ERC FUNDED PROJECTS

The numerical simulation of complex compressible flow problem is still a challenge nowaday even for simple models. In our opinion, the most important hard points that need currently to be tackled and solved is how to obtain stable, scalable, very accurate, easy to code and to maintain schemes on complex geometries. The method should easily handle mesh refinement, even near the boundary where the most interesting engineering quantities have to be evaluated. Unsteady uncertainties in the model, for example in the geometry or the boundary conditions should represented efficiently.This proposal goal is to design, develop and evaluate solutions to each of the above problems. Our work program will lead to significant breakthroughs for flow simulations. More specifically, we propose to work on 3 connected problems: 1-A class of very high order numerical schemes able to easily deal with the geometry of boundaries and still can solve steep problems. The geometry is generally defined by CAD tools. The output is used to generate a mesh which is then used by the scheme. Hence, any mesh refinement process is disconnected from the CAD, a situation that prevents the spread of mesh adaptation techniques in industry! 2-A class of very high order numerical schemes which can utilize possibly solution dependant basis functions in order to lower the number of degrees of freedom, for example to compute accurately boundary layers with low resolutions. 3-A general non intrusive technique for handling uncertainties in order to deal with irregular probability density functions (pdf) and also to handle pdf that may evolve in time, for example thanks to an optimisation loop. The curse of dimensionality will be dealt thanks Harten's multiresolution method combined with sparse grid methods. Currently, and up to our knowledge, no scheme has each of these properties. This research program will have an impact on numerical schemes and industrial applications.

1 432 769 €

Start date: 2008-12-01, End date: 2013-11-30

The purpose of this project is to study basic questions in algebraic and Kähler geometry. It is well known that the structure of projective or Kähler manifolds is governed by positivity or negativity properties of the curvature tensor. However, many fundamental problems are still wide open. Since the mid 1980's, I have developed a large number of key concepts and results that have led to important progress in transcendental algebraic geometry. Let me mention the discovery of holomorphic Morse inequalities, systematic applications of L² estimates with singular hermitian metrics, and a much improved understanding of Monge-Ampère equations and of singularities of plurisuharmonic functions. My first goal will be to investigate the Green-Griffiths-Lang conjecture asserting that an entire curve drawn in a variety of general type is algebraically degenerate. The subject is intimately related to important questions concerning Diophantine equations, especially higher dimensional generalizations of Faltings' theorem - the so-called Vojta program. One can rely here on a breakthrough I made in 2010, showing that all such entire curves must satisfy algebraic differential equations. A second closely related area of research of this project is the analysis of the structure of projective or compact Kähler manifolds. It can be seen as a generalization of the classification theory of surfaces by Kodaira, and of the more recent results for dimension 3 (Kawamata, Kollár, Mori, Shokurov, ...) to other dimensions. My plan is to combine powerful recent results obtained on the duality of positive cohomology cones with an analysis of the instability of the tangent bundle, i.e. of the Harder-Narasimhan filtration. On these ground-breaking questions, I intend to go much further and to enhance my national and international collaborations. These subjects already attract many young researchers and postdocs throughout the world, and the grant could be used to create even stronger interactions.

1 809 345 €

Start date: 2015-09-01, End date: 2020-08-31

Malaria parasite infection in humans has been called “the strongest known force for evolutionary selection in the recent history of the human genome”, and I hypothesize that a similar statement may apply to the mosquito vector, which is the definitive host of the malaria parasite. We previously discovered efficient malaria-resistance mechanisms in natural populations of the African malaria vector, Anopheles gambiae. Aim 1 of the proposed project will implement a novel genetic mapping design to systematically survey the mosquito population for common and rare genetic variants of strong effect against the human malaria parasite, Plasmodium falciparum. A product of the mapping design will be living mosquito families carrying the resistance loci. Aim 2 will use the segregating families to functionally dissect the underlying molecular mechanisms controlled by the loci, including determination of the pathogen specificity spectra of the host-defense traits. Aim 3 targets arbovirus transmission, where Anopheles mosquitoes transmit human malaria but not arboviruses such as Dengue and Chikungunya, even though the two mosquitoes bite the same people and are exposed to the same pathogens, often in malaria-arbovirus co-infections. We will use deep-sequencing to detect processing of the arbovirus dsRNA intermediates of replication produced by the RNAi pathway of the mosquitoes. The results will reveal important new information about differences in the efficiency and quality of the RNAi response between mosquitoes, which is likely to underlie at least part of the host specificity of arbovirus transmission. The 3 Aims will make significant contributions to understanding malaria and arbovirus transmission, major global public health problems, will aid the development of a next generation of vector surveillance and control tools, and will produce a definitive description of the major genetic factors influencing host-pathogen interactions in mosquito immunity.

2 307 800 €

Start date: 2013-03-01, End date: 2018-02-28

"This project is concerned with problems that involve a very large number of variables, and whose efficient numerical treatment is challenged by the so-called curse of dimensionality, meaning that computational complexity increases exponentially in the variable dimension. The PI intend to establish in his host institution a scientific leadership on the mathematical understanding and numerical treatment of these problems, and to contribute to the development of this area of research through international collaborations, organization of workshops and research schools, and training of postdocs and PhD students. High dimensional problems are ubiquitous in an increasing number of areas of scientific computing, among which statistical or active learning theory, parametric and stochastic partial differential equations, parameter optimization in numerical codes. There is a high demand from the industrial world of efficient numerical methods for treating such problems. The practical success of various numerical algorithms, that have been developed in recent years in these application areas, is often limited to moderate dimensional setting. In addition, these developments tend to be, as a rule, rather problem specific and not always founded on a solid mathematical analysis. The central scientific objectives of this project are therefore: (i) to identify fundamental mathematical principles behind overcoming the curse of dimensionality, (ii) to understand how these principles enter in relevant instances of the above applications, and (iii) based on the these principles beyond particular problem classes, to develop broadly applicable numerical strategies that benefit from such mechanisms. The performances of these strategies should be provably independent of the variable dimension, and in that sense break the curse of dimensionality. They will be tested on both synthetic benchmark tests and real world problems coming from the afore-mentioned applications."

1 848 000 €

Start date: 2014-01-01, End date: 2018-12-31