ERC FUNDED PROJECTS

The fundamental 3D-BioMat project aims at providing a biomineralization model to explain the formation of microscopic calcareous single-crystals produced by living organisms. Although these crystals present a wide variety of shapes, associated to various organic materials, the observation of a nanoscale granular structure common to almost all calcareous crystallizing organisms, associated to an extended crystalline coherence, underlies a generic biomineralization and assembly process. A key to building realistic scenarios of biomineralization is to reveal the crystalline architecture, at the mesoscale, (i. e., over a few granules), which none of the existing nano-characterization tools is able to provide. 3D-BioMat is based on the recognized PI’s expertise in the field of synchrotron coherent x-ray diffraction microscopy. It will extend the PI’s disruptive pioneering microscopy formalism, towards an innovative high-throughput approach able at giving access to the 3D mesoscale image of the crystalline properties (crystal-line coherence, crystal plane tilts and strains) with the required flexibility, nanoscale resolution, and non-invasiveness. This achievement will be used to timely reveal the generics of the mesoscale crystalline structure through the pioneering explorations of a vast variety of crystalline biominerals produced by the famous Pinctada mar-garitifera oyster shell, and thereby build a realistic biomineralization scenario. The inferred biomineralization pathways, including both physico-chemical pathways and biological controls, will ultimately be validated by comparing the mesoscale structures produced by biomimetic samples with the biogenic ones. Beyond deciphering one of the most intriguing questions of material nanosciences, 3D-BioMat may contribute to new climate models, pave the way for new routes in material synthesis and supply answers to the pearl-culture calcification problems.

1 966 429 €

Start date: 2017-03-01, End date: 2022-02-28

The understanding of spatial, social and dynamical organization of large numbers of agents is presently a fundamental issue in modern science. ADORA focuses on problems motivated by biology because, more than anywhere else, access to precise and many data has opened the route to novel and complex biomathematical models. The problems we address are written in terms of nonlinear partial differential equations. The flux-limited Keller-Segel system, the integrate-and-fire Fokker-Planck equation, kinetic equations with internal state, nonlocal parabolic equations and constrained Hamilton-Jacobi equations are among examples of the equations under investigation. The role of mathematics is not only to understand the analytical structure of these new problems, but it is also to explain the qualitative behavior of solutions and to quantify their properties. The challenge arises here because these goals should be achieved through a hierarchy of scales. Indeed, the problems under consideration share the common feature that the large scale behavior cannot be understood precisely without access to a hierarchy of finer scales, down to the individual behavior and sometimes its molecular determinants. Major difficulties arise because the numerous scales present in these equations have to be discovered and singularities appear in the asymptotic process which yields deep compactness obstructions. Our vision is that the complexity inherent to models of biology can be enlightened by mathematical analysis and a classification of the possible asymptotic regimes. However an enormous effort is needed to uncover the equations intimate mathematical structures, and bring them at the level of conceptual understanding they deserve being given the applications motivating these questions which range from medical science or neuroscience to cell biology.

2 192 500 €

Start date: 2017-09-01, End date: 2022-08-31

The goal of this project is to investigate two conjectures in arithmetic geometry pertaining to the geometry of projective varieties over finite and number fields. These two conjectures, formulated by Tate and Grothendieck in the 1960s, predict which cohomology classes are chern classes of line bundles. They both form an arithmetic counterpart of a theorem of Lefschetz, proved in the 1940s, which itself is the only known case of the Hodge conjecture. These two long-standing conjectures are one of the aspects of a more general web of questions regarding the topology of algebraic varieties which have been emphasized by Grothendieck and have since had a central role in modern arithmetic geometry. Special cases of these conjectures, appearing for instance in the work of Tate, Deligne, Faltings, Schneider-Lang, Masser-Wüstholz, have all had important consequences. My goal is to investigate different lines of attack towards these conjectures, building on recent work on myself and Jean-Benoît Bost on related problems. The two main directions of the proposal are as follows. Over finite fields, the Tate conjecture is related to finiteness results for certain cohomological objects. I want to understand how to relate these to hidden boundedness properties of algebraic varieties that have appeared in my recent geometric proof of the Tate conjecture for K3 surfaces. The existence and relevance of a theory of Donaldson invariants for moduli spaces of twisted sheaves over finite fields seems to be a promising and novel direction. Over number fields, I want to combine the geometric insight above with algebraization techniques developed by Bost. In a joint project, we want to investigate how these can be used to first understand geometrically major results in transcendence theory and then attack the Grothendieck period conjecture for divisors via a number-theoretic and complex-analytic understanding of universal vector extensions of abelian schemes over curves.

1 222 329 €

Start date: 2016-12-01, End date: 2021-11-30

I propose to use large clouds of cold Ytterbium atoms to observe Anderson localization of light in three dimensions, which has challenged theoreticians and experimentalists for many decades. After the prediction by Anderson of a disorder-induced conductor to insulator transition for electrons, light has been proposed as ideal non interacting waves to explore coherent transport properties in the absence of interactions. The development in experiments and theory over the past several years have shown a route towards the experimental realization of this phase transition. Previous studies on Anderson localization of light using semiconductor powders or dielectric particles have shown that intrinsic material properties, such as absorption or inelastic scattering of light, need to be taken into account in the interpretation of experimental signatures of Anderson localization. Laser-cooled clouds of atoms avoid the problems of samples used so far to study Anderson localization of light. Ab initio theoretical models, available for cold Ytterbium atoms, have shown that the mere high spatial density of the scattering sample is not sufficient to allow for Anderson localization of photons in three dimensions, but that an additional magnetic field or additional disorder on the level shifts can induce a phase transition in three dimensions. The role of disorder in atom-light interactions has important consequences for the next generation of high precision atomic clocks and quantum memories. By connecting the mesoscopic physics approach to quantum optics and cooperative scattering, this project will allow better control of cold atoms as building blocks of future quantum technologies. Time-resolved transport experiments will connect super- and subradiant assisted transmission with the extended and localized eigenstates of the system. Having pioneered studies on weak localization and cooperative scattering enables me to diagnostic strong localization of light by cold atoms.

2 490 717 €

Start date: 2019-10-01, End date: 2024-09-30