ERC FUNDED PROJECTS

At the end of their life, stars spread their inner material into the diffuse interstellar medium. This diffuse medium gets locally denser and form dark clouds (also called dense or molecular clouds) whose innermost part is shielded from the external UV field by the dust, allowing for molecules to grow and get more complex. Gravitational collapse occurs inside these dense clouds, forming protostars and their surrounding disks, and eventually planetary systems like (or unlike) our solar system. The formation and evolution of molecules, minerals, ices and organics from the diffuse medium to planetary bodies, their alteration or preservation throughout this cosmic chemical history set the initial conditions for building planets, atmospheres and possibly the first bricks of life. The current view of interstellar chemistry is based on fragmental works on key steps of the sequence that are observed. The objective of this proposal is to follow the fractionation of the elements between the gas-phase and the interstellar grains, from the most diffuse medium to protoplanetary disks, in order to constrain the chemical composition of the material in which planets are formed. The potential outcome of this project is to get a consistent and more accurate description of the chemical evolution of interstellar matter. To achieve this objective, I will improve our chemical model by adding new processes on grain surfaces relevant under the diffuse medium conditions. This upgraded gas-grain model will be coupled to 3D dynamical models of the formation of dense clouds from diffuse medium and of protoplanetary disks from dense clouds. The computed chemical composition will also be used with 3D radiative transfer codes to study the chemical tracers of the physics of protoplanetary disk formation. The robustness of the model predictions will be studied with sensitivity analyses. Finally, model results will be confronted to observations to address some of the current challenges.

1 166 231 €

Start date: 2013-09-01, End date: 2018-08-31

Aeroelastic instabilities are at the origin of large deformations of structures and are limiting the capacities of products in various industrial branches such as aeronautics, marine industry, or wind electricity production. If suppressing aeroelastic instabilities is an ultimate goal, a paradigm shift in the technological development is to take advantage of these instabilities to achieve others objectives, as reducing the drag of these flexible structures. The ground-breaking challenges addressed in this project are to design fundamentally new theoretical methodologies for (i) describing mathematically aeroelastic instabilities, (ii) suppressing them and (iii) using them to reduce mean drag of structures at a low energetic cost. To that aim, two types of aeroelastic phenomena will be specifically studied: the flutter, which arises as a result of an unstable coupling instability between two stable dynamics, that of the structures and that the flow, and vortex-induced vibrations which appear when the fluid dynamics is unstable. An aeroelastic global stability analysis will be first developed and applied to problems of increasing complexity, starting from two-dimensional free-vibrating rigid structures and progressing towards three-dimensional free-deforming elastic structures. The control of these aeroelastic instabilities will be then addressed with two different objectives: their suppression or their use for flow control. A theoretical passive control methodology will be established for suppressing linear aeroelastic instabilities, and extended to high Reynolds number flows and experimental configurations. New perturbation methods for solving strongly nonlinear problems and adjoint-based control algorithm will allow to use these aeroelastic instabilities for drag reduction. This project will allow innovative control solutions to emerge, not only in flutter or vortex-induced vibrations problems, but also in a much broader class of fluid-structure problems.

1 377 290 €

Start date: 2015-07-01, End date: 2020-06-30

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

One already available method to expand the range of material properties is to adjust the composition of materials at the molecular level using chemistry. We would like to develop the alternative approach of homogenization which broadens the definition of a material to include artificially structured media (fluids and solids) in which the effective electromagnetic, hydrodynamic or elastic responses result from a macroscopic patterning or arrangement of two or more distinct materials. This project will explore the latter avenue in order to markedly enhance control of surface water waves and elastodynamic waves propagating within artificially structured fluids and solid materials, thereafter called acoustic metamaterials. Pendry's perfect lens, the paradigm of electromagnetic metamaterials, is a slab of negative refractive index material that takes rays of light and causes them to converge with unprecedented resolution. This flat lens is a combination of periodically arranged resonant electric and magnetic elements. We will draw systematic analogies with resonant mechanical systems in order to achieve similar control of hydrodynamic and elastic waves. This will allow us to extend the design of metamaterials to acoustics to go beyond the scope of Snell-Descartes' laws of optics and Newton's laws of mechanics. Acoustic metamaterials allow the construction of invisibility cloaks for non-linear surface water waves (e.g. tsunamis) propagating in structured fluids, as well as seismic waves propagating in thin structured elastic plates. Maritime and civil engineering applications are in the protection of harbours, off-shore platforms and anti-earthquake passive systems. Acoustic cloaks for an enhanced control of pressure waves in fluids will be also designed for underwater camouflaging. Light and sound interplay will be finally analysed in order to design controllable metamaterials with a special emphasis on undetectable microstructured fibres (acoustic wormholes).

1 280 391 €

Start date: 2011-10-01, End date: 2016-09-30

The key ideas motivating this project are that: 1) precise control of the properties of porous systems can be obtained by exploiting bacteria and their fantastic abilities; 2) conversely, porous media (large surface to volume ratios, complex structures) could be a major part of bacterial synthetic biology, as a scaffold for growing large quantities of microorganisms in controlled bioreactors. The main scientific obstacle to precise control of such processes is the lack of understanding of biophysical mechanisms in complex porous structures, even in the case of single-strain biofilms. The central hypothesis of this project is that a better fundamental understanding of biofilm biomechanics and physical ecology will yield a novel theoretical basis for engineering and control. The first scientific objective is thus to gain insight into how fluid flow, transport phenomena and biofilms interact within connected multiscale heterogeneous structures - a major scientific challenge with wide-ranging implications. To this end, we will combine microfluidic and 3D printed micro-bioreactor experiments; fluorescence and X-ray imaging; high performance computing blending CFD, individual-based models and pore network approaches. The second scientific objective is to create the primary building blocks toward a control theory of bacteria in porous media and innovative designs of microbial bioreactors. Building upon the previous objective, we first aim to extract from the complexity of biological responses the most universal engineering principles applying to such systems. We will then design a novel porous micro-bioreactor to demonstrate how the permeability and solute residence times can be controlled in a dynamic, reversible and stable way - an initial step toward controlling reaction rates. We envision that this will unlock a new generation of biotechnologies and novel bioreactor designs enabling translation from proof-of-concept synthetic microbiology to industrial processes.

1 649 861 €

Start date: 2019-01-01, End date: 2023-12-31

Boundary layer theory is a large component of fluid dynamics. It is ubiquitous in Oceanography, where boundary layer currents, such as the Gulf Stream, play an important role in the global circulation. Comprehending the underlying mechanisms in the formation of boundary layers is therefore crucial for applications. However, the treatment of boundary layers in ocean dynamics remains poorly understood at a theoretical level, due to the variety and complexity of the forces at stake. The goal of this project is to develop several tools to bridge the gap between the mathematical state of the art and the physical reality of oceanic motion. There are four points on which we will mainly focus: degeneracy issues, including the treatment Stewartson boundary layers near the equator; rough boundaries (meaning boundaries with small amplitude and high frequency variations); the inclusion of the advection term in the construction of stationary boundary layers; and the linear and nonlinear stability of the boundary layers. We will address separately Ekman layers and western boundary layers, since they are ruled by equations whose mathematical behaviour is very different. This project will allow us to have a better understanding of small scale phenomena in fluid mechanics, and in particular of the inviscid limit of incompressible fluids. The team will be composed of the PI, two PhD students and three two-year postdocs over the whole period. We will also rely on the historical expertise of the host institution on fluid mechanics and asymptotic methods.

1 267 500 €

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

Some of the primary questions in extragalactic astronomy concern the formation and evolution of galaxies in the distant Universe. In particular, little is known about the less luminous (and therefore less massive) galaxy populations, which are currently missed from large observing surveys and could contribute significantly to the overall star formation happening at early times. One way to overcome the current observing limitations prior to the arrival of the future James Webb Space Telescope or the European Extremely Large Telescopes is to use the natural magnification of strong lensing clusters to look at distant sources with an improved sensitivity and resolution. The aim of CALENDS is to build and study in great details a large sample of accurately-modelled, strongly lensed galaxies at high redshift (1<z<5) selected in the fields of massive clusters, and compare them with the more luminous or lower redshift populations. We will develop novel techniques in this process, in order to improve the accuracy of strong-lensing models and precisely determine the mass content of these clusters. By performing a systematic modelling of the cluster sample we will look into the relative distribution of baryons and dark matter as well as the amount of substructure in cluster cores. Regarding the population of lensed galaxies, we will study their global properties through a multiwavelength analysis covering the optical to millimeter domains, including spectroscopic information from MUSE and KMOS on the VLT, and ALMA. We will look for scaling relations between the stellar, gas and dust parameters, and compare them with known relations for lower redshift and more massive galaxy samples. For the most extended sources, we will be able to spatially resolve their inner properties, and compare the results of individual regions with predictions from simulations. We will look into key physical processes: star formation, gas accretion, inflows and outflows, in these distant sources.

