Doctoral research positions available in mathematical sciences and its applications. SAMBa offers a 4-year PhD programme, including initial training to develop breadth of knowledge and research skills.

Introduction to the SAMBa Programme

SAMBa offers a 4-year PhD programme, including initial training to develop breadth of knowledge and research skills.

The initial phase of SAMBa consists of courses, projects and symposia tailored to the individual student, together with Integrative Think Tanks (ITTs). ITTs are facilitated, week-long, off-campus workshops involving around 50-80 participants. They include postgraduate students, academics from mathematical sciences, application-focused researchers, and collaborators from around the world. Students work in collaboration with academics and industrialists to synthesise relevant mathematical formulations for addressing industrial and cross-disciplinary problems.

Students can either pursue an industry co-designed PhD project developed from an ITT (see below for projects currently available), or a project formulated with an academic supervisor during the training phase. All students will work intensively on PhD research in years 2-4.

Throughout your training we will offer a wide range of activities to complement your PhD, such as conference and workshop participation, placement and secondment opportunities, and industrial and international collaboration.

SAMBa graduates work in academia, industry and governmental organisations, and are ready to work in leading academic and industrial roles, collaborating with individuals from different backgrounds, and communicating effectively to both experts and nonexperts.

We are open for applications for entry in September 2024. There is currently no formal deadline, but you are encouraged to apply early as we have limited places available.

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Integrative Think Tanks

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Research areas

SAMBa students receive training and carry out research across statistics, mathematical modelling (deterministic and probabilistic) and numerical methods. SAMBa currently has a vibrant cohort of 85 students carrying out research in areas including:

  • inverse problems
  • image processing
  • optimisation
  • Monte Carlo methods
  • spatio-temporal statistical modelling
  • asymptotic analysis
  • stochastic processes on graphs and networks
  • mathematical and statistical physics
  • fluid mechanics
  • mathematical machine learning
  • interacting particle systems
  • dynamical systems

The department has significant expertise in mathematical machine learning and there will be opportunities to receive training in this area.

Application & industrial areas

Topics range from problems which are industrially motivated, to more abstract problems. Application and industrial areas include:

  • healthcare
  • epidemiology
  • biology
  • environment and natural hazards
  • energy and transportation
  • materials imaging and spectroscopy

You will have the opportunity to pursue an industry co-designed PhD project developed from an ITT, or a project formulated with an academic supervisor during the training phase.

The projects shown below have been co-designed with our industrial partners. If you have an interest in one of these projects, please let us know when you submit your expression of interest (see How to Apply).

1. Landslide prediction

Landslide prediction in Brazil
Partner: CEMADEN
Supervisor: Tristan Pryer

This PhD project aims to develop an advanced mathematical framework to predict landslides, a critical endeavor given the devastating impacts of such events, exemplified by the 2011 catastrophe in Rio de Janeiro, Brazil, which resulted in significant loss of life and economic damage. Brazil’s energy infrastructure, predominantly hydroelectric, is particularly vulnerable, with transmission lines traversing landslide-prone mountainous terrains to supply power to major urban and industrial centres.

The project will focus on constructing a robust landslide prediction methodology, integrating local hydrological modelling with geotechnical and geophysical data. This methodology will be applied to high-risk areas in Brazil, serving as an operational model for the National Centre for Monitoring and Alerts of Natural Disasters (CEMADEN), enabling real-time prediction and mitigation of potential landslides. The mathematical models developed will be pivotal in understanding the intricate dynamics of landslides, providing insights into the interplay between various environmental factors and offering a foundation for developing preventive strategies, thus contributing to the safeguarding of lives and infrastructure in regions susceptible to such extreme events.

2. Radiotherapy treatment planning

Quantifying the personalised impact of physical and biological uncertainties in customised radiotherapy treatment planning
Partner: National Physical Laboratory
Supervisor: Tristan Pryer

Radiotherapy (RT) is a major modality in the management of cancer, either alone or in combination with other treatments. The goal of RT is to deliver a highly localised dose to the tumour whilst sparing healthy tissue, thus aiming to give the highest probability of curing cancer while reducing the risk of side effects.

The complexity of RT and the technology is constantly evolving to deliver higher precision treatment, which comes at the cost of being more susceptible to treatment delivery (physical) and patient response (biological) uncertainties, which are currently not combined. For example, large biological uncertainties due to individual sensitivity of patients to radiation and physical uncertainties, which are normally negligible, could significantly alter treatment outcome. An accurate understanding of the sources and magnitudes of these uncertainties is essential for producing treatment plans which give the highest chance of delivering the desired treatment outcome. It is currently unclear how to incorporate all elements that contribute to plan uncertainty into a single protocol nor which assessment metrics to use.

This PhD project, in collaboration with the National Physical Laboratory, aims to help produce safer, more targeted treatments by quantifying the personalised impact of physical and biological uncertainties in customising radiotherapy treatment planning. The goal is to develop a mathematical formalism for the evaluation of uncertainty quantification, guidance on combining and incorporating uncertainties into high precision, minimally invasive and maximum impact personalised treatment plans to improve clinical outcomes.

