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Our research combines diverse aspects of modelling and analysis, including developing and studying mathematical models of varied applications including blood flow, powder flow and hydrothermal eruptions.
We work on industrial problems involving physical systems and transport processes.
Differential equations are used in a wide range of applications. Our researchers focus on studying ordinary, partial, stochastic, delayed, discontinuous and non-local differential equations, and solving them analytically and numerically. We also have expertise in geometric integration and domain decomposition methods.
We are advancing theoretical aspects of dynamical system including developing and using multiscale methods and dimension reduction techniques for complex dynamical systems.
We also study applications including stellar dynamics and celestial mechanics, networks of coupled oscillators and cardio-respiratory system function.
We study non-linear elasticity, materials science and low dimensional topology and geometry, particularly hyperbolic geometry, discrete groups and their associated universal constants, and relations between arithmetic and geometry.
We model continuum mechanics, flow in porous media, heat and mass transfer, geophysical systems and pollution transport, stellar dynamics and celestial mechanics, breathing and gas exchange and the spread of infectious diseases.
We are using powerful mathematical techniques to investigate problems in physics, biophysics and interdisciplinary areas. The main focus is on theoretical particle physics, particularly the quark structure of matter and the properties of neutrinos. We also have expertise in random matrices.
We study special functions' properties, especially elliptic and theta functions and modular forms, and their applications in number theory and combinatorics.
Research focuses on the application of combinatorial techniques to a wide range of problems, including links in three and higher dimensions.
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The brain has tens of billions of neurons and is one of the most complicated networks that we know. This makes any analysis of brain function hugely time consuming.
Dr Carlo Laing is working with a colleague at Princeton University in the US on the phenomenon of spike timing dependent plasticity. This is where the strengths of connections between neurons are modified as a result of the precise “firing” times of individual neurons.
Many areas of modern science, such as climate science, physics, and chemistry, rely on solving large systems of equations on computers. Usually, these equations cannot be solved exactly and small errors can build up over time. Distinguished Professor Robert McLachlan and PhD student Christian Offen are working on new types of computational methods known as geometric integrators that give more reliable results by preserving certain features of the equations such as mass and energy.
Dr Alona Ben-Tal led a project that developed mathematical equations to describe how the avian respiratory system works. In birds, air flows in one direction during both inspiration and expiration, in an area of the lungs where gas exchange occurs. The project provides a new explanation on the way in which this unidirectional flow is generated.
Robert McLachlan was awarded a prestigious James Cook Fellowship by the Royal Society of New Zealand in 2012. The fellowships are awarded to researchers who have achieved national and international recognition in their area of scientific research.Distinguished Professor Robert McLachlan
James Cook Fellowship
Internationally renowned mathematician, Distinguished Professor Gaven Martin, and his former PhD student Timothy Marshall, have received the Kalman Prize for their work solving a problem formulated by Carl Ludwig Siegel in 1942. It asks to determine the minimal co-volume lattices of hyperbolic 3-space.Distinguished Professor Gaven Martin
Kalman Prize for 74-year-old-problem
Professor Mick Roberts was awarded $415,000 from the Royal Society's Marsden Fund for the research project 'Biodiversity and the ecology of emerging infectious diseases '.Professor Mick Roberts
Marsden funding for ecology of infectious diseases research
Professor Carlo Laing was awarded $415,000 from the Royal Society's Marsden Fund for the research project 'Function from structure: accurate reduced models of neuronal networks'.Professor Carlo Laing
Marsden funding for neural network research
Dr Gaven Martin has been awarded $671,000 for a project to advance nonlinear analysis and low dimensional topology and geometry.Distinguished Professor Gaven Martin
Marsden funding for nonlinear analysis and low dimensional topology and geometry
Dr David Simpson, along with Professor Paul Glendinning of the University of Manchester, received $500,000 for the project 'Organised chaos: Using geometry to explain robust chaotic dynamics in switched dynamical systems'.Dr David Simpson
Marsden funding for switched dynamical systems
In 2007 Distinguished Professor Robert McLachlan was awarded the Dalquist Prize. This international award recognises original contributions to fields in the area of numerical analysis as applied to differential equations.Distinguished Professor Robert McLachlan
SIAM Dalquist Prize