School of Mathematical Sciences

Leverhulme Doctoral Scholarships


Modelling and Analytics for a Sustainable Society  


MASS: 'Modelling and Analytics for a Sustainable Society’ is an interdisciplinary doctoral training centre that aims to tackle the ongoing global problems of food shortages, water scarcity and insufficient clean energy. It brings together mathematicians with researchers from across the University developing improved crops, bioenergy sources and biological methods to clean contaminated water; renewable energy sources,storageand distribution.

Mathematics plays a crucial role in helping to understand resource use by quantifying and predicting the effects of alternative approaches through predictive modelling, statistical analysis and uncertainty quantification.

High-quality funded PhD opportunities

The programme will fund 15 fully-funded four-year PhD scholarships over three intakes; the first cohort of four students started their scholarships in September 2015. We are currently recruiting for the second cohort of six scholarships to commence in Autumn 2016.

The scholarships will cover PhD tuition fees for UK/EU students, plus a tax-free stipend of £14,057 per annum (2015/16 rate). While the scholarships may be held by students of all nationalities, the Leverhulme Trust has a particular interest in supporting UK or EU students. International students would be expected to cover the difference between international and UK/EU tuition fees (currently approximately £10,000 per annum).Students will be based within the School of Mathematical Sciences, and co-supervised by one or more academics from partner schools.


To apply for a scholarship on the programme, please consult the project list below and:

  • identify three projects of interest;
  • apply online via the University of Nottingham application page (for question 1a please select PhD in Mathematics - G10N);
  • in the personal statement section indicate that you are applying to the 'Mathematics for a Sustainable Society' programme;
  • make sure to include a ranked list of your three preferred projects, together with a CV of no more than two pages.

Applications will remain open until the scholarships are filled.

Available projects

For queries in relation to a particular project, please contact the supervisors associated with that project.

Energy projects

Bayesian inverse problems in the built environment

Supervisors: Dr Marco Iglesias (Mathematical Sciences), Dr Christopher Wood (Engineering)

Policy-making relies on modelling and simulation of the energy demand and performance of buildings. However, inaccurate predictions can arise from the uncertainty of thermal properties of structures such as walls. The student will develop fast and robust Bayesian inverse methods for characterisation of thermal properties of walls, using in-situ experimental data.

Sustainability applications of first-principles calculation of physical properties, via machine learning

Supervisors: Dr Richard Graham (Mathematical Sciences), Dr Richard Wheatley (Chemistry)

Carbon capture and storage (CCS) has the potential to hugely reduce CO2 emissions. However, CO2 from combustion contains many impurities, which affect the cost and safety of CCS. This PhD project will develop a fundamental understanding of impure CO2 by modeling the interactions between the constituent molecules. These interactions can be calculated from first-principles, but such calculations are too expensive numerically for most applications. We have recently developed a machine-learning technique that, via a small number of ab-initio calculations, can efficiently model the entire energy surface. This project will exploit this technique to create first-principles predictions of properties that are important to the safety, design and cost of CO2 pipelines.


Food projects

Modelling the physical and biological properties of soil

Supervisors: Professor Ian Dryden (Mathematical Sciences), Professor Sacha Mooney (Biosciences)

Soil quality and structure is critical for crop yield, however it is dynamic, with multiple factors influencing productivity. This project will model the physical and biological properties of soil, determining the impacts of irrigation, no till and environmental inputs. Statistical regression models will be developed in the topical area of Object Data Analysis, where geometrical objects are predicted using functional or geometrical covariates.

Bacterial infections in food animals as a problem for food security

Supervisors: Professor Michael Tretyakov (Mathematical Sciences), Dr Michael Jones (Veterinary Medicine and Science)

Campylobacter jejuni is a major cause of food-borne infections, and consequently a problem for food security. This project will develop stochastic models for C. jejuni mutation and selection and the evolution of antibiotic resistance. A significant mathematical challenge will be to estimate model parameters using a relatively small amount of in vitro and in vivo data. The student will be trained in foundations of microbiology and genetics as well as becoming an expert in stochastic modelling of biological processes and associated modern statistical techniques.

Mathematical modelling of the effect of temperature stress on crop fertility

Supervisors: Professor John King (Mathematical Sciences), Professor Zoe Wilson (Biosciences)

Increased temperatures during flowering have extreme affects on pollen development and thus reproductive success and yield in plants. It has been predicted that this may be the key factor in determining future productivity for many crops, particularly in the temperate cereals such as wheat and barley. This project will model the effects of temperature changes on reproductive success, focusing in particular on the impact this may have on yields for wheat.

It will also explore the influence of this temperature stress on the molecular pathways regulating pollen development by modelling of how the dynamic changes in hormone levels and gene expression are influenced by elevated temperature.

Towards sustainable antimicrobial use in agriculture: quantifying the risks of emergence of antimicrobial pathogens

Supervisors: Professor Michael Tretyakov (Mathematical Sciences), Dr Dov Stekel & Dr Jon Hobman (Biosciences)

Antimicrobial resistance is a major threat both to human and animal health. The majority of antibiotic use is in agriculture, thus the threat of antimicrobial resistance, and the appropriate use of antibiotics, are essential to sustainable agriculture and food production. The aim of this project is to develop mathematical models that can improve our capacity to predict the risk of emergence of antimicrobial resistant pathogens within a sustainable agriculture context. Specifically, the student will develop and analyze both spatially homogeneous and heterogeneous stochastic models for the spread of antimicrobial resistance between populations of bacteria in dairy slurry. The model will be based upon the real dairy slurry system in the University of Nottingham farm in Sutton Bonington.

In addition to being based in the sustainability programme, the project will be supported by on-going research in antimicrobial resistance in agriculture and will benefit from experimental measurements carried out by colleagues in Biosciences, Pharmacy and Engineering.


Water projects

Multi-scale modelling of flow through heterogeneous geo-materials

Supervisors: Dr Kris van der Zee (Mathematical Sciences), Dr Xia Li (Engineering)

Permeability of geomaterials is critical in predicting pollutant contamination and nitriation transport in groundwater. However, geo-materials are often heterogenous. The micro-defects and rock fractures provide channels for rapid groundwater flow, and consequently, the effective in-situ permeability could be larger than the lab measurement by several orders of magnitude.

This research will develop mathematical models to simulate the groundwater flow through heterogeneous geo-materials and the multi-scale homogenisation techniques that connects the field-scale permeability to intact rock properties and the statistics of micro-defects and fractures. The findings will inform and support effect groundwater management.


Society projects

The following project link specific resources to their societal context, and hence also appear in the resource sections above.

Engaging school teachers and learners in the mathematics of sustainability

Supervisors: Dr Ria Symonds (Mathematical Sciences), Dr Stephen Hibberd (Mathematical Sciences), Professor Andrew Noyes (Education)

In partnership with a small number of school mathematics departments, the student will design, develop and assess the effectiveness of curriculum materials that engage teachers and learners in the mathematics of sustainability [1]. The materials would support specific curricular goals (e.g. learning of algebra, proportional reasoning). The project will also investigate young people's understanding of sustainability and the effectiveness of the materials in enhancing this understanding and developing critical-mathematical literacy. 

[1] Maths Awareness Month, Sustainability Counts.  

Leverhulme Trust logo

The Leverhulme Trust

The centre is funded through the Leverhulme Doctoral Scholarships scheme by the Leverhulme Trust

a philanthropic organisation established by William Hesketh Lever, the founder of Lever Brothers, in 1925. MASS is one of 14 such centres funded around the UK.

Contact Us

For general enquiries about the MASS programme, please contact the admissions team.

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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