Mathematics Institute News
- Filip Rindler awarded EPSRC Fellowship (24th February 2014)
- Martin Hairer & José Luis Rodrigo win ERC Consolidator grants (4th February 2014)
24th February 2014
Filip Rindler awarded EPSRC Fellowship
Filip Rindler, a Warwick Zeeman Lecturer, has been awarded a 3-year EPSRC Fellowship to investigate Singularities in Nonlinear PDEs which is to start in October 2014 and which includes funding for a related workshop.
This project aims to further the theoretical understanding of singularities, manifested as oscillations and concentrations, in solutions to nonlinear partial differential equations. Since such singularities are not only physically relevant, but also present many technical challenges in the pursuit to prove meaningful assertions about PDEs, this proposal bridges theoretical and applied mathematics. On the applied side, it is related to material microstructure (for example in alloys) and the emergence of complex macroscopic material behaviour from microscopic oscillations. On the theory side, oscillations and concentrations precisely distinguish between weak and strong compactness of sequences in Lebesgue and Sobolev spaces and “quantifying” this difference in a meaningful way is a pivotal goal of this project. Based on recently developed new tools, we aim to improve our understanding of these phenomena and to develop new applications to concrete PDE questions. Collaborations are planned with both applied and theoretical researchers in the field. Furthermore, as part of the grant, a research workshop on the topic will be organised.
4th February 2014
Martin Hairer & José Luis Rodrigo win ERC Consolidator grants
The European Research Council (ERC) has awarded two of its new ERC Consolidator Grants to Warwick mathematicians Martin Hairer and José Luis Rodrigo, the only awards in the UK for mathematics. A further two grants were awarded to Warwick in Chemistry. These prestigious new awards will enable already independent excellent researchers to consolidate their own research teams and to develop their most innovative ideas across the European Research Area.
President of the ERC, Professor Jean-Pierre Bourguignon commented: “I am very impressed by the quality of the selected projects. Judging by the ever increasing demand for ERC grants, especially from early- and mid-career researchers, it is clear that funding of this kind is much needed.”
European Commissioner for Research, Innovation and Science Máire Geoghegan-Quinn said: “These researchers are doing ground-breaking work that will advance our knowledge and make a difference to society. The ERC is supporting them at a key moment where funding is often hard to come by: when they need to move forward in their career and develop their own research and teams.”
Martin Hairer's project studies Behaviour near criticality. One of the main challenges of modern mathematical physics is to understand the behaviour of systems at or near criticality. In a number of cases, one can argue heuristically that this behaviour should be described by a nonlinear stochastic partial differential equation. Some examples of systems of interest are models of phase coexistence near the critical temperature, one-dimensional interface growth models, and models of absorption of a diffusing particle by random impurities. Unfortunately, the equations arising in all of these contexts are mathematically ill-posed to the extent that they defeat all current stochastic PDE techniques.
Recently, the theory of regularity structures has allowed us to give a rigorous mathematical interpretation to such equations and to build the mathematical objects conjectured to describe the above-mentioned systems near criticality. The aim of the proposal is to study the convergence of a variety of concrete microscopic models to these limiting objects. The project will yield unique insight in the large-scale behaviour of a number of physically relevant systems in regimes where both nonlinear effects and random fluctuations compete with equal strength.
José Luis Rodrigo's project concerns 3D Euler, Vortex Dynamics and PDE which deals with a collection of problems in analysis and partial differential equations arising from fluid mechanics. In particular, the main equation under consideration is the three dimensional Euler equation (for the evolution of an incompressible, inviscid fluid). Main objectives include the understanding of the evolution of isolated vortex lines for this equation, and the construction and understanding of the geometry and evolution of highly concentrated vortex tubes.
ERC Press release (PDF)