1 450 992 €

Start date: 2013-09-01, End date: 2019-08-31

Bacteria are tiny; yet their collective dynamics generate large-scale flows and profoundly modify a fluid’s viscosity or diffusivity. So do autophoretic microswimmers, an example of active microscopic particles that draw their motion from physico-chemical exchanges with their environment. How do such ``active fluids'' turn individual microscopic propulsion into macroscopic fluid dynamics? What controls this self-organization process? These are fundamental questions for biologists but also for engineers, to use these suspensions for mixing or chemical sensing and, more generally, for creating active fluids whose macroscopic physical properties can be controlled precisely. Self-propulsion of autophoretic swimmers was reported only recently. Major scientific gaps impair the quantitative understanding of their individual and collective dynamics, which is required to exploit these active fluids. Existing models scarcely account for important experimental characteristics such as complex hydrodynamics, physico-chemical processes and confinement. Thus, these models cannot yet be used as predictive tools, even at the individual level. Further, to use phoretic suspensions as active fluids with microscopically-controlled properties, quantitatively-predictive models are needed for the collective dynamics. Instead of ad-hoc interaction rules, collective models must be built on a detailed physico-mechanical description of each swimmer’s interaction with its environment. This project will develop these tools and validate them against experimental data. This requires overcoming several major challenges: the diversity of electro-chemical processes, the confined geometry, the large number of particles, and the plurality of interaction mechanisms and their nonlinear coupling. To address these issues, rigorous physical, mathematical and numerical models will be developed to obtain a complete multi-scale description of the individual and collective dynamics of active particles.

1 497 698 €

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

"The purpose of this project is to use the ubiquitous nature of certain combinatorial topological objects called maps in order to unveil deep connections between several areas of mathematics. Maps, that describe the embedding of a graph into a surface, appear in probability theory, mathematical physics, enumerative geometry or graph theory, and different combinatorial viewpoints on these objects have been developed in connection with each topic. The originality of our project will be to study these approaches together and to unify them. The outcome will be triple, as we will: 1. build a new, well structured branch of combinatorics of which many existing results in different areas of enumerative and algebraic combinatorics are only first fruits; 2. connect and unify several aspects of the domains related to it, most importantly between probability and integrable hierarchies thus proposing new directions, new tools and new results for each of them; 3. export the tools of this unified framework to reach at new applications, especially in random graph theory and in a rising domain of algebraic combinatorics related to Tamari lattices. The methodology to reach the unification will be the study of some strategic interactions at different places involving topological expansions, that is to say, places where enumerative problems dealing with maps appear and their genus invariant plays a natural role, in particular: 1. the combinatorial theory of maps developped by the "French school" of combinatorics, and the study of random maps; 2. the combinatorics of Fermions underlying the theory of KP and 2-Toda hierarchies; 3; the Eynard-Orantin "topological recursion" coming from mathematical physics. We present some key set of tasks in view of relating these different topics together. The pertinence of the approach is demonstrated by recent research of the principal investigator."

1 086 125 €

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

A contact structure on an odd dimensional manifold in a maximally non integrable hyperplane field. It is the odd dimensional counterpart of a symplectic structure. Contact and symplectic topology is a recent and very active area that studies intrinsic questions about existence, (non) uniqueness and rigidity of contact and symplectic structures. It is intimately related to many other important disciplines, such as dynamical systems, singularity theory, knot theory, Morse theory, complex analysis, ... Legendrian submanifolds are a distinguished class of submanifolds in a contact manifold, which are tangent to the contact distribution. These manifolds are of a particular interest in contact topology. Important classes of Legendrian submanifolds can be described using generating families, and this description can be used to define Legendrian invariants via Morse theory. Other the other hand, Legendrian contact homology is an invariant for Legendrian submanifolds, based on holomorphic curves. The goal of this research proposal is to study the relationship between these two approaches. More precisely, we plan to show that the generating family homology and the linearized Legendrian contact homology can be defined for the same class of Legendrian submanifolds, and are isomorphic. This correspondence should be established using a parametrized version of symplectic homology, being developed by the Principal Investigator in collaboration with Oancea. Such a result would give an entirely new type of information about holomorphic curves invariants. Moreover, it can be used to obtain more general structural results on linearized Legendrian contact homology, to extend recent results on existence of Reeb chords, and to gain a much better understanding of the geography of Legendrian submanifolds.

710 000 €

Start date: 2009-11-01, End date: 2014-10-31

One of the main challenges in condensed matter physics is to understand strongly correlated quantum systems. Our purpose is to approach this issue from the point of view of rigorous mathematical analysis. The goals are twofold: develop a mathematical framework applicable to physically relevant scenarii, take inspiration from the physics to introduce new topics in mathematics. The scope of the proposal thus goes from physically oriented questions (theoretical description and modelization of physical systems) to analytical ones (rigorous derivation and analysis of reduced models) in several cases where strong correlations play the key role. In a first part, we aim at developing mathematical methods of general applicability to go beyond mean-field theory in different contexts. Our long-term goal is to forge new tools to attack important open problems in the field. Particular emphasis will be put on the structural properties of large quantum states as a general tool. A second part is concerned with so-called fractional quantum Hall states, host of the fractional quantum Hall effect. Despite the appealing structure of their built-in correlations, their mathematical study is in its infancy. They however constitute an excellent testing ground to develop ideas of possible wider applicability. In particular, we introduce and study a new class of many-body variational problems. In the third part we discuss so-called anyons, exotic quasi-particles thought to emerge as excitations of highly-correlated quantum systems. Their modelization gives rise to rather unusual, strongly interacting, many-body Hamiltonians with a topological content. Mathematical analysis will help us shed light on those, clarifying the characteristic properties that could ultimately be experimentally tested.

1 056 664 €

Start date: 2018-01-01, End date: 2022-12-31

Cosmic explosions, the violent deaths of stars, play a crucial role in many of the most interesting open questions in physics today. These events serve as “cosmic accelerators” for ultra-high-energy particles that are beyond reach for even to most powerful terrestrial accelerators, as well as distant sources for elusive neutrinos. Explosions leave behind compact neutron stars and black hole remnants, natural laboratories to study strong gravity. Acting as cosmic furnaces, these explosions driven the chemical evolution of the Universe Cosmic explosions trigger and inhibit star formation processes, and drive galactic evolution (“feedback”). Distances measured using supernova explosions as standard candles brought about the modern revolution in our view of the accelerating Universe, driven by enigmatic “dark energy”. Understanding the nature of cosmic explosions of all types is thus an extremely well-motivated endeavour. I have been studying cosmic explosions for over a decade, and since the earliest stages of my career, have followed an ambition to figure out the nature of cosmic explosions of all types, and to search for new types of explosions. Having already made several key discoveries, I now propose to undertake a comprehensive program to systematically tackle this problem.I review below the progress made in this field and the breakthrough results we have achieved so far, and propose to climb the next step in this scientific and technological ladder, combining new powerful surveys with comprehensive multi-wavelength and multi-disciplinary (observational and theoretical) analysis. My strategy is based on a combination of two main approaches: detailed studies of single objects which serve as keys to specific questions; and systematic studies of large samples, some that I have, for the first time, been able to assemble and analyze, and those expected from forthcoming efforts. Both approaches have already yielded tantalizing results.

1 499 302 €

Start date: 2012-09-01, End date: 2017-08-31

Statistical physics is a theory allowing the derivation of the statistical behavior of macroscopic systems from the description of the interactions of their microscopic constituents. For more than a century, lattice models (i.e. random systems defined on lattices) have been introduced as discrete models describing the phase transition for a large variety of phenomena, ranging from ferroelectrics to lattice gas. In the last decades, our understanding of percolation and the Ising model, two classical exam- ples of lattice models, progressed greatly. Nonetheless, major questions remain open on these two models. The goal of this project is to break new grounds in the understanding of phase transition in statistical physics by using and aggregating in a pioneering way multiple techniques from proba- bility, combinatorics, analysis and integrable systems. In this project, we will focus on three main goals: Objective A Provide a solid mathematical framework for the study of universality for Bernoulli percolation and the Ising model in two dimensions. Objective B Advance in the understanding of the critical behavior of Bernoulli percolation and the Ising model in dimensions larger or equal to 3. Objective C Greatly improve the understanding of planar lattice models obtained by general- izations of percolation and the Ising model, through the design of an innovative mathematical theory of phase transition dedicated to graphical representations of classical lattice models, such as Fortuin-Kasteleyn percolation, Ashkin-Teller models and Loop models. Most of the questions that we propose to tackle are notoriously difficult open problems. We believe that breakthroughs in these fundamental questions would reshape significantly our math- ematical understanding of phase transition.

