ERC FUNDED PROJECTS

"The A2C2 project treats two major challenges in climate and atmospheric research: the time dependence of the climate attractor to external forcings (solar, volcanic eruptions and anthropogenic), and the attribution of extreme climate events occurring in the northern extra-tropics. The main difficulties are the limited climate information, the computer cost of model simulations, and mathematical assumptions that are hardly verified and often overlooked in the literature. A2C2 proposes a practical framework to overcome those three difficulties, linking the theory of dynamical systems and statistics. We will generalize the methodology of flow analogues to multiple databases in order to obtain probabilistic descriptions of analogue decompositions. The project is divided into three workpackages (WP). WP1 embeds the analogue method in the theory of dynamical systems in order to provide a metric of an attractor deformation in time. The important methodological step is to detect trends or persisting outliers in the dates and scores of analogues when the system yields time-varying forcings. This is done from idealized models and full size climate models in which the forcings (anthropogenic and natural) are known. A2C2 creates an open source toolkit to compute flow analogues from a wide array of databases (WP2). WP3 treats the two scientific challenges with the analogue method and multiple model ensembles, hence allowing uncertainty estimates under realistic mathematical hypotheses. The flow analogue methodology allows a systematic and quasi real-time analysis of extreme events, which is currently out of the reach of conventional climate modeling approaches. The major breakthrough of A2C2 is to bridge the gap between operational needs (the immediate analysis of climate events) and the understanding long-term climate changes. A2C2 opens new research horizons for the exploitation of ensembles of simulations and reliable estimates of uncertainty."

1 491 457 €

Start date: 2014-03-01, End date: 2019-02-28

The primary purpose of this project is to build on recent spectacular progress in the Langlands program to study the arithmetic properties of automorphic motives constructed in the cohomology of Shimura varieties. Because automorphic methods are available to study the L-functions of these motives, which include elliptic curves and certain families of Calabi-Yau varieties over totally real fields (possibly after base change), they represent the most accessible class of varieties for which one can hope to verify fundamental conjectures on special values of L-functions, including Deligne's conjecture and the Main Conjecture of Iwasawa theory. Immediate goals include the proof of irreducibility of automorphic Galois representations; the establishment of period relations for automorphic and potentially automorphic realizations of motives in the cohomology of distinct Shimura varieties; the construction of p-adic L-functions for these and related motives, notably adjoint and tensor product L-functions in p-adic families; and the geometrization of the p-adic and mod p Langlands program. All four goals, as well as the others mentioned in the body of the proposal, are interconnected; the final goal provides a bridge to related work in geometric representation theory, algebraic geometry, and mathematical physics.

1 491 348 €

Start date: 2012-06-01, End date: 2018-05-31

Actanthrope intends to promote a neuro-robotics perspective to explore original models of anthropomorphic action. The project targets contributions to humanoid robot autonomy (for rescue and service robotics), to advanced human body simulation (for applications in ergonomics), and to a new theory of embodied intelligence (by promoting a motion-based semiotics of the human action). Actions take place in the physical space while they originate in the –robot or human– sensory-motor space. Geometry is the core abstraction that makes the link between these spaces. Considering that the structure of actions inherits from that of the body, the underlying intuition is that actions can be segmented within discrete sub-spaces lying in the entire continuous posture space. Such sub-spaces are viewed as symbols bridging deliberative reasoning and reactive control. Actanthrope argues that geometric approaches to motion segmentation and generation as promising and innovative routes to explore embodied intelligence: - Motion segmentation: what are the sub-manifolds that define the structure of a given action? - Motion generation: among all the solution paths within a given sub-manifold, what is the underlying law that makes the selection? In Robotics these questions are related to the competition between abstract symbol manipulation and physical signal processing. In Computational Neuroscience the questions refer to the quest of motion invariants. The ambition of the project is to promote a dual perspective: exploring the computational foundations of human action to make better robots, while simultaneously doing better robotics to better understand human action. A unique “Anthropomorphic Action Factory” supports the methodology. It aims at attracting to a single lab, researchers with complementary know-how and solid mathematical background. All of them will benefit from unique equipments, while being stimulated by four challenges dealing with locomotion and manipulation actions.

2 500 000 €

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

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