ERC FUNDED PROJECTS

The rupture of an Aortic Aneurysm (AA), which is often lethal, is a mechanical phenomenon that occurs when the wall stress state exceeds the local strength of the tissue. Our current understanding of arterial rupture mechanisms is poor, and the physics taking place at the microscopic scale in these collagenous structures remains an open area of research. Understanding, modelling, and quantifying the micro-mechanisms which drive the mechanical response of such tissue and locally trigger rupture represents the most challenging and promising pathway towards predictive diagnosis and personalized care of AA. The PI's group was recently able to detect, in advance, at the macro-scale, rupture-prone areas in bulging arterial tissues. The next step is to get into the details of the arterial microstructure to elucidate the underlying mechanisms. Through the achievements of AArteMIS, the local mechanical state of the fibrous microstructure of the tissue, especially close to its rupture state, will be quantitatively analyzed from multi-photon confocal microscopy and numerically reconstructed to establish quantitative micro-scale rupture criteria. AArteMIS will also address developing micro-macro models which are based on the collected quantitative data. The entire project will be completed through collaboration with medical doctors and engineers, experts in all required fields for the success of AArteMIS. AArteMIS is expected to open longed-for pathways for research in soft tissue mechanobiology which focuses on cell environment and to enable essential clinical applications for the quantitative assessment of AA rupture risk. It will significantly contribute to understanding fatal vascular events and improving cardiovascular treatments. It will provide a tremendous source of data and inspiration for subsequent applications and research by answering the most fundamental questions on AA rupture behaviour enabling ground-breaking clinical changes to take place.

1 499 783 €

Start date: 2015-04-01, End date: 2020-03-31

"Combustion is essential to the world’s energy generation and transport needs, and will remain so for the foreseeable future. Mitigating its impact on the climate and human health, by reducing its associated emissions, is thus a priority. One significant challenge for gas-turbine combustion is combustion instability, which is currently inhibiting reductions in NOx emissions (these damage human health via a deterioration in air quality). Combustion instability is caused by a two-way coupling between unsteady combustion and acoustic waves - the large pressure oscillations that result can cause substantial mechanical damage. Currently, the lack of fast, accurate modelling tools for combustion instability, and the lack of reliable ways of suppressing it are severely hindering reductions in NOx emissions. This proposal aims to make step improvements in both fast, accurate modelling of combustion instability, and in developing reliable active control strategies for its suppression. It will achieve this by coupling low order combustor models (these are fast, simplified models for simulating combustion instability) with advances in analytical modelling, CFD simulation, reduced order modelling and control theory tools. In particular: * important advances in accurately incorporating the effect of entropy waves (temperature variations resulting from unsteady combustion) and non-linear flame models will be made; * new active control strategies for achieving reliable suppression of combustion instability, including from within limit cycle oscillations, will be developed; * an open-source low order combustor modelling tool will be developed and widely disseminated, opening access to researchers worldwide and improving communications between the fields of thermoacoustics and control theory. Thus the proposal aims to use analytical and computational methods to contribute to achieving low NOx gas-turbine combustion, without the penalty of damaging combustion instability."

1 489 309 €

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

I propose to establish a research group to develop completely new tools in order to solve three important problems on the relationships between automorphic forms and Galois representations, which lie at the heart of the Langlands program. The first is to prove Serre’s conjecture for real quadratic fields. I will use automorphic induction to transfer the problem to U(4) over the rational numbers, where I will use automorphy lifting theorems and results on the weight part of Serre's conjecture that I established in my earlier work to reduce the problem to proving results in small weight and level. I will prove these base cases via integral p-adic Hodge theory and discriminant bounds. The second is to develop a geometric theory of moduli spaces of mod p and p-adic Galois representations, and to use it to establish the Breuil–Mézard conjecture in arbitrary dimension, by reinterpreting the conjecture in geometric terms. This will transform the subject by building the first connections between the p-adic Langlands program and the geometric Langlands program, providing an entirely new world of techniques for number theorists. As a consequence of the Breuil-Mézard conjecture, I will be able to deduce far stronger automorphy lifting theorems (in arbitrary dimension) than those currently available. The third is to completely determine the reduction mod p of certain two-dimensional crystalline representations, and as an application prove a strengthened version of the Gouvêa–Mazur conjecture. I will do this by means of explicit computations with the p-adic local Langlands correspondence for GL_2(Q_p), as well as by improving existing arguments which prove multiplicity one theorems via automorphy lifting theorems. This work will show that the existence of counterexamples to the Gouvêa-Mazur conjecture is due to a purely local phenomenon, and that when this local obstruction vanishes, far stronger conjectures of Buzzard on the slopes of the U_p operator hold.