1 499 912 €

Start date: 2018-09-01, End date: 2023-08-31

Cytoplasmic motion is a key determinant of organelle transport, protein-protein interactions, RNA transport and drug delivery, to name but a few cellular phenomena. Nucleic acid trafficking is important in antisense and gene therapy based on viral and synthetic vectors. This proposal is dedicated to the theoretical study of intracellular transport of proteins, organelles and DNA particles. We propose to construct a mathematical model to quantify and predict the spatiotemporal dynamics of complex structures in the cytosol and the nucleus, based on the physical characteristics and the micro-rheology of the environment (viscosity). We model the passive motion of proteins or DNA as free or confined diffusion, while for the organelle and virus motion, we will include active cytoskeleton-dependent transport. The proposed mathematical model of cellular trafficking is based on physical principles. We propose to estimate the mean arrival time and the probability of viruses and plasmid DNA to arrive to a nuclear pore. The motion will be described by stochastic dynamics, containing both a drift (along microtubules) and a Brownian (free diffusion) component. The analysis of the equations requires the development of new asymptotic methods for the calculation of the probability and the mean arrival time of a particle to a small hole on the nucleus surface. We will extend the analysis to DNA movement in the nucleus after cellular irradiation, when the nucleus contains single and double broken DNA strands (dbDNAs). The number of remaining DNA breaks determines the activation of the repair machinery and the cell decision to enter into apoptosis. We will study the dsbDNA repair machinery engaged in the task of finding the DNA damage. We will formulate and analyze, both numerically and analytically, the equations that link the level of irradiation to apoptosis. The present project belongs to the new class of initiatives toward a quantitative analysis of intracellular trafficking.

750 000 €

Start date: 2009-01-01, End date: 2014-06-30

Active volcanoes emit high temperature gases that modify the chemical composition of the Earth’s atmosphere. It is crucial to be able to quantify the contribution of volcanogenic gases to the atmosphere so that the global atmospheric effects of a major eruption can be predicted and so that volcanogenic effects can be discriminated from anthropogenic emissions. At the scale of one volcano, monitoring of gas plumes is a major tool in volcanic risk management. Volcanologists have long measured gas composition and fluxes between and during eruptions and often noted a decoupling between degassing flux and magmatic flux. In parallel, experimental petrologists are now able to calculate the gas composition that is in equilibrium with the magma at depth. However, when the calculated gas composition is compared to that measured at the surface, a general disagreement arises. As a result, it is currently impossible to determine whether a plume is generated in response to passive degassing or to magma ascent. This is a serious drawback as these processes have opposite implications for volcanic activity. Such difficulties are mainly due to the fact that the interplay between degassing mechanisms and gas chemistry has not been addressed. To improve the application of volcanic gas analyses to understanding global geochemical budgets and for the mitigation of volcanic risk, we propose to link deep magmatic processes and surface emissions. Our objective is to model the quantity and composition of volcanic gases as a function of the petrology of the magma at depth and the eruptive regime, and compare those calculations with new measures of plumes at active volcanoes. We will achieve this by modeling the chemical kinetics of degassing in volcanic conduits by using a combination of experimental, field, and numerical approaches. We anticipate building a tool linking flux and composition of gases to eruptive regime, thus opening the door to inverse modeling of volcanic gas observations.

1 364 478 €

Start date: 2008-09-01, End date: 2012-12-31

High-dimensional problems with a geometric flavor appear in quite a few branches of mathematics, mathematical physics and theoretical computer science. A priori, one would think that the diversity and the rapid increase of the number of configurations would make it impossible to formulate general, interesting theorems that apply to large classes of high-dimensional geometric objects. The underlying theme of the proposed project is that the contrary is often true. Mathematical developments of the last decades indicate that high dimensionality, when viewed correctly, may create remarkable order and simplicity, rather than complication. For example, Dvoretzky's theorem demonstrates that any high-dimensional convex body has nearly-Euclidean sections of a high dimension. Another example is the central limit theorem for convex bodies due to the PI, according to which any high-dimensional convex body has approximately Gaussian marginals. There are a number of strong motifs in high-dimensional geometry, such as the concentration of measure, which seem to compensate for the vast amount of different possibilities. Convexity is one of the ways in which to harness these motifs and thereby formulate clean, non-trivial theorems. The scientific goals of the project are to develop new methods for the study of convexity in high dimensions beyond the concentration of measure, to explore emerging connections with other fields of mathematics, and to solve the outstanding problems related to the distribution of volume in high-dimensional convex sets.

998 000 €

Start date: 2013-01-01, End date: 2018-12-31

There are many parallels between Lie group actions on homogeneous spaces and the action of $\SL_2(\R)$ and its subgroups on strata of translation or half-translation surfaces. I propose to investigate these two spaces in parallel, focusing on the dynamical behavior, and more specifically, the description of orbit-closures. I intend to utilize existing and emerging measure rigidity results, and to develop new topological approaches. These should also shed light on the geometry and topology of the spaces. I propose to apply results concerning these spaces to the study of diophantine approximations (approximation on fractals), geometry of numbers (Minkowski's conjecture), interval exchanges, and rational billiards.

850 000 €

Start date: 2011-10-01, End date: 2016-09-30

The primary questions that drive the Mars exploration program focus on life. Has the Martian climate ever been favorable for life development? Such scenario would imply a distinct planetary system from today with a magnetic flied able to retain the atmosphere. Where is the evidence of such past climate and intern conditions? The clues for answering these questions are locked up in the geologic record of the planet. The volume of data acquired in the past 15 years by the 4 Martian orbiters (ESA and NASA) reach the petaoctet, what is indecent as regard to the size of the Martian community. e-Mars propose to built a science team composed by the PI, Two post-doctorates, one PhD student and one engineer to exploit the data characterizing the surface of Mars. e-Mars proposes the unprecedented approach to combine topographic data, imagery data in diverse spectral domain and hyperspectral data from multiple orbiter captors to study the evolution of Mars and to propose pertinent landing sites for next missions. e-Mars will focus on three scientific themes: the composition of the Martian crust to constraint the early evolution of the planet, the research of possible habitable places based on evidence of past liquid water activity from both morphological record and hydrated mineral locations, and the study of current climatic and geological processes driven by the CO2 cycle. These scientific themes will be supported by three axis of methodological development: the geodatabase management via Geographic Information Systems (G.I.S.)., the automatic hyperspectral data analysis and the age estimates of planetary surface based on small size crater counts.

1 392 000 €

Start date: 2011-11-01, End date: 2017-10-31

Understanding the nature of Dark Energy (DE) in the Universe is the central challenge of modern cosmology. Einstein’s Cosmological Constant (Λ) provides the simplest explanation fitting the available cosmological data thus far. However, its unnaturally tuned value indicates that other hypothesis must be explored. Furthermore, current observations do not by any means rule out alternative models in favor of the simplest “concordance” ΛCDM. In the absence of theoretical prejudice, observational tests have mainly focused on the DE equation of state. However, the detection of the inhomogeneous nature of DE will provide smoking-gun evidence that DE is dynamical, ruling out Λ. This key aspect has been mostly overlooked so far, particularly in the optimization design of the next generation of surveys dedicated to DE searches which will map the distribution of matter in the Universe with unprecedented accuracy. The success of these observations relies upon the ability to model the non-linear gravitational processes which affect the collapse of Dark Matter (DM) at small and intermediate scales. Therefore, it is of the highest importance to investigate the role of DE inhomogeneities throughout the non-linear evolution of cosmic structure formation. To achieve this, we will use specifically designed high-resolution numerical simulations and analytical methods to study the non-linear regime in different DE models. The hypothesis to be tested is whether the intrinsic clustering of DE can alter the predictions of the standard ΛCDM model. We will investigate the observational consequences on the DM density field and the properties of DM halos. The results will have a profound impact in the quest for DE and reveal new observable imprints on the distribution of cosmic structures, whose detection may disclose the ultimate origin of the DE phenomenon.

1 468 800 €

Start date: 2012-04-01, End date: 2017-08-31

The proposal is to look for, and investigate, new ergodic theoretic types of behavior for dynamical systems which act on non compact spaces. These could include transience and non-trivial ways of escape to infinity, critical phenomena similar to phase transitions, and new types of measure rigidity. There are potential applications to smooth ergodic theory (non-uniform hyperbolicity), algebraic ergodic theory (actions on homogeneous spaces), and probability theory (weakly dependent stochastic processes).

