil, plant-soil-atmosphere system.
Research at the interface of optimisation theory (convex, nonconvex, and stochastic), Bayesian inference, and applications to high dimensional inverse problems. I am particularly interested in designing new optimisation methods, with theoretical guaranties, efficient to solve “real word” problems encountered in data science. Applications include computational imaging (e.g. in areas such as astronomy or biomedical), statistical graph processing (e.g. for computer vision), etc.
Modelling and simulation of complex socio-economic systems, Interaction and propagation on social networks, Network science, Human behaviour modelling, Financial markets and Econophysics, Cryptocurrencies, Agent-based simulations.
Explicit numerical algorithms for nonlinear random systems of (typically) high dimension and their interplay with data science techniques. Examples of these algorithms are stochastic approximation/stochastic gradient methods, explicit numerical schemes for stochastic (partial) differential equations, parameters and MCMC algorithms (TULA = Tamed Unadjusted Langevin Algorithm).
Calculus of variations and partial differential equations, homogenisation (deterministic and stochastic), harmonic analysis. Applications in material science: plasticity and dislocations, non-local aggregation problems, nonlinear elasticity, fracture and damage.
Collective behaviour, Bayesian inference, data-driven modelling, cell-level models, stem cells, developmental biology, regenerative medicine.
Mathematical modelling of spatiotemporal patterns in ecology, biology and medicine. Example projects:deconstructing models for vegetation patterning in semi-arid environments; mathematical modelling of cell adhesion in wound healing.
Machine Learning, Inference and Probabilistic Models: Deep learning and neural networks, machine learning markets, Hamiltonian Monte-Carlo, learning and inference in stochastic differential systems, stochastic optimization, game theory approaching in ML,.
Bayesian modelling and inference in stochastic processes for partially observed populations. Inter-disciplinary work involving statistical methodology applied in epidemiology, morbidity, actuarial mathematics and life sciences.
Probabilistic representations to construct efficient computational methods for high dimensional problems. Topics include non-linear, non-local PDEs, Mean-Field models, Particle Systems, Monte Carlo Methods, Deep Neural Networks, Statistical Sampling, Game Theory, Stochastic Control and Reinforcement learning.
My research interests are at the interface of numerical analysis, statistics and data science. I am particularly interested in uncertainty quantification in simulation with complex computer models, with recent research focussing on multilevel sampling methods, Bayesian inverse problems and Gaussian process emulators. Example projects: numerical analysis of Gaussian process emulators;efficient sampling methods for Bayesian inverse problems.
Fluid dynamics, mostly applied to oceanography, using geometric, asymptotic, stochastic and numerical methods. Example projects:mixing properties of multiphase flows inferred from PEPT data; geometric methods in oceanography.
My research interests lie on the intersection between statistics and machine learning, with a strong interest in Bayesian nonparametrics and developing novel methodology and computationally efficient inference for complex and high-dimensional data. Example project: nonlinear scalar-on-image regression models.
The use of deterministic and stochastic models to understand ecological and infectious disease systems. The models have applications to species conservation and disease managment strategies. Example projects: mathematical models of biological invasions; mathematical models of wildlife disease reservoirs.
My research interests lie in large scale inverse problems for computational imaging, with underpinning theory in sampling, optimisation, Bayesian inference, and machine learning. My research group specifically develops fast sensing techniques, fast parallel algorithms, and data dimensionality reduction techniques, with application to computational imaging in astronomy and medicine.
Stochastic analysis, its application to mathematical and computational finance, and the analysis of stochastic differential systems and their algebraic structures. Example project: numerical methods for financial market models
Marine Renewable Energy, Air-sea exchange of gases and particles, Global carbon cycle.
Euclidean harmonic analysis and its interactions with a variety of surrounding subject areas; integral geometry, number theory and Lie theory.
My research interests are in the field of optimization. I am interested the theoretical and methodological aspects as well as the development of optimization models and solution methods for real-life problems by exploiting the particular underlying structure of the problem. I am also particularly interested in computational aspects and the development of efficient implementation of the algorithms. As such, my interests are related to and overlap with all three aspects of MAC-MIGS, including modelling, analysis, and computation. I am especially interested in applications arising in various domains and, in particular, have experience on optimization problems arising from wireless networks, electricity markets, and logistics systems.