1 131 339 €

Start date: 2012-10-01, End date: 2017-09-30

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

We are concerned with localization properties of solutions to hyperbolic PDEs, especially problems with a geometric component: how do boundaries and heterogeneous media influence spreading and concentration of solutions. While our first focus is on wave and Schrödinger equations on manifolds with boundary, strong connections exist with phase space localization for (clusters of) eigenfunctions, which are of independent interest. Motivations come from nonlinear dispersive models (in physically relevant settings), properties of eigenfunctions in quantum chaos (related to both physics of optic fiber design as well as number theoretic questions), or harmonic analysis on manifolds. Waves propagation in real life physics occur in media which are neither homogeneous or spatially infinity. The birth of radar/sonar technologies (and the raise of computed tomography) greatly motivated numerous developments in microlocal analysis and the linear theory. Only recently toy nonlinear models have been studied on a curved background, sometimes compact or rough. Understanding how to extend such tools, dealing with wave dispersion or focusing, will allow us to significantly progress in our mathematical understanding of physically relevant models. There, boundaries appear naturally and most earlier developments related to propagation of singularities in this context have limited scope with respect to crucial dispersive effects. Despite great progress over the last decade, driven by the study of quasilinear equations, our knowledge is still very limited. Going beyond this recent activity requires new tools whose development is at the heart of this proposal, including good approximate solutions (parametrices) going over arbitrarily large numbers of caustics, sharp pointwise bounds on Green functions, development of efficient wave packets methods, quantitative refinements of propagation of singularities (with direct applications in control theory), only to name a few important ones.

1 293 763 €

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

Many parts of Graph Theory have witnessed a huge growth over the last years, partly because of their relation to Theoretical Computer Science and Statistical Physics. These connections arise because graphs can be used to model many diverse structures. The focus of this proposal is on asymptotic results, i.e. the graphs under consideration are large. This often unveils patterns and connections which remain obscure when considering only small graphs. It also allows for the use of powerful techniques such as probabilistic arguments, which have led to spectacular new developments. In particular, my aim is to make decisive progress on central problems in the following 4 areas: (1) Factorizations: Factorizations of graphs can be viewed as partitions of the edges of a graph into simple regular structures. They have a rich history and arise in many different settings, such as edge-colouring problems, decomposition problems and in information theory. They also have applications to finding good tours for the famous Travelling salesman problem. (2) Hamilton cycles: A Hamilton cycle is a cycle which contains all the vertices of the graph. One of the most fundamental problems in Graph Theory/Theoretical Computer Science is to find conditions which guarantee the existence of a Hamilton cycle in a graph. (3) Embeddings of graphs: This is a natural (but difficult) continuation of the previous question where the aim is to embed more general structures than Hamilton cycles - there has been exciting progress here in recent years which has opened up new avenues. (4) Resilience of graphs: In many cases, it is important to know whether a graph `strongly’ possesses some property, i.e. one cannot destroy the property by changing a few edges. The systematic study of this notion is a new and rapidly growing area. I have developed new methods for deep and long-standing problems in these areas which will certainly lead to further applications elsewhere.

818 414 €

Start date: 2012-12-01, End date: 2018-11-30

Back pain affects eight out of ten adults during their lifetime. It a huge economic burden on society, estimated to cost as much as 1-2% of gross national product in several European countries. Treatments for back pain have lower levels of success and are not as technologically mature as those for other musculoskeletal disorders such as hip and knee replacement. This application proposes to tackle one of the major barriers to the development of better surgical treatments for back pain. At present, new spinal devices are commonly assessed in isolation in the laboratory under standardised conditions that do not represent the variation across the patient population. Consequently many interventions have failed during clinical trials or have proved to have poor long term success rates. Using a combination of computational and experimental models, a new testing methodology will be developed that will enable the variation between patients to be simulated for the first time. This will enable spinal implants and therapies to be more robustly evaluated across a virtual patient population prior to clinical trial. The tools developed will be used in collaboration with clinicians and basic scientists to develop and, crucially, optimise new treatments that reduce back pain whilst preserving the unique functions of the spine. If successful, this approach could be translated to evaluate and optimise emerging minimally invasive treatments in other joints such as the hip and knee. Research in the spine could then, for the first time, lead rather than follow that undertaken in other branches of orthopaedics.