539 479 €

Start date: 2009-10-01, End date: 2014-09-30

"Our aim is to built on recent combinatorial and algorithmic progress to attack a series of deeply connected problems that have independantly surfaced in enumerative topology, statistical physics, and data compression. The relation between these problems lies in the notion of ""combinatorial map"", the natural discrete mathematical abstraction of objects with a 2-dimensional structures (like geographical maps, computer graphics' meshes, or 2d manifolds). A whole new set of properties of these maps has been uncovered in the last few years under the impulsion of the principal investigator. Rougly speaking, we have shown that classical graph exploration algorithms, when correctly applied to maps, lead to remarkable decompositions of the underlying surfaces. Our methods resort to algorithmic and enumerative combinatorics. In statistical physics, these decompositions offer an approach to the intrinsec geometry of discrete 2d quantum gravity: our method is here the first to outperform the celebrated ""topological expansion of matrix integrals"" of Brezin-Itzykson-Parisi-Zuber. Exploring its implications for the continuum limit of these random geometries is our great challenge now. From a computational geometry perspective, our approach yields the first encoding schemes with asymptotically optimal garanteed compression rates for the connectivity of triangular or polygonal meshes. These schemes improve on a long series of heuristically efficient but non optimal algorithms, and open the way to optimally compact data structures. Finally we have deep indications that the properties we have uncovered extend to the realm of ramified coverings of the sphere. Intriguing computations on the fundamental Hurwitz's numbers have been obtained using the ELSV formula, famous for its use by Okounkov et al. to rederive Kontsevich's model. We believe that further combinatorial progress here could allow to bypass the formula and obtaine an elementary explanation of these results."

750 000 €

Start date: 2008-07-01, End date: 2013-06-30

Since the discoveries of giant planets outside our Solar System, over 800 extra-solar planets have been detected and several thousands candidates are awaiting confirmation. They have revolutionized planetary science, by placing our once unique solar system into context. The subset of extrasolar planets that transit their parent star have had most impact on our understanding of their planetary structure and atmospheric physics: they are the only ones for which one can simultaneously measure mass and radius, and therefore infer internal composition. The few that transit a host star bright enough for detailed spectroscopic follow-up provide, in addition, observational information on the composition and physics of extrasolar planetary atmospheres. Much interest is now focused on finding and characterizing terrestrial mass planets, ideally in the habitable zone of their host stars. The present ERC project offers a novel method to dramatically improve the precision of both the detection and the characterization of exoplanets. The method makes use of multi-object spectrographs to add spectroscopic resolution on traditional differential photometry. This enables the fine correction of the atmospheric variations that would otherwise hinder ground-based observations. We propose to setup small-size telescopes equipped with a multi-object near-IR spectrograph and observe 800 M dwarfs. This will be the most sensitive survey for Earth-size planets transiting bright nearby stars. It shall yield dozens exo-Earths amenable to atmospheric characterization, including several habitable exo-Earths. To perform their atmospheric characterization, we also propose to apply the technique of differential spectro-photometry with multi-object spectrographs available on large telescopes. Our observations will represent a step forward in transmission spectroscopy and prepare for the identification of bio-markers in exo-Earth atmospheres with the future ELTs.

2 000 000 €

Start date: 2014-07-01, End date: 2019-06-30

We propose to study the fractal geometry of invariant sets for endomorphisms of compact abelian groups, specifically a family of conjectures by Furstenberg on the dimensions of orbit closures under such dynamics, and on the size of sums and intersections of invariant sets. These conjectures are related to problems on expansion in integer bases, in Diophantine approximation, measure rigidity, analysis and equidistribution. The project focuses on the conjectures themselves and some related problems, e.g. Bernoulli convolutions, and on applications to equidistribution on tori. Our approach combines tools from ergodic theory, geometric measure theory and additive combinatorics, building on recent progress in these fields and recent partial results towards the main conjectures.

1 107 000 €

Start date: 2012-10-01, End date: 2018-09-30

While modern societies are facing urgent challenges related to reduction of particulate matter emissions from transportation engines, recent discoveries on the extraordinary properties of carbonaceous functional nanomaterials have revealed opportunities associated with large-scale, flame-based synthesis of these otherwise unwanted combustion products. In both cases, our ability to study new, optimized solutions based on the specific industrial end-user needs is limited by the absence of theoretical tools able to accurately predict the fluid dynamics and the chemistry involved in nanoparticle formation. Indeed, current knowledge on this fascinating but complex process is still rather incomplete. The proposed research program, FUN-PM, will apply an innovative multi-disciplinary, multi-step approach in order to finally answer many unresolved kinetic questions concerning in particular: 1) formation and growth of molecular PAH precursors; 2) particle inception; 3) subsequent particle growth and oxidation. Each single step will be experimentally isolated taking full advantage of complementary conventional shock tube techniques and up-to-date synchrotron-based detection technologies coupled to a newly constructed high-rate repetition shock tube. If successful, the novel synchrotron-shock tube techniques will be utilized for the first time to obtain unique information on unknown key processes. The experimental results, with extensive theoretical ab-initio calculations on relevant PAH reaction pathways, will constitute the base for the development of a comprehensive, detailed chemical kinetic model for particle chemistry applied to Real Fuels. Such model will improve the prediction capabilities of current CFD codes for use in engine design, fuel reformulation, or industrial process optimization, with considerable benefits to the standards of living of European citizens, the environment, and the EU economy, towards the future of clean transportations and novel nanomaterials.

1 493 839 €

Start date: 2018-02-01, End date: 2023-01-31

The formation of dark matter structures in our Universe can be explained by the standard cosmological model, but the populations of galaxies observed in the distant and nearby Universe pose major challenges to our understanding of galaxy formation. There is increasing recognition that the visible, baryonic part of galaxies does not passively follow the hierarchical build-up of dark halos. A large part of the baryons can be accreted from cold gas flows along the cosmic web. The evolution of galaxies could then be mostly driven by their internal evolution, in addition to interactions and mergers. Many scall-scale processes with major effects on galaxy evolution have been unveiled. They have, however, been studied mostly one by one, ignoring the large-scale cosmological environment. Conversely, cosmological models do not resolve the small-scale internal processes properly yet. This dramatically limits our understanding of galaxy formation. The project is to develop an multi-scale understanding of galaxy formation. We will build comprehensive numerical models of the small-scale gas physics and star formation processes in, and incorporate them in large-scale cosmological simulations. Taking benefit from the best forthcoming computing facilities, this will develop a new understanding of the role of internal physics and external processes in structuring galaxies. Theoretical predictions will be confronted to observations, preparing and using the next generation of instruments along the whole duration of the project. Owing to a uniquely comprehensive approach including physical processes at different scales and an original combination of theory, simulation and observation, a new understanding of the evolution of the baryons through cosmic times can emerge from the project.

988 400 €

Start date: 2011-02-01, End date: 2016-01-31

"The aim of this project of 5 years is to create a research group on geometric control methods in PDEs with the arrival of the PI at the CNRS Laboratoire CMAP (Centre de Mathematiques Appliquees) of the Ecole Polytechnique in Paris (in January 09). With the ERC-Starting Grant, the PI plans to hire 4 post-doc fellows, 2 PhD students and also to organize advanced research schools and workshops. One of the main purpose of this project is to facilitate the collaboration with my research group which is quite spread across France and Italy. The PI plans to develop a research group studying certain PDEs for which geometric control techniques open new horizons. More precisely the PI plans to exploit the relation between the sub-Riemannian distance and the properties of the kernel of the corresponding hypoelliptic heat equation and to study controllability properties of the Schroedinger equation. In the last years the PI has developed a net of high level international collaborations and, together with his collaborators and PhD students, has obtained many important results via a mixed combination of geometric methods in control (Hamiltonian methods, Lie group techniques, conjugate point theory, singularity theory etc.) and noncommutative Fourier analysis. This has allowed to solve open problems in the field, e.g., the definition of an intrinsic hypoelliptic Laplacian, the explicit construction of the hypoelliptic heat kernel for the most important 3D Lie groups, and the proof of the controllability of the bilinear Schroedinger equation with discrete spectrum, under some ""generic"" assumptions. Many more related questions are still open and the scope of this project is to tackle them. All subjects studied in this project have real applications: the problem of controllability of the Schroedinger equation has direct applications in Nuclear Magnetic Resonance; the problem of nonisotropic diffusion has applications in models of human vision."

