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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.
The human brain is a remarkable organ, but how did it evolve to give us such unprecedented cognitive abilities? ERC grantee Pierre Vanderhaeghen and his team from ULB, VIB-KU Leuven turned to the genome for answers: a specific set of genes, found only in humans, could play a determinant role on the size of our brain. Published today in Cell, Vanderhaeghen's EU-funded research helps to unlock the secrets of human evolution.
Prof. Gregoire Courtine believes paralysed patients will be able to walk again. This belief has represented the focus of years of work aimed at regenerating the functions of the spinal cord after injury. Thanks to his ERC funding in both 2010 and 2015, Prof. Courtine and his team have been able to develop so-called “personalised neuroprosthetics” that have led immobile rats, and more recently monkeys, to overcome their paralysis.
Ole Kamstrup, MD., MSc., is a pensioner and lives north of Copenhagen in Denmark. He has been diagnosed with Parkinson's disease ten years ago. Since 2013, Mr Kamstrup has been in contact with Professor Deniz Kirik, a neuroscientist at Lund University in Sweden. Professor Kirik, who was awarded an ERC Starting Grant in 2009, develops new therapies for Parkinson’s disease, using viral vectors to deliver therapeutic genes to the brain. An ERC Proof of Concept grant enabled him to start carrying out a market evaluation and writing a business plan for the promising therapy.
Originally published in March 2017 as part of the multimedia campaign "ERC - 10 years – 10 portraits."