1 498 777 €

Start date: 2012-12-01, End date: 2018-11-30

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

The agile and efficient flight of birds shows what flight performance is physically possible, and in theory could be achieved by unmanned air vehicles (UAVs) of the same size. The overall aim of this project is to enhance the performance of small scale UAVs by developing novel technologies inspired by understanding how birds are adapted to interact with airflows. Small UAVs have the potential to dramatically change current practices in many areas such as, search and rescue, surveillance, and environmental monitoring. Currently the utility of these systems is limited by their operational endurance and their inability to operate in strong turbulent winds, especially those that often occur in urban environments. Birds are adapted to be able to fly in these conditions and actually use them to their advantage to minimise their energy output. This project is composed of three tracks which contain elements of technology development, as well as scientific investigation looking at bird flight behaviour and aerodynamics. The first track looks at developing path planning algorithms for UAVs in urban environments based on how birds fly in these areas, by using GPS tracking and computational fluid dynamics alongside trajectory optimization. The second track aims to develop artificial wings with improved gust tolerance inspired by the features of feathered wings. Here, high speed video measurements of birds flying through gusts will be used alongside wind tunnel testing of artificial wings to discover what features of a bird’s wing help to alleviate gusts. The third track develops novel force and flow sensor arrays for autonomous flight control based on the sensor arrays found in flying animals. These arrays will be used to make UAVs with increased agility and robustness. This unique bird inspired approach uses biology to show what is possible, and engineering to find the features that enable this performance and develop them into functional technologies.

1 998 546 €

Start date: 2016-04-01, End date: 2021-03-31

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

Craniosynostosis is a group of congenital craniofacial abnormalities consisting in premature fusion (ossification) of one or more cranial sutures during infancy. This results in growth restriction perpendicular to the axis of the suture and promotes growth parallel to it, causing physical deformation of the cranial and facial skeleton, as well as distortion of the underling brain, with potential detrimental effects on its function: visual loss, sleep apnoea, feeding and breathing difficulties, and neurodevelopment delay. Conventional management of craniosynostosis involves craniofacial surgery delivered by excision of the prematurely fused sutures, multiple bone cuts and remodelling of the skull deformities, with the primary goal of improving patient function, while normalising their appearance. Cranial vault remodelling surgical procedures, aided by internal and external devices, have proven functionally and aesthetically effective in correcting skull deformities, but final results remain unpredictable and often suboptimal because of an incomplete understanding of the biomechanical interaction between the device and the skull. The overall aim of this grant is to create a validated and robust computational framework that integrates patient information and device design to deliver personalised care in paediatric craniofacial surgery in order to improve clinical outcomes. A virtual model of the infant skull with craniosynostosis, including viscoelastic properties and mechano-biology regulation, will be developed to simulate device implantation and performance over time, and will be validated using clinical data from patient populations treated with current devices. Bespoke new devices will be designed allowing for pre-programmed 3D shapes to be delivered with continuous force during the implantation period. Patient specific skull models will be used to virtually test and optimise the personalised devices, and to tailor the surgical approach for each individual case.

