School of Mathematical Sciences

Leverhulme Doctoral Scholarships


Mathematics for a Sustainable Society 


Mathematics for a Sustainable Society (MASS) 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.

Mathematical analysis of 4D micro CT data for crack propagation in power electronics

Supervisors: Dr Yves van Gennip (Mathematical Sciences), Dr Pearl Agyakwa (Engineering)

Wire bonds are an essential but life-limiting component of most power electronic modules used in renewable energy generation. The student will use time varying tomography data to study defect formation in wire bonds. New Bregman methods will be developed for nonlinear denoising, Ginzburg-Landau segmentation will be adapted to identify the wires and defects, and 4D optimal transport and optical flow methods with novel material guided costs for registration. These highly novel approaches will offer a superior and non-destructive technique to study wire defects and predict component lifetimes.

Social-network inspired agent-based models to test strategies for behaviour change

Supervisors: Professor Markus Owen & Dr Daniele Avitabile (Mathematical Sciences), Professor Darren Robinson (Engineering)

This project will integrate expertise from quantitative behavioural modelling, sociology, computer science and mathematics in order to develop social-networking inspired agent based models for patterns of energy use. Rather than only brute-force simulations, we will develop and use state-of-the-art numerical methods to detect tipping points in behaviour. In contrast to traditional empirical behavioural models, this work will enable the testing of strategies for bringing about changes in investment and operational behaviour.


Food projects

Vertical farming

Supervisors: Dr Chris Brignell (Mathematical Sciences), Dr Chungui Lu (Biosciences)

This project will develop statistical models and employ optimisation techniques to assess the costs and benefits of vertical farming as an urban alternative to traditional food production, which is constrained by the limited availability of high quality agricultural land. This analysis will encompass inputs (including energy and water) and yields, waste production, logistical efficiency (e.g. by producing locally grown food) and consumer perceptions of such growing regimes. This will determine the opportunities and impacts for production of food in urban environments.

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.

Statistical analysis of agricultural/soils/climate data to aid food security under environmental change

Supervisors: Professor Andy Wood (Mathematical Sciences), Professor Neil Crout (Biosciences)

Crop yield increases are hampered by environmental change and in particular extremes of weather. This project will utilise agricultural/soils/climate data to model crop productivity and develop effective strategies for maintaining yield, thus developing the ability to ensure food security under environmental change.

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 temp 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.

Mathematical modelling for sustainable crops: using SimRoot to optimise root growth and nutrient uptake

Supervisors: Professor Markus Owen (Mathematical Sciences), Professor Malcolm Bennett (Biosciences) & Jonathan Lynch (Biosciences)

The dynamic architecture of plant roots can be a crucial determinant of crop growth and yields, and is hence of widespread interest in the context of food security. Furthermore, links with water and fertiliser use place root growth firmly in the energy-food-water nexus. This project will use and develop innovative mathematical and computational models (using SimRoot) of the growth of wheat root systems and uptake of nutrients by those systems. Simulating the impact of root architecture and soil properties on the uptake of water and nutrients, such as nitrate and phosphate, will help to optimise wheat performance. The project will draw on state-of-the-art data from the non-invasive imaging of wheat roots in soil, using X-ray Computed Tomography (μCT). 


Water projects

Evaluating antimicrobial resistance in dairy farming: understanding real world interactions within the wastewater slurry environment

Supervisors: Professor John King (Mathematical Sciences), Dr Jon Hobman, Professor Chris Dodd & Dr Stephen Ramsden (Biosciences), Professor Dave Barrett (Pharmacy), Dr Rachel Gomes (Engineering)

Antimicrobial resistance is a growing global problem where we face a rise in the number of bacteria becoming resistant to existing antibiotics. The environment plays an important role, as does the way humans and animals interact with the environment. The dairy farm environment plays an integral role to water quality and food security, where the health of the dairy herd is supported through application of antibiotics. This research will aim to develop a mathematical model of spread of antibiotic resistance and antibiotic prevalence in wastewater slurry systems that will seek to quantify the risk of emergence and spread of antibiotic resistant human and animal pathogens within our dairy farm system, linking this to herd treatment and farming practices; identify measures that could mitigate against these risks; and model the economic and societal impacts associated with these risks and interventions in dairy farms operating on a similar basis.

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.

Social-network inspired agent-based models to test strategies for behaviour change

Supervisors: Professor Markus Owen (Mathematical Sciences), Professor Darren Robinson (Engineering), Dr Daniele Avitabile (Mathematical Sciences)

This project will integrate expertise from quantitative behavioural modelling, sociology, computer science and mathematics in order to develop social-networking inspired agent based models for patterns of energy use. Rather than only brute-force simulations, we will develop and use state-of-the-art numerical methods to detect tipping points in behaviour. In contrast to traditional empirical behavioural models, this work will enable the testing of strategies for bringing about changes in investment and operational behaviour.

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

telephone: +44 (0) 115 951 4949
fax: +44 (0) 115 951 4951