785 000 €

Start date: 2010-05-01, End date: 2016-04-30

The GEODESI project aims at interpreting current and forthcoming cosmological observations in a renewed theoretical framework about cosmological inflation and its ending. The simplest toy models of inflation economically explain all current data, leaving no observational clue to guide theorists towards a finer physical understanding. In this context, I very recently unveiled an hitherto unnoticed instability at play in the primordial universe that potentially affects all inflationary models and drastically modifies the interpretation of cosmological observations in terms of fundamental physics. The so-called Geometrical Destabilization of inflation reshuffles our understanding of the origin of structures in the universe, offers a new mechanism to end inflation, and promises unrivaled constraints on high-energy physics. It is crucial to develop this fresh look before a host of high-quality data from large-scale structure surveys and cosmic microwave background observations become available within the 5 year timescale of the project. With the ERC grant I plan to build a group at the Institute of Astrophysics of Paris (IAP-CNRS) with the objective of determining the full theoretical and observational consequences of the geometrical destabilization of inflation. We will combine insights from non-standard cosmological perturbation theory and lattice simulations to constrain realistic models of inflation in high-energy physics, producing accurate theoretical predictions for a wide variety of observables, including the spectra and the non-Gaussianities of primordial fluctuations and stochastic backgrounds of gravitational waves.

1 476 672 €

Start date: 2018-02-01, End date: 2023-01-31

"The goal of this project is to develop new numerical methods for the approximation of evolution equations possessing strong geometric properties such as Hamiltonian systems or stochastic differential equations. In such situations the exact solutions endow with many physical properties that are consequences of the geometric structure: Preservation of the total energy, momentum conservation or existence of ergodic invariant measures. However the preservation of such qualitative properties of the original system by numerical methods at a reasonable cost is not guaranteed at all, even for very precise (high order) methods. The principal aim of geometric numerical integration is the understanding and analysis of such problems: How (and to which extend) reproduce qualitative behavior of differential equations over long time? The extension of this theory to partial differential equations is a fundamental ongoing challenge, which require the invention of a new mathematical framework bridging the most recent techniques used in the theory of nonlinear PDEs and stochastic ordinary and partial differential equations. The development of new efficient numerical schemes for geometric PDEs has to go together with the most recent progress in analysis (stability phenomena, energy transfers, multiscale problems, etc..) The major challenges of the project are to derive new schemes by bridging the world of numerical simulation and the analysis community, and to consider deterministic and stochastic equations, with a general aim at deriving hybrid methods. We also aim to create a research platform devoted to extensive numerical simulations of difficult academic PDEs in order to highlight new nonlinear phenomena and test numerical methods."

971 772 €

Start date: 2011-09-01, End date: 2016-08-31

Long gamma ray bursts (long GRBs) and core-collapse supernovae (CCSNe) are two of the most spectacular explosions in the Universe. They are a focal point of research for many reasons. Nevertheless, despite considerable effort during the last several decades, there are still many fundamental open questions regarding their physics. Long GRBs and CCSNe are related. We know that they are both an outcome of a massive star collapse, where in some cases, such collapse produces simultaneously a GRB and a SN. However, we do not know how a single stellar collapse can produce these two apparently very different explosions. The GRB-SN connection raises many questions, but it also offers new opportunities to learn on the two types of explosions. The focus of the proposed research is on the connection between CCSNe and GRBs, and on the physics of shock breakout. As I explain in this proposal, shock breakouts play an important role in this connection and therefore, I will develop a comprehensive theory of relativistic and Newtonian shock breakout. In addition, I will study the propagation of relativistic jets inside stars, including the effects of jet propagation and GRB engine on the emerging SN. This will be done by a set of interrelated projects that carefully combine analytic calculations and numerical simulations. Together, these projects will be the first to model a GRB and a SN that are simultaneously produced in a single star. This in turn will be used to gain new insights into long GRBs and CCSNe in general. This research will also make a direct contribution to cosmic explosions research in general. Any observable cosmic explosion must go through a shock breakout and a considerable effort is invested these days in large field of view surveys in search for these breakouts. This program will provide a new theoretical base for the interpretation of the upcoming observations.

1 468 180 €

Start date: 2012-01-01, End date: 2017-12-31

This proposal is concerned with several themes which lie in the crossroads of Harmonic Analysis and Discrete Geometry. Harmonic Analysis is fundamental in all areas of science and engineering, and has vast applications in most branches of mathematics. Discrete Geometry deals with some of the most natural and beautiful problems in mathematics, which often turn out to be also very deep and difficult in spite of their apparent simplicity. The proposed project deals with some fundamental problems which involve an interplay between these two important disciplines. One theme of the project deals with tilings of the Euclidean space by translations, and the interaction of this subject with questions in orthogonal harmonic analysis. The PI has recently developed an approach to attack some problems in connection with the famous conjecture due to Fuglede (1974), concerning the characterization of domains which admit orthogonal Fourier bases in terms of their possibility to tile the space by translations, and in relation with the theory of multiple tiling by translates of a convex polytope, or by a function. A main goal of this project is to further develop new methods and extend some promising intermediate results obtained by the PI in these directions. Another theme of the proposed research lies in the mathematical theory of quasicrystals. This area has received a lot of attention since the experimental discovery in the 1980's of the physical quasicrystals, namely, of non-periodic atomic structures with diffraction patterns consisting of spots. Recently, by a combination of harmonic analytic and discrete combinatorial methods, the PI was able to answer some long-standing questions of Lagarias (2000) concerning the geometry and structure of these rigid point configurations. In the present project, the PI intends to continue the investigation in the mathematical theory of quasicrystals, and to analyze some basic problems which are still open in this field.

1 260 625 €

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

Atmospheric composition provides essential markers of the most fundamental properties of exoplanets, such as their formation mechanism or internal structure. New-generation exoplanet imagers have been designed to achieve high contrast for the detection of young giant planets in the near-infrared, but they only provide very low spectral resolutions (R<100) for their characterization. For a major breakthrough in the comprehension of young exoplanets and their atmospheres, an increase of a factor 100 to 1000 in spectral resolution is absolutely required. This proposal ambitions to develop a novel demonstrator that will combine the capabilities of two flagship instruments installed on the ESO Very Large Telescope, the high-contrast exoplanet imager SPHERE and the high-resolution spectrograph CRIRES+, with the goal of answering fundamental questions on the formation, composition and evolution of young planets. The work will be organized along two axes interconnected with transverse activities: (i) the astrophysics block will investigate signal extraction from high-resolution data and atmospheric modeling, and (ii) the instrumentation block will develop a demonstrator designed to pick up the near-infrared light in SPHERE and feed CRIRES+ via a dedicated injection module and optical fiber relay. We will explore all the key aspects of the project using a combination of instrumental and astrophysical simulations, as well as laboratory validation of components and methods on our high-contrast imaging testbed. We will use the demonstrator to observe a sample of directly imaged companions and obtain high-resolution spectroscopy of their atmospheres. From the data we will (1) determine their formation mechanism through an accurate determination of the carbon and oxygen abundances in their atmospheres, and (2) map the temporal variability of their photosphere through time-resolved Doppler imaging to study dynamical processes related to the formation and evolution of clouds.

1 496 730 €

Start date: 2017-12-01, End date: 2022-11-30

It is widely acknowledged that polar sea ice plays a critical role in global climate change. As such, sea ice reconstructions are of paramount importance in establishing climatic evolution of the geological past. In the current project, some well characterised organic chemicals (biomarkers) from microalgae will be used as proxy indicators of current and past sea ice in the Arctic and Antarctic regions. These biomarkers, so-called highly branched isoprenoids (HBIs), possess a number of characteristics that make them attractive as sea ice proxies. Firstly, some HBIs are unique to sea ice diatoms, so their presence in polar sediments can be directly correlated with the previous occurrence of sea ice. Secondly, they are relatively resistant to degradation, which extends their usefulness in the geological record. Thirdly, their relative abundance makes them straightforward to measure with a high degree of geological resolution. One component of this project will consist of performing regional calibrations of the proxies. Concentrations of selected biomarkers in recent Arctic and Antarctic sediments will be correlated with the sea ice abundances determined using satellite technology over the last 30 years. The successful calibration of the proxies will then enable reconstructions of past sea ice extents to be performed at unprecedented high resolution. Sediment cores will be obtained from key locations across both of the Arctic and Antarctic regions and the data derived from these studies will be used for climate modelling studies. As a complement to these physico-chemical studies on sea ice, a second component of the project will investigate the use of these biomarkers for studying sea ice-biota interactions and, by examining the transfer of these chemicals through food chains, new tools for determining the consequences of future climate change on polar ecosystems will be established.

