The amount of currently available biomedical data is overwhelming. Large databases exist at different scales, from genes, to proteins, to patients' histories. But what do scientists do with all this information? Serbian-born Professor Nataša Pržulj, from University College London, works with Big Data to establish patterns and gain knowledge that could revolutionise how we treat diseases.
Group theory, functional analysis and ergodic theory – three distinct areas of mathematics that meet within the theory of von Neumann algebras. The RIGIDITY project, funded by the ERC, aims to classify families of von Neumann algebras.
Understanding complex structures means separating irrelevant information to get to something simpler and easier to understand. When you look at something from a distance – although you don’t see all the details, you can still describe what you see. ERC grantee Balázs Szegedy has developed several mathematical tools for providing a compressed yet useful view of complex structures.
How does one infer the dynamics of a DNA minicircle in solution? How does one align the neuronal firing patterns of several neurons across individuals? These questions are intrinsically statistical, but nevertheless escape the traditional tools of statistics. The ComplexData project investigated such questions from a mathematical and an applied context.
Once limited to modelling physical problems in engineering, today Partial Differential Equations (PDEs) are used by a diverse array of fields, from natural resources to meteorology, aeronautics, oil and gas and biomedicine – to name only a few. But key mathematical issues remain unsolved, particularly when addressing their control, a must in technological transfer. The ERC-funded DYCON project aims to find answers.
Funded by the ERC, Prof. Anna Wienhard studies several new geometric forms that have been discovered over the past 20 years. These structures are closely related to the generalisation of Teichmüller space, which describes how the surface of a pretzel can be endowed with the geometry of an Escher painting.
How do you study arithmetic objects like integer points using the theory of dynamical systems? The answer is homogenous dynamics, and this connection goes both ways. The GMODGAMMADYNAMICS project, funded by an ERC grant, took a broad approach towards studying this rich interplay.
Chaotic systems are everywhere: the weather, molecules in a gas, the stock market. Small variations in initial conditions can lead to a drastically different time evolution, a phenomenon known as the butterfly effect. Systems can be classified according to how fast different, nearby initial conditions diverge in time. Supported by the ERC, Prof. Corinna Ulcigrai is investigating systems for which nearby initial conditions diverge slowly in time, to uncover mechanisms which explain their complex behaviour.
Travellers already benefit from applications harnessing data from sensor networks and smartphone users. They calculate alternative routes, help plan carpooling routes, or support the optimisation of public transport. With her ERC grant, Prof. Vana Kalogeraki works on a comprehensive software framework that will simplify the development of such mobile human-centred systems and make them more predictable and reliable.
Is a precise answer always better than a slightly less detailed one? Not necessarily. Some problems could take forever to compute and tie up vast IT capacity. Where solutions are needed urgently, e.g. in business or manufacturing, near-enough can be more than enough. ERC-funded research has produced a library of fast, powerful approximation algorithms.