1 498 772 €

Start date: 2018-03-01, End date: 2023-02-28

In the epoch of Gaia, fundamental stellar properties will be made widely available for large numbers of stars. These properties are expected to unleash a new wave of discovery in the field of astrophysics. But while many properties of stars are measurable, meaningful Helium abundances (Y) remain elusive and as a result fundamental properties are not accurate. Helium enrichment laws, which underpin most stellar properties, link initial Y to initial metallicity, but these relations are very uncertain with gradients (dY/dZ) spanning the range 1 to 3. This uncertainty is the initial Y problem and this is a bottleneck that must be overcome to unleash the true potential of Gaia. Without measurements of initial Y for all stars we need to find alternative observables that trace out the evolution of initial Y. We will search for better tracers using the power of asteroseismology as a calibrator. Asteroseismic measures of Helium will be used to construct a map from observable properties (fundamental, chemical or even dynamical) back to initial Helium. This is a challenge that can only be solved through the use of the latest asteroseismic techniques coupled to a rigorous yet flexible statistical scheme. I am uniquely qualified in the cutting edge methods of asteroseismology and the application of advanced multi-level statistical models. The intersection of these two skill sets will allow me to solve the initial Helium problem. The motivation for a timely solution to this problem could not be stronger. We have just entered an age of large asteroseismic datasets, vast spectroscopic surveys, and the billion star program of Gaia. The next wave of scientific breakthroughs in stellar physics, exoplanetary science, and Galactic archeology will be held back unless accurate fundamental stellar properties are available. We can only produce these accurate properties with a reliable map of stellar Helium.

1 496 203 €

Start date: 2019-04-01, End date: 2024-03-31

The proposed project aims at analyzing fundamental problems from combinatorics using the most current methods available and at providing new structural and algorithmic insights to such problems. The problems considered will be treated on a general level of classes of combinatorial objects of the same kind and the developed general methods will also be applied to specific open problems. Classes of dense and sparse objects will be treated using different techniques. Dense combinatorial objects appear in extremal combinatorics and tools developed to handle them found their applications in different areas of mathematics and computer science. The project will focus on extending known methods to new classes of combinatorial objects, in particular those from algebra, and applying the most current techniques including Razborov flag algebras to problems from extremal combinatorics. Applications of the obtained results in property testing will also be considered. On the other hand, algorithmic applications often include manipulating with sparse objects. Examples of sparse objects are graphs embeddable in a fixed surface and more general minor-closed classes of graphs. The project objectives include providing new structural results and algorithmic metatheorems for classes of sparse objects using both classical tools based on the theory of graph minors as well as new tools based on the framework of classes of nowhere-dense structures.

849 000 €

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

"Magnetism plays a profound role in stars and planets. In the Sun, magnetic fields are ultimately responsible for solar flares and coronal mass ejections that can impact our technological society. Earth's own magnetic field partly shields us from these events, but solar storms can still interrupt satellite communications, disrupt power grids, and pose a danger to astronauts on spacewalks. More generally, magnetic fields partly control the rotational evolution of stars, likely impact the habitability of extrasolar planets, and may modify the sizes and internal structures of low-mass stars and gaseous planets. In all cases, the magnetism is generally thought to arise from a convective dynamo -- but a detailed theoretical understanding of this process, and its influence on the overall evolution of stars and planets, has remained elusive. Particularly fascinating observational puzzles have recently come from the study of low-mass M-dwarf stars: the most numerous type of stars in our galaxy and perhaps the most likely to host habitable planets. We therefore propose to study how stars and sub-stellar objects build magnetic fields using 3-D magnetohydrodynamic simulations, and to quantify the effects of those fields on stellar structure and evolution. Using the Anelastic Spherical Harmonic (ASH) and Compressible Spherical Segment (CSS) codes, we will examine (a) how global magnetic field generation in these stars depends upon parameters like stellar mass, rotation rate, and the presence of a stable core, and (b) how the deep convection and magnetism imprints through (and is shaped by) the near-surface layers of these objects. We will (c) determine the impact of the resulting fields on the convective transport of heat and angular momentum, incorporate our results into state of the art 1-D evolutionary models of stars, and explore the consequences for stellar evolution. Separately, we will (d) develop and maintain a public database of 3-D convective dynamo models."