1 888 594 €

Start date: 2008-10-01, End date: 2013-09-30

This research project is organized along three seemingly unrelated directions: (1) Mathematical Liouville gravity deals with the geometry of large random planar maps. Historically, conformal invariance was a key ingredient in the construction of Liouville gravity in the physics literature. Conformal invariance has been restored recently with an attempt of understanding large random combinatorial planar maps once conformally embedded in the plane. The geometry induced by these embeddings is conjecturally described by the exponential of a highly oscillating distribution, the Gaussian Free Field. This conjecture is part of a broader program aimed at rigorously understanding the celebrated KPZ relation. The first major goal of my project is to make significant progress towards the completion of this program. I will combine for this several tools such as Liouville Brownian motion, circle packings, QLE processes and Bouchaud trap models. (2) Euclidean statistical physics is closely related to area (1) through the above KPZ relation. I plan to push further the analysis of critical statistical physics models successfully initiated by the works of Schramm and Smirnov. I will focus in particular on dynamics at and near critical points with a special emphasis on the so-called noise sensitivity of these systems. (3) 3d turbulence. A more tractable ambition than solving Navier-Stokes equation is to construct explicit stochastic vector fields which combine key features of experimentally observed velocity fields. I will make the mathematical framework precise by identifying four axioms that need to be satisfied. It has been observed recently that the exponential of a certain log-correlated field, as in (1), could be used to create such a realistic velocity field. I plan to construct and analyse this challenging object by relying on techniques from (1) and (2). This would be the first genuine stochastic model of turbulent flow in the spirit of what Kolmogorov was aiming at.

935 000 €

Start date: 2016-09-01, End date: 2021-08-31

Mathematical statistical physics has seen spectacular progress in recent years. Existing problems which were previously unattainable were solved, opening a way to approach some of the classical open questions in the field. The proposed research focuses on phenomena of localization and long-range order in physical systems of large size, identifying several fundamental questions lying at the interface of Statistical Physics, Probability Theory and Combinatorics. One circle of questions concerns the fluctuation behavior of random surfaces, where the PI has recently proved delocalization in two dimensions answering a 1975 question of Brascamp, Lieb and Lebowitz. A main goal of the research is to establish some of the long-standing universality conjectures for random surfaces. This study is also tied to the localization features of random operators, such as random Schrodinger operators and band matrices, as well as those of reinforced random walks. The PI intends to develop this connection further to bring the state-of-the-art to the conjectured thresholds. A second circle of questions regards long-range order in high-dimensional systems. This phenomenon is predicted to encompass many models of statistical physics but rigorous results are quite limited. A notable example is the PI’s proof of Kotecky’s 1985 conjecture on the rigidity of proper 3-colorings in high dimensions. The methods used in this context are not limited to high dimensions and were recently used by the PI to prove the analogue for the loop O(n) model of Polyakov’s 1975 prediction that the 2D Heisenberg model and its higher spin versions exhibit exponential decay of correlations at any temperature. Lastly, statistical physics methods are proposed for solving purely combinatorial problems. The PI has applied this approach successfully to solve questions of existence and asymptotics for combinatorial structures and intends to develop it further to answer some of the tantalizing open questions in the field.

1 136 904 €

Start date: 2016-01-01, End date: 2020-12-31

"Understanding star formation remains one of the greatest challenges of modern astronomy. Indeed in this field the progresses have been limited due, first, to the huge dynamics of spatial and temporal relevant scales and, second, the great variety and non-linearity of the physical processes involved in the formation of stars. The present proposal will contribute to provide a complete and coherent picture of the star formation process by self-consistently following the evolution of the interstellar matter from the very diffuse gas up to the protostars. This will be achieved by performing a series of heavy MHD numerical simulations with an adaptive mesh refinement code while subdivising the problem in three major steps namely the formation of large scale molecular clouds, the formation of star forming cores and the collapse of protostellar cores. In particular, the impact of the magnetic field and the radiative processes will be self-consistently treated using appropriate schemes. At each step, comparisons with both analytical models and observations will be performed by using existing models or developing new ones and calculating synthetic observations. The simulation results will also be used to test and improve the methods and the algorithms used by observers to extract the physical information from their data. An existing database, where the simulation results are available, will be further developed. The present proposal pursues two aims: i) achieving a global understanding of the star formation process, in particular by elucidating the link between the physical properties of the large scale ISM and the characteristics of the protostars, such as their mass, magnetisation and angular momentum ii) provide a better insight of the structure, nature and role of the magnetic field and the turbulence from the diffuse to the dense parts of the ISM."

1 312 267 €

Start date: 2013-01-01, End date: 2017-12-31

"Rotation and angular momentum transport play a critical role in the formation and evolution of astrophysical objects, including the fundamental bricks of astrophysical structures: stars. Stars like our Sun form when rotating dense cores, in the interstellar medium, collapse until they eventually reach temperatures at which nuclear fusion begins; while planets, including the Earth, form in the rotationally supported disks around these same young stars. One of the major challenges of modern astrophysics is the “angular momentum problem"": observations show that a typical star-forming cloud needs to reduce its specific angular momentum by 5 to 10 orders of magnitude to form a typical star such as our Sun. It is also crucial to solve the angular momentum problem to understand the formation of protoplanetary disks, stellar binaries and the initial mass function of newly formed stars. Magnetic fields are one of the key ways of transporting angular momentum in astrophysical structures: understanding how angular momentum is transported to allow star formation requires characterizing the role of magnetic fields in shaping the dynamics of star-forming structures. The MagneticYSOs project aims at characterizing the role of magnetic field in the earliest stage of star formation, during the main accretion phase. The simultaneous major improvements of instrumental and computational facilities provide us, for the first time, with the opportunity to confront observational information to magnetized models predictions. Polarization capabilities on the last generation of instrument in large facilities are producing sensitive observations of magnetic fields with a great level of detail, while numerical simulations of star formation are now including most of the physical ingredients for a detailed description of protostellar collapse at all the relevant scales, such as resistive MHD, radiative transfer and chemical networks. These new tools will undoubtedly lead to major discovery in the fields of planets and star formation in the coming years. It is necessary to conduct comprehensive projects able to combine theory and observations in a detailed fashion, which in turn require a collaboration with access to cutting edge observational datasets and numerical models. Through an ambitious multi-faceted program of dedicated observations probing magnetic fields (polarized dust emission and Zeeman effect maps), gas kinematics (molecular lines emission maps), ionization rates and dust properties in Class 0 protostars, and their comparison to synthetic observations of MHD simulations of protostellar collapse, we aim to transform our understanding of: 1) The long-standing problem of angular momentum in star formation 2) The origin of the stellar initial mass function 3) The formation of multiple stellar systems and circumstellar disks around young stellar objects (YSOs) Not only this project will enable a major leap forward in our understanding of low-mass star formation, answering yet unexplored questions with innovative methods, but it will also allow to spread the expertise in interpreting high-angular resolution (sub-)mm polarization data. Although characterizing magnetic fields in astrophysical structures represents the next frontier in many fields (solar physics, evolved stars, compact objects, galactic nuclei are a few examples), only a handful of astronomers in the EU community are familiar with interferometric polarization data, mostly because of the absence of large european facilities providing such capabilities until the recent advent of ALMA. It is now crucial to strengthen the European position in this research field by training a new generation of physicists with a strong expertise on tailoring, analyzing and interpreting high angular resolution polarization data."

1 500 000 €

Start date: 2016-07-01, End date: 2021-06-30

This proposal focuses on the mathematics of three cross-disciplinary, very active and deeply interlaced research themes: interacting particle systems with kinetic constraints, bootstrap percolation cellular automata and mixed order phase transitions. These topics belong to the fertile area of mathematics at the intersection of probability and mathematical statistical mechanics. They are also extremely important in physics. Indeed they are intimately connected to the fundamental problem of understanding the liquid-glass transition, one of the longstanding open questions in condensed matter physics. The funding of this project will allow the PI to lead a highly qualified team with complementary expertise. Such a diversity will allow a novel, interdisciplinary and potentially groundbreaking approach. Even if research on each one of the above topics has been lately quite lively, very few exchanges and little cross-fertilization occurred among them. One of our main goals is to overcome the barriers among the three different research communities and to explore the interfaces of these yet unconnected fields. We will open two novel and challenging chapters in the mathematics of interacting particle systems and cellular automata: interacting particle glassy systems and bootstrap percolation models with mixed order critical and discontinuous transitions. In order to achieve our groundbreaking goals we will have to go well beyond the present mathematical knowledge. We believe that the novel concepts and the unconventional approaches that we will develop will have a deep impact also in other areas including combinatorics, theory of randomized algorithms and complex systems. The scientific background and expertise of the PI, with original and groundbreaking contributions in each of the above topics and with a broad and clearcut vision of the mathematics of the proposed research as well as of the fundamental physical questions,make the PI the ideal leader of this project.

