Statistics, inverse problems, uncertainty quantification and data science
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Our researchers combine statistical and mathematical models, data science and computational algorithms to solve realworld problems.
To tackle the complex challenges of modern society, and due to increases in available computing power and data, traditional disciplines in statistics and applied mathematics are merging into exciting new interdisciplinary fields.
Building on a strong tradition of statistics and numerical analysis in Manchester, our researchers work in a range of interconnected areas, combining statistics, mathematical models, data science and computational algorithms to solve problems arising in engineering, life sciences and public health.
Areas of expertise
From methodological research to data analysis and development of software, we have expertise in the following core areas:

Inverse problems
In inverse problems researchers look inside solid objects or deduce complex models from data using mathematics.
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Mathematical epidemiology
The mathematical epidemiology area of expertise in the Department of Mathematics at The University of Manchester is interested in a diverse range of methodological approaches and applications to infectious and chronic disease modelling.
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Mathematical foundations of data science and AI
Data science refers to the study of theory, methods, algorithms, and applications focused around data, and is a highly interdisciplinary subject which relies on solid foundations of mathematical and statistical fundamentals.
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Statistics
Statistics is concerned with the analysis and interpretation of data, the design of experiments and decisionmaking under uncertainty.
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Uncertainty quantification
Uncertainty quantification is a modern interdisciplinary science that cuts across traditional research groups and combines statistics, numerical analysis and computational applied mathematics.
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Research seminars
Research seminars on topics associated with statistics, inverse problems, uncertainty quantification and data science take place regularly in the following series:
PhD research opportunities
We welcome applications for PhD study in all areas of statistics, inverse problems, uncertainty quantification and mathematical aspects of data science. PhD enquiries related to this theme can be directed to Sean Holman (applied mathematics and numerical analysis) and Olatunji Johnson (statistics projects).
Before applying: visit the 'areas of expertise' pages listed above to find out more about potential PhD supervisors.
To discover the PhD opportunities available in the Department of Mathematics, explore our Postgraduate research in mathematics.