1 469 070 €

Start date: 2013-12-01, End date: 2018-11-30

Galaxy formation is one of the most fascinating yet challenging fields of astrophysics. The desire to understand galaxy formation has led to the design of ever more sophisticated telescopes which show a bewildering variety of galaxies in the Universe. However, the degree to which an interpretation of this wealth of data can succeed depends critically on having accurate and realistic theoretical models of galaxy formation. While cosmological simulations of galaxy formation provide the most powerful technique for calculating the non-linear evolution of cosmic structures, the enormous dynamic range and poorly understood baryonic physics are main uncertainties of present simulations. This impacts on their predictive power and is the major obstacle to our understanding of observational data. The objective of this proposal is to drastically improve upon the current state-of-the-art by i) including more realistic physical processes, such as those occurring at the sphere of influence of a galaxy’s central black hole and ii) greatly extending spatial dynamical range with the aid of a novel technique I have developed. With this technique I want to address one of the major unsolved issues of galaxy formation: “How do galaxies and their central black holes coevolve?” Specifically, I want to focus on three crucial areas of galaxy formation: a) How and where the very first black holes form, what are their observational signatures, and when is the coevolution with host galaxies established? b) Is black hole heating solely responsible for the morphological transformation and quenching of massive galaxies, or are other processes important as well? c) What is the impact of supermassive black holes on galaxy clusters and can we calibrate baryonic physics in clusters to use them as high precision cosmological probes? The requested funding is for 50% of the PI’s time and three postdoctoral researchers to establish an independent research group at the KICC and IoA, Cambridge.

1 975 062 €

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

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

The early universe is a “laboratory” for testing physics at very high energies, up to a trillion times greater than the energies reached by the Large Hadron Collider. The origin of structure in the universe is deeply tied to this extreme physics, which is imprinted in the primordial ripples seen in the cosmic microwave background (CMB). CMB data have thus far led the way in constraining early universe physics, and ESA’s Planck satellite is currently mapping the CMB at the highest precision ever achieved. However, next generation galaxy surveys – such as the Dark Energy Survey (DES), starting next year – will rival the CMB in their ability to unlock the secrets of the primordial universe. I will use the Planck and DES data to rigorously test the theory of inflation, the dominant paradigm for the origin of cosmic structure, and to seek signatures of new physics that are likely to exist at these unexplored energies. I have already played a leading role in bringing theory and robust data analysis together to understand the very early universe. This proposal aims, for the first time, to go beyond simply testing generic predictions of the inflationary paradigm, to gain a fundamental understanding of the physics responsible for the origin of cosmic structure. The keys to achieving this goal are: theoretical modelling at the cutting edge of fundamental physics (describing not just the inflationary period but also pre- and post-inflationary physics); advanced Bayesian and wavelet methods to extract reliable information from the data; a deep understanding of data limitations and control of systematics. The project will produce definitive results at the interface of cosmology and high energy physics, defining the frontiers of these fields well beyond the lifetimes of the surveys themselves.

1 493 066 €

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

"Rarely in astrophysics are there opportunities to spectrally classify a completely new group of astrophysical objects. This is the challenge facing the exoplanets christened “hot Jupiters”. The detection and subsequent spectroscopic information now achievable for a large number of these exoplanets are now allowing for detailed comparative exoplanetology. This project uses a twofold approach to advance both the theory and observation of these exoplanets beyond their current limitations. Hot Jupiter atmospheric spectra are built from two large observational survey programmes headed by Dr. Sing to obtain a vast amount of high quality data on transmission spectra. One large programme uses the HST which alone will quadruple the number of broadband exoplanet transmission spectra. The Hubble survey will be augmented by a large programme on the GTC telescope, where we will put efforts into pioneering multi-object spectroscopy, capable of delivering space-like quality spectra. Both large programmes will be further complemented by followup observations, as well as existing near-IR spectroscopy. This project will combine this plethora of data in a coherent fashion, enabling studies of nearly the entire planetary atmosphere. Our observational efforts will be combined with a broad and inclusive theoretical modeling programme, where we will incorporate clouds and hazes, modelling the complete atmosphere in a self-consistent manner with a 3D global circulation model. Our library of transmission spectra across the hot-Jupiter class will be used to address long outstanding and complex issues. We will focus our efforts on two key areas, addressing why some hot Jupiters have hazes & clouds while others do not, and the outstanding issue on the presence or absence of stratospheres. For the first time a comprehensive set of high quality exoplanet spectra will be available with which to inter-compare using the required set of theoretical tools."