883 250 €

Start date: 2016-09-01, End date: 2021-08-31

According to biologists, there is a need for quantitative models that are able to cope with the complexity of problems arising in the field of life sciences. Here, complexity refers to the interplay between various scales that are not clearly separate. The great challenge of the MESOPROBIO project is to analyse complex PDE models for biological propagation phenomena at the mesoscale. By analogy with the kinetic theory of gases, this is an intermediate level of description between the microscale (individual-based models) and the macroscale (parabolic reaction-transport-diffusion equations). The specific feature common to all the models involved in the project is the local heterogeneity with respect to a structure variable (velocity, phenotypical trait, age) which requires new mathematical methods. I propose to push analysis beyond classical upscaling arguments and to track the local heterogeneity all along the analysis. The biological applications are: concentration waves of bacteria, evolutionary aspects of structured populations (with respect to dispersal ability or life-history traits), and anomalous diffusion. The mathematical challenges are: multiscale analysis of PDE having different properties in different directions of the phase space, including nonlocal terms (scattering, competition), and possibly lacking basic features of reaction-diffusion equations such as the maximum principle. The outcomes are: travelling waves, accelerating fronts, approximation of geometric optics, nonlocal Hamilton-Jacobi equations, optimal foraging strategies and evolutionary dynamics of phenotypical traits. Emphasis will be placed on quantitative results with strong feedback towards biology. The project will be conducted in Lyon, a French hub for mathematical biology and hyperbolic equations. There will be close interaction with biologists in order to establish the most appropriate questions to answer. Several collaborations in Europe (UK, Austria) will be developed.

1 091 688 €

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

The main theme of this proposal is the Geometric Representation Theory of reductive algebraic groups over algebraically closed fields of positive characteristic. Our primary goal is to obtain character formulas for simple and for indecomposable tilting representations of such groups, by developing a geometric framework for their categories of representations. Obtaining such formulas has been one of the main problems in this area since the 1980's. A program outlined by G. Lusztig in the 1990's has lead to a formula for the characters of simple representations in the case the characteristic of the base field is bigger than an explicit but huge bound. A recent breakthrough due to G. Williamson has shown that this formula cannot hold for smaller characteristics, however. Nothing is known about characters of tilting modules in general (except for a conjectural formula for some characters, due to Andersen). Our main tools include a new perspective on Soergel bimodules offered by the study of parity sheaves (introduced by Juteau-Mautner-Williamson) and a diagrammatic presentation of their category (due to Elias-Williamson).

882 844 €

Start date: 2016-09-01, End date: 2021-08-31

Implantable neuroprosthetic devices offer the promise of restoring neurological functions to disabled individuals. Tests demonstrated that an array of microelectrodes implanted in cortex allows to record activity of the brain and to induce a movement on prosthetic limbs or electrical stimulations restore some visual sensations. For these applications the life time and stability of the electrodes are critical features for the reliable operation of any implantable neuronal device. It’s also necessary to have high density implant with small electrodes to cover a large surface of the cortex to have access of neuronal code. A reliable packaging for long term implantable devices are in titanium or glass but not suitable in the case of ECoG (ElectroCorticoGraphy) implant. Indeed, it is necessary to achieve a polymer implant as a core material, to follow the topology of the brain surface. But in long term the polymer swells and moisture penetrates the implant and degrades its performances therefore reducing the lifetime. The goal of NEURODIAM project is to address two major challenges: - increase the lifetime of implant by a specific packaging, - reduce the size of the electrodes to be equivalent to the neurones size (10 µm) without degradation of noise and consequently increase the electrode density for a fine mapping of the cortex. To avoid performance drift of the implant, a new packaging solution completely hermetic will be developed based on the last developments of micro and nano structuration of diamond layer that combines conductive and intrinsic synthetic diamond. Fast ageing tests will be settled to demonstrate the viability of this diamond technology. In-vitro and in-vivo assessment will be performed to demonstrate the efficiency of these implants for recording and stimulation of neuronal tissue. This project will produce high performance diamond based technology that can be later used for various implants dedicated to fundamental studies in neurosciences.

1 499 865 €

Start date: 2018-05-01, End date: 2023-04-30

This project is devoted to the mathematical and numerical analysis in statistical physics with a special interest to applications in Plasma Physics and nanotechnology with Micro Electro Mechanical Systems (MEMS). We propose to achieve numerical simulations in plasma physics by fully deterministic methods. Using super-computers, a non stationary collisional plasma can be modelled taking into account Coulombian interactions and self-consistent electromagnetic fields to study different regimes and instabilities. These methods are based on high order and conservative finite volume schemes for the transport and fast multi-grid methods for the treatment of collisions. The first application is the simulation of fast ignition or Inertial Confinement Fusion, which is an important issue in plasma physics. Here, the main difficulty concerns the modelling of collisions of relativistic particles and the development of new algorithms for their treatment. Another part is devoted to the derivation of moments models which require less computational effort but keep the main properties of the initial models. The second application concerns micro and nanotechnologies, which are expected to play a very important role in the development of MEMS. Since the scale of micro flows is often comparable with the molecular mean free path, it is necessary to adopt the point of view of kinetic theory. Then applications of kinetic theory methods to micro flows are becoming very important and an accurate approximation of the Boltzmann equation is a key issue. Even nowadays a deterministic numerical solution of the Boltzmann equation still represents a challenge for scientific computing. Recently, a new class of algorithms based on spectral techniques in the velocity space has been been developed for the trend to equilibrium. The next important step is to treat applications for MEMS in nanotechnology for which the main difficulty is to treat complex geometries and moving boundary problems.

490 000 €

Start date: 2010-01-01, End date: 2014-12-31

Gamma-ray Astronomy pinpoints celestial high energy particle accelerators and may reveal the origin of the cosmic-rays, a century after their discovery. Now is a time of extraordinary opportunity. Cherenkov telescopes have opened up a new domain and more than 70 very-high energy gamma-ray sources have been detected above 100 GeV, especially by the European experiments H.E.S.S. and MAGIC. NASA's Fermi Large Area Telescope, devoted to the study of the gamma-ray sky between 20 MeV and 300 GeV, was launched in June 2008 and has published the positions of 1500 previously unknown gamma-ray sources spread across the sky. However, among all the sources detected by satellite and Cherenkov telescopes, hundreds of Galactic gamma-ray sources have no obvious counterpart at optical, radio, or X-ray wavelengths. What are these sources ? What role do they play in the Galaxy's energy budget ? Many of them must be pulsars or nebulae powered by pulsars. In this project, I propose to use my expertise in both TeV and GeV gamma-ray analysis together with the excellent links of our team with radio observatories to identify the nature of these sources, focusing on pulsars and pulsar wind nebulae as primary candidates. I further propose to use the theoretical models of these cosmic accelerators that I have developed in the past both to enhance the search, and to interpret the results. The range of competences required for the proposed research project is very large and difficult to gather in one single team: pulsar timing, experience with data analysis of extended sources and theoretical know-how in pulsar wind nebulae and high energy phenomena. The P-WIND team would therefore be unique in gamma-ray Astronomy.

592 680 €

Start date: 2011-01-01, End date: 2013-12-31

Concepts from the theory of high-dimensional phenomena play a role in several areas of mathematics, statistics and computer science. Many results in this theory rely on tools and ideas originating in adjacent fields, such as transportation of measure, semigroup theory and potential theory. In recent years, a new symbiosis with the theory of stochastic calculus is emerging. In a few recent works, by developing a novel approach of pathwise analysis, my coauthors and I managed to make progress in several central high-dimensional problems. This emerging method relies on the introduction of a stochastic process which allows one to associate quantities and properties related to the high-dimensional object of interest to corresponding notions in stochastic calculus, thus making the former tractable through the analysis of the latter. We propose to extend this approach towards several long-standing open problems in high dimensional probability and geometry. First, we aim to explore the role of convexity in concentration inequalities, focusing on three central conjectures regarding the distribution of mass on high dimensional convex bodies: the Kannan-Lov'asz-Simonovits (KLS) conjecture, the variance conjecture and the hyperplane conjecture as well as emerging connections with quantitative central limit theorems, entropic jumps and stability bounds for the Brunn-Minkowski inequality. Second, we are interested in dimension-free inequalities in Gaussian space and on the Boolean hypercube: isoperimetric and noise-stability inequalities and robustness thereof, transportation-entropy and concentration inequalities, regularization properties of the heat-kernel and L_1 versions of hypercontractivity. Finally, we are interested in developing new methods for the analysis of Gibbs distributions with a mean-field behavior, related to the new theory of nonlinear large deviations, and towards questions regarding interacting particle systems and the analysis of large networks.

