Areas of expertise
Research in the Department of Mathematics is concentrated in a number of diverse, fascinating areas of the subject of maths.
Explore the areas that our researchers specialise in, from algebra to uncertainty quantification.

Algebra
Algebra is the study of abstract objects arising from across mathematics, unifying apparently distant areas.
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Analysis and geometry
Analysis and geometry are core areas of mathematics which are also key to understanding many areas of theoretical physics.
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Approximation theory
Approximation theory is a key component of contemporary algorithms used in computational science and engineering.
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Biomechanics and transport processes
We investigate the mechanical properties of diverse biological structures, from individual cells to entire tissues and organisms.
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Dynamical systems
Dynamical systems describes time dependent behaviour, including chaos, in difference and differential equations and has applications across the sciences.
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Ergodic theory and dimension
Ergodic theory gives a probabilistic view of dynamics via measures. Different definitions of dimensions are used to characterize complicated (fractal) structures.
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Financial and insurance mathematics
Mathematical finance is concerned with mathematical/probabilistic modelling of financial markets. We promote and capitalise on the strong interplay between research in finance and insurance.
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Fluid dynamics
Our fluid dynamics research group is one of the largest within the UK and Europe and spans many important subareas of fluid dynamics research.
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Geophysics and planetary science
Our research in the area of geophysical and planetary science covers many areas including avalanche dynamics and the search for meteorites in the Antarctic.
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Granular materials
Despite their abundance in the world around us our understanding of the way that granular materials behave is still relatively basic. We're tackling issues ranging from fundamental understanding through to practical problems of importance to industry.
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Inverse problems
In inverse problems researchers look inside solid objects or deduce complex models from data using mathematics.
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Logic
Logic studies formal languages and reasoning, often focusing on the interplay between axiomatic theories and their models.
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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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Number theory
Number theory is an ancient area of mathematics involving the study of integers, wellknown for the simplicity of its statements and beauty of its proofs.
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Numerical linear algebra
Numerical linear algebra is at the heart of computational algorithms used in science and engineering, and in industry.
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Probability
One of the most intriguing problems that is ubiquitous in virtually every aspect of life is how to predict the outcome of a future event in which uncertainty plays a role.
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Scientific computing
Scientific computing is the study of the techniques that underpin disciplinespecific fields of computational science.
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Semigroups and semirings
A semigroup is an algebraic structure with a single associative binary operation; if it has an identity element it is called a 'monoid'.
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Solid mechanics and soft matter
The manner in which solid and soft materials deform is of critical importance in a range of applications. We're tackling a number of important problems, including the study of complex composites.
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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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Waves and metamaterials
The area of wave propagation covers a broad range of physical scenarios including acoustics, electromagnetic waves, water waves, nondestructive testing and seismic waves. Metamaterials aim to manipulate waves in novel ways.
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