1 495 824 €

Start date: 2013-11-01, End date: 2018-10-31

The project proposes the development of an intelligent crystallisation system by combining state-of-the-art process analytical technologies and novel model-based and statistical feedback control approaches, to provide a fully integrated and adaptive system for efficient engineering of particulate products. The developed adaptive and robust control approaches will be incorporated in a Crystallisation Process Informatics System, to provide an intelligent decision support system, which triggers the suitable control algorithm taking into account the effect of crystallisation on the downstream processing units and final product properties. In this way crystallisation becomes a key intelligent “process actuator” in the whole production system, that manipulates final properties of the solid product taking into account operational, regulatory and economic constraints of the entire process, opening the way towards novel product engineering approaches. The project will bring the implementation of a new generation of integrated, intensified and intelligent crystallisation systems with drastically improved flexibility, predictability, stability and controllability. The system will be used for detailed evaluation of the current paradigm shift from batch to continuous processes in the pharmaceutical industries. Besides providing a breakthrough in crystallisation science the results could revolutionise the methods in which crystallisation will be designed and controlled in the future, yielding to the development of the emerging research field of Pharmaceutical Systems Engineering, by providing a comprehensive framework for the development of novel integrated pharmaceutical production units and product engineering technologies, for sustainable pharmaceutical production, with the aim of reducing time-to-market and increasing product quality, therefore providing considerable increase in quality of life, for example, by making new products available more quickly and at lower cost.

1 263 702 €

Start date: 2011-09-01, End date: 2017-08-31

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

Core formation represents the major chemical differentiation event on the terrestrial planets, involving the separation of a metallic liquid from the silicate matrix that subsequently evolves into the current silicate crust and mantle. The generation of the Earth’s magnetic field is ultimately tied to the segregation and crystallization of the core, and is an important factor in establishing planetary habitability. The processes that control core segregation and the depths and temperatures at which this process took place are poorly understood, however. We propose to study those processes. Specifically, the density of the core is lower than would be expected for pure iron, indicating that a light component (O, Si, S, C, H) must be present. Similarly, the Earth’s mantle is richer in iron-loving (“siderophile”) elements, e.g, V, W, Mo, Ru, Pd, etc., than would be expected based upon low pressure metal-silicate partitioning data. Solutions to these problems are hampered by the pressure range of existing experimental data, < 25 GPa, equivalent to ~700 km in the Earth. We propose to extend the accessible range of pressures and temperatures by developing protocols that link the laser-heated diamond anvil cell with analytical techniques such as (i) the NanoSIMS, (ii) the focused ion beam device (FIB), (iii) and transmission and secondary electron microscopy, allowing us to obtain quantitative data on element partitioning and chemical composition at extreme conditions relevant to the Earth’s lower mantle. The technical motivation follows from the fact that the real limitation on trace element partitioning studies at ultra high-pressure has been the grain size of the phases produced at high P-T, relative to the spatial resolution of the analytical methods available to probe the experiments; we can bridge the gap by combining state-of-the-art laser heating experiments with new nano-scale analytical techniques.

1 509 200 €

Start date: 2008-11-01, End date: 2013-10-31

I propose to measure the growth of non-linear structure in the dark universe to answer two fundamental questions in cosmology: Is the Cold Dark Matter structure formation theory compatible with the galaxy distribution on group scales? Is the accelerating expansion of the Universe caused by Dark Energy? This frontier research probes two key components of our standard cosmological model. This study is fundamental for understanding structure formation and galaxy evolution, leading to possible ground-breaking changes in our comprehension of gravitational physics. I will tackle this ambitious research plan by exploiting my extensive knowledge of galaxy survey analyses and propose to critically test our standard model by measuring three key properties: the shape and evolution of the Cold Dark Matter halo mass function; the efficiency of galaxy formation in Local Group sized systems; the evolution of the growth of structure. To achieve those decisive goals, I will build the DEGAS Team, an inter-disciplinary unit dedicated to solve photometric and spectroscopic survey systematics, to develop optimal clustering statistics for imaging surveys and to create a large variety of state-of-the-art mock Universes to interpret the statistical analyses. The techniques developed will be applied to two world-leading galaxy surveys: GAMA, a multi-wavelength redshift survey of which I am a founder and co-PI, and Pan-STARRS PS1, a unique 3/4-sky imaging survey. Using innovative clustering statistics accounting for individual photometric redshift distributions and statistically robust methods for halo mass function estimates, my DEGAS Team will provide the ultimate test for structure formation models, gain key insights on galaxy evolution and present novel constraints on the nature of gravity.