1 308 188 €

Start date: 2019-01-01, End date: 2023-12-31

The presence of organic compounds was essential to the emergence of life on Earth 3.5 to 3.8 billion years ago. Such compounds may have had several different origins; amongst them the ocean-atmosphere coupled system (the primordial soup theory), or exogenous inputs by meteorites, comets and Interplanetary Dust Particles. Titan, the largest moon of Saturn, is the best known observable analogue of the Early Earth. I recently identified a totally new source of prebiotic material for this system: the upper atmosphere. Nucleobases have been highlighted as components of the solid aerosols analogues produced in a reactor mimicking the chemistry that occurs in the upper atmosphere. The specificity of this external layer is that it receives harsh solar UV radiations enabling the chemical activation of molecular nitrogen N2, and involving a nitrogen rich organic chemistry with high prebiotic interest. As organic solid aerosols are initiated in the upper atmosphere of Titan, a new question is raised that I will address: what is the evolution of these organic prebiotic seeds when sedimenting down to the surface? Aerosols will indeed undergo the bombardment of charged particles, further UV radiation, and/or coating of condensable species at lower altitudes. I expect possible changes on the aerosols themselves, but also on the budget of the gas phase through emissions of new organic volatiles compounds. The aerosols aging may therefore impact the whole atmospheric system. An original methodology will be developed to address this novel issue. The successive aging sequences will be experimentally simulated in chemical reactors combining synchrotron and plasma sources. The interpretation of the experimental results will moreover be supported by a modelling of the processes. This complementary approach will enable to decipher the aerosols evolution in laboratory conditions and to extrapolate the impact on Titan atmospheric system.

1 487 500 €

Start date: 2015-09-01, End date: 2021-08-31

This project is dedicated to the study of two distinct classes of dynamical systems which display a quasiperiodic component. The first class consists of quasiperiodic cocycles, and we will largely focus on connections with the spectral theory of quasiperiodic Schrodinger operators. Up to very recently, our understanding had been mostly restricted to situations where the potential would have some clear characteristics of large or small potentials. In particular, no genuinely global theory had been devised that could go so far as give insight on the phase-transition between large-like and small-like potentials. With the introduction by the PI of techniques to analyze the parameter dependence of one-frequency potentials which involve much less control of the dynamics of associated cocycles, and the discovery of new regularity features of this dependence, it is now possible to elaborate a precise conjectural global picture, whose proof is one of the major goals of the project. The second class consists of translation flows on higher genus surfaces. The Teichmuller flow acts as renormalization in this class, and its chaotic features have permitted a detailed description of the dynamics of typical translation flows. This project will concentrate on the the development of techniques suitable to the analysis of non-typical families of translation flows, which arise naturally in the context of certain applications, as for rational billiards. We aim to obtain results regarding the spectral gap for restrictions of the SL(2,R action, the existence of polynomial deviations outside exceptional cases, and the weak mixing property for certain billiards.

1 020 840 €

Start date: 2010-12-01, End date: 2015-11-30

The goal of this project is to study random walks on groups, with the focus on boundary theory. We plan to establish new criteria for estimates of the entropy and Poisson-Furstenberg boundary triviality and apply this method to study the following question: which groups admit simple random walks with trivial boundary? In particular, we want to produce a classification for classes of solvable groups, more generally elementary amenable groups, and groups acting on rooted trees. We plan to make a contibution in the solution of the conjecture of Vershik and Kaimanovich, posed in the early eighties, that states that any group of exponential growth admits a symmetric measure with non-trivial boundary. We plan to study applications of random walks to growth of groups. In my previous work I have produced a method to use boundaries in order to obtain new low estimates for groups of Grigorchuk of intermediate growth. We plan to construct new classes of groups of intermediate growth, and to refine the existing method to obtain sharp bounds of the growth function. We also want to address Grigorchuk's conjecture about the gap in the range of possible growth functions of groups. Further applications include large scale geometrical properties of amenable groups, including amenable groups acting on rooted trees, as well as groups of orientation preserving diffeomorphisms of the interval, in particular, Richard Thompson group F

856 320 €

Start date: 2010-09-01, End date: 2015-08-31

Current chemotherapeutic agents are potent enough to kill cancer cells. Nonetheless, failure of chemotherapies for many cancers (e.g. breast and pancreatic cancers and various sarcomas) is primarily because these agents cannot reach cancer cells in amounts sufficient to cause complete cure. The abnormal microenvironment of these tumors drastically reduces perfusion and results in insufficient delivery of therapeutic agents. Tumor structural abnormalities is in large part an effect of mechanical stresses developed within the tumor due to unchecked cancer cell proliferation that strains the tumor microenvironment. Alleviation of these stresses has the potential to normalize the tumor, enhance delivery of drugs and improve treatment efficacy. Here, I propose to test the hypothesis that re-engineering the tumor microenvironment with stress-alleviating drugs has the potential to enhance chemotherapy. To explore this hypothesis, I will make use of a mixture of cutting-edge computational and experimental techniques. I will develop sophisticated models for the biomechanical response of tumors to analyze how stresses are generated and transmitted during tumor progression. Subsequently, I will perform animal studies to validate model predictions and indentify the drug that more effectively alleviates stress levels, normalizes the tumor microenvironment and improves chemotherapy. Successful completion of this research will reveal the mechanisms for stress generation and storage in tumors and will lead to new strategies for the use of chemotherapy.

1 440 360 €

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

"The least action principle is one of the most classical tools in the study of convex Hamiltonian systems. It consists in finding specific orbits by minimizing the Lagrangian action functional. Another powerful classical tool in Hamiltonian dynamics is the theory of canonical transformations, which provides a large class of admissible changes of coordinates, allowing to put many systems into simplified normal forms. These two tools are difficult to use simultaneously because the Lagrangian action does not behave well under canonical transformations. A large part of the development of symplectic geometry in the second half of the last century consisted in bridging this gap, by developing a framework encompassing a large part of both theories. For example, the direct study of the Hamiltonian action functional (which, as opposed to the Lagrangian action functional, behaves well under canonical transformations) allowed to recover, refine, and generalize beyond the convexity hypothesis, most of the results concerning the existence of periodic orbits which had been proved with the least action principle. Twenty years ago, under the impulsion of John Mather, a renewed use of the least action principle led to the proof of the existence of complicated invariant sets and unstable orbits. This collection of new methods has been called weak KAM theory in view of some similarities with the classical KAM theory. Weak KAM theory, however, uses the least action principle in such a fundamental way that it does not not enter yet into the symplectic framework. My project is to address this problem. This overarching goal federates a number of questions in weak KAM theory, in Hamiltonian dynamics, in symplectic geometry and even in partial differential equations which will be the starting directions of my investigations."

840 000 €

Start date: 2012-09-01, End date: 2017-08-31

Amyloid diseases are of increasing concern in our aging society. These diseases all involve the aggregation of misfolded proteins, called amyloid, which are specific for each disease (PrP for Prion, Abeta for Alzheimer's). When misfolded these proteins propagate the abnormal configuration and aggregate to others, forming very long polymers also called fibrils. Elucidating the intrinsic mechanisms of these chain reactions is a major challenge of molecular biology: do polymers break or coalesce? Do specific sizes polymerize faster? What is the size of the so-called nucleus, i.e., the minimum stable size for polymers? On which part of the reactions should a treatment focus to arrest the disease ? Up to now, only very partial and partially justified answers have been provided. This is mainly due to the extremely high complexity of the considered processes, which may possibly involve an infinite number of species and reactions (and thus, an infinite system of equations). The great challenge of this project is to design new mathematical methods in order to model fibril reactions, analyse experimental data, help the biologists to discover the key mechanisms of polymerization in these diseases, predict the effects of new therapies. Our approach is based on a new mathematical model which consists in the nonlinear coupling of a size-structured Partial Differential Equation (PDE) of fragmentation-coalescence type, with a small number of Ordinary Differential Equations. On the one hand, we shall solve new and broad mathematical issues, in the fields of PDE analysis, numerical analysis and statistics. These problems are mathematically challenging and have a wide field of applications. On the other hand we want to test their efficacy on real data, thanks to an already well-established collaboration with a team of biophysicists. With such a continuing comparison with experiments, we aim at constantly aligning our mathematical problems to biological concerns.

1 203 569 €

Start date: 2012-12-01, End date: 2018-07-31