3. Transport across the placenta

Transport of agrochemicals across the placenta
Partner: Syngenta
Supervisor: Jennifer Tweedy

This project is in collaboration with Syngenta, who manufacture agrochemicals. The placenta is an organ that develops in the uterus of a mother-to-be during pregnancy. It fulfils several key roles, including facilitating transfer of oxygen and nutrients required for fetal development from the maternal to the fetal blood, removal of waste products from the fetal blood and synthesising special pregnancy hormones.

This project will focus on developing a mathematical model of maternal-to-fetal transport for certain chemicals. As well as oxygen and nutrients, other substances in the maternal blood can transfer to the fetus, and this project is particularly concerned with so-called endocrine-disrupting chemicals, which may be present in agrochemicals, and whose properties directly influence fetal development. Transport across the tissue separating maternal and fetal blood takes place in a variety of ways, depending on the chemical involved: small molecules are transported by passive diffusion across the tissue, larger molecules diffuse through specialised channels, other molecules are transported via active transport by specialised transporters, and yet others by subcellular vesicles. Transport mechanisms also depend on properties such as hydrophobicity and hydrophilicity and whether the molecule is polarised. Thus, predicting transfer rates is not always straightforward. The aim is to predict placental transfer for compounds relevant to the agricultural industry.

4. Analysis of flood models

Benchmarking analysis of flood models and their response to climate and other perturbations
Partner: Environmental Agency and JBA TrustSupervisor: Phil Trinh

Over the last few years, together with Dr. Piotr Morawiecki (SAMBa student 2019-2023) and Phil Trinh (Bath, Mathematics), we have been developing powerful mathematical methods improving our understanding statistical, physical, and conceptual models of flooding. These projects have grown through multiple successful Integrative Think Tanks between Bath and the Environmental Agency and JBA Trust. These interactions have stressed the importance of better modelling and predictive tools, with flood risk considered as one of the most significant risks to public and economy in the UK.However, there is an unusual situation that has emerged in the science of flood prediction, which is that there exists hundreds of competing models. As indicated by Keith Beven in 2018: “We currently have a situation in hydrology where a wide variety of models are used to do essentially the same types of predictions and future projections of river flows and other variables of interest”. Moreover, as the world pivots towards data-centric and machine-learning models, it becomes increasingly important to better understand the underlying mechanisms of models—and to provide rigorous theory on their limitations.This PhD will be driven by this need to develop rigorous mathematical theory on the “whys and hows” of flood prediction. The student will use techniques known as asymptotic analysis to produce a framework for how models should behave in certain limits of interest (like high periods of rain, like steeply sloped areas, etc.). The student will also work together with the Environmental Agency, the JBA Trust, and other collaborators to benchmark models used in industry, and to study the intrinsic differences between such models. Finally, there is wide scope to study interesting features of predictive models of flooding, such as the effects of flash flooding or the effects of complex drainage features (i.e. different soils, rocks, etc. and their effects).Interested students would be interested-in learning or already have a background in: (i) physical applied mathematics; (ii) fluid/continuum mechanics; (iii) physics and the natural sciences; (iv) modelling.For more information, see the recent PhD work of Piotr Morawiecki: 

5. Ptychography imaging

Mathematics of ptychography imaging
Partner: Diamond Light Source
Supervisor: Sergey Dolgov

This project concerns the development of new mathematical algorithms and their software implementation for X-ray ptychography. Ptychography computes a high-resolution image by assimilating many lower resolution images, or diffraction patterns. However, this assimilation is a challenging mathematical problem, and fast and reliable ptychography reconstruction methods are still sought. In addition to working on theoretical and numerical aspects of new imaging algorithms, you would have an opportunity to join experimental sessions in a lab. This project is run jointly by the University of Bath and Diamond Light Source Ltd (DLS), subject to contract. DLS is the UK’s national synchrotron facility located at the Harwell Science and Innovation Campus near Oxford that produces high brilliance X-rays in order to investigate a broad range of science areas, from the physical to life sciences.

X-ray imaging is limited by the performance of the available lenses. By replacing the objective lens of the imaging system with a reconstruction algorithm, ptychography can provide the ultimate in spatial resolution and phase sensitivity – assuming the non-convex optimisation problem underpinning the ptychography can be solved to the global minimiser. To make this problem more tractable, the project will investigate novel optimisation and regularisation methods, such as low-rank constraints on the image.

Thanks to the penetration power of X-rays, X-ray ptychography can be easily combined with tomography providing nanoscale electron density maps in 3D. Combing ptychographic-tomography (PXCT) with near-edge spectroscopy methods, such as XANES, it is now possible to extend these into a hyperspectral map, including spatially distributed chemical information. However, the data produced for this are currently vast and the combination of collection and reconstruction times are limiting the application of the method. Another theme to the project is to tackle this big data problem and associated time burden, in terms of both experimental and computing time. This will be done by undersampling the data collection, with accurate reconstruction still being possible due to the significant information redundancy in the data as a whole. An example of this would be to exploit the strong correlation between images at neighbouring energies.

Project keywords: imaging, inverse problems, optimisation, ptychography, optics.