1 256 696 €

Start date: 2011-01-01, End date: 2016-12-31

Discrete subgroups of Lie groups, whose study originated in Fuchsian differential equations and crystallography at the end of the 19th century, are the basis of a large aspect of modern geometry. They are the object of fundamental theories such as Teichmüller theory, Kleinian groups, rigidity theories for lattices, homogeneous dynamics, and most recently Higher Teichmüller theory. They are closely related to the notion of a geometric structure on a manifold, which has played a crucial role in geometry since Thurston. In summary, discrete subgroups are a meeting point of geometry with Lie theory, differential equations, complex analysis, ergodic theory, representation theory, algebraic geometry, number theory, and mathematical physics, and these fascinating interactions make the subject extremely rich. In real rank one, important classes of discrete subgroups of semisimple Lie groups are known for their good geometric, topological, and dynamical properties, such as convex cocompact or geometrically finite subgroups. In higher real rank, discrete groups beyond lattices remain quite mysterious. The goal of the project is to work towards a classification of discrete subgroups of semisimple Lie groups in higher real rank, from two complementary points of view. The first is actions on Riemannian symmetric spaces and their boundaries: important recent developments, in particular in the theory of Anosov representations, give hope to identify a number of meaningful classes of discrete groups which generalise in various ways the notions of convex cocompactness and geometric finiteness. The second point of view is actions on pseudo-Riemannian symmetric spaces: some very interesting geometric examples are now well understood, and recent links with the first point of view give hope to transfer progress from one side to the other. We expect powerful applications, both to the construction of proper actions on affine spaces and to the spectral theory of pseudo-Riemannian manifolds

1 049 182 €

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

Active galactic nuclei (AGN) represent the active growing phases of supermassive black holes. For the first time, we are able to resolve the dusty gas on parsec scales and directly test our standard picture of these objects. While this “unification scheme” relates the parsec-scale IR emission with a geometrically-thick disk, I have recently found that the bulk of the dust emission comes from the polar region of the alleged disk where gas is blown out from the vicinity of the black hole. Along with these polar features, the compactness of the dust distribution seems to depend on the accretion state of the black hole. Neither of these findings have been predicted by current models and lack a physical explanation. To explain the new observations, I proposed a revision to the AGN unification scheme that involves a dusty wind driven by radiation pressure. Depending on their masses, velocities, and frequency, such dusty winds might play a major role in self regulating AGN activity and, thus, impact the interplay between host and black hole evolution. However, as of now we do not know if these winds are ubiquitous in AGN and how they would work physically. Upon completion of the research program, I want to • characterise the pc-scale mass distribution, its kinematics, and the connection to the accretion state of the AGN, • have a physical explanation of the dusty wind features and constrain its impacts on the AGN environment, and • have established dust parallax distances to several nearby AGN, as a multi-disciplinary application of the constraints on the dust distribution. For that, I will combine the highest angular resolution observations in the IR and sub-mm to create the first pc-scale intensity, velocity, and density maps of a sample of 11 AGN. I will develop a new model that combines hydrodynamic simulations with an efficient treatment of radiative transfer to simulate dusty winds. Finally, direct distances to 12 AGN with a combined 3% precision will be measured.

1 475 171 €

Start date: 2016-05-01, End date: 2021-04-30

In our project we address several fundamental questions regarding ergodic-theoretical properties of actions of large groups. The problems that we plan to tackle are not only of central importance in the abstract theory of dynamical systems, but they also lead to solutions of a number of open questions in Diophantine geometry such as the Batyrev--Manin and Peyre conjectures on the asymptotics and the distribution of rational points on algebraic varieties, a generalisation of the Oppenheim conjecture on distribution of values of polynomial functions, a generalisation of Khinchin and Dirichlet theorems on Diophantine approximation in the setting of homogeneous varieties, and estimates on the number of integral points (with almost prime coordinates satisfying polynomial and congruence equations. The proposed research is expected to imply profound connections between diverse areas of mathematics simultaneously enriching each of them. For instance, we expect to establish a precise relation between the generalised Ramanujan conjecture in the theory of automorphic forms and the order of Diophantine approximation on algebraic varieties. We also plan to use our results on counting lattice points to derive estimates on multiplicities of automorphic representations and prove results in direction of Sarnak&apos;s density hypothesis. We investigate the problem of distribution of orbits, raised by Arnold and Krylov in sixties, the problem of multiple recurrence, pioneered by Furstenberg in seventies, and the problem of rigidity of group actions, formulated by Zimmer in eighties. We plan to compute the asymptotic distribution of orbits for actions on general homogeneous spaces, to establish multiple recurrence for large classes of actions of nonamenable groups, to prove isomorphism and factor rigidity of homogeneous actions and rigidity of actions under perturbations.

630 000 €

Start date: 2010-02-01, End date: 2016-01-31

Although short-lived chronometers have yielded a precise chronology of the Early Earth differentiation, there is insufficient data available on the chemical fractionation related to these processes to model the Early Earth’s differentiation. 142Nd isotope data suggest that a reservoir enriched in rare earth elements (REE) has existed since 4.53 Ga, but has not been sampled since its formation. A key question is whether such a reservoir could remain hidden for more than 4.5 Gyr in the convective mantle. The first goal of this project is to test whether the REE alternatively could be stored in the core. Information on the mantle composition and the extent of chemical differentiation in the Early Earth will be also obtained by measurement of Sm-Nd, Pt-Re-Os and Lu-Hf radiogenic systems of Archean samples. This work will provide valuable information on (1) the redox state of the Early Earth, (2) the nature of the precursor material forming the Earth, the chronology of Earth's differentiation relative to the Moon formation, and (4) for reconstructing a model for terrestrial magma ocean crystallization. This proposal will provide the possibility of tackling a topic from a number of angles, using new instrumentation. New approaches and collaborations will be combined in order to constrain the most realistic model of the early Earth evolution.

453 286 €

Start date: 2008-08-01, End date: 2012-11-30

Combinatorics forms a challenging and fundamental part of pure mathematics, but is in the happy position of being relatively accessible to a wider audience. One of its most exciting and rapidly developing branches is Extremal Combinatorics, which has a wide range of direct applications both to other areas of mathematics and other academic disciplines. Thus it makes its influence felt indirectly when the theoretical power it brings to these disciplines is in turn used for more practical applications. The proposed project addresses a range of important problems at the frontier of Extremal Combinatorics, principally those motivated by a question of Turan, an open problem that mathematicians have battled with for over sixty years, which has led to many developments in the theory of graphs and hypergraphs. Recently there has been a lot of progress in this area, so it is an exciting topic for future research. The PI has identified some key intermediate goals to pursue for this first objective, and also for a second objective involving various ways to extend the scope of this area, including a rainbow variant that has impressive potential applications in additive number theory. A third area being studied is the theory of set systems with restricted intersections, which has a rich history in combinatorics, and has also found applications to computer science, particular in the theories of complexity and communication. It is also closely connected to the concepts of trace and VC-dimension, which play a central role in many areas of statistics, discrete and computational geometry and learning theory. The PI will co-ordinate a research team of two postdocs and one doctoral student with clearly defined goals that will bring this project to fruition over a five-year period.

780 000 €

Start date: 2010-01-01, End date: 2015-12-31

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

Studying the nature of the first generation of galaxies to form in the Universe is central to efforts to understand the earliest phases of galaxy evolution and the physical processes driving cosmic reionization. Building on my recent success investigating galaxy evolution at redshifts z>6, I propose to recruit and lead the research team necessary to fully exploit my involvement in two Hubble Space Telescope (HST) imaging programmes focused on the high-redshift Universe. The first of these is a new, ultra-deep, proprietary imaging programme in the Hubble Ultra-Deep Field (on which I am co-PI) which will deliver the deepest near-IR image ever obtained and the first robust sample of z>9 galaxies. This dataset will produce the definitive measurement of the faint-end of the high-redshift galaxy luminosity function in the pre-JWST era, a key observational constraint necessary for understanding reionization. The second HST programme is the on-going, wide-area, CANDELS imaging survey, which will provide the first statistically significant sample of massive galaxies at redshifts 6<z<8, many of which will be suitable for spectroscopic follow-up. Consequently, I intend to assemble a team with the necessary skills to take full advantage of my leading position in these two key imaging datasets and to exploit opportunities for spectroscopic follow-up with the next generation of multi-object optical/near-IR spectrographs. Finally, I also propose to recruit the necessary expertise to accurately interpret the new observational results within the context of the latest spectral synthesis and galaxy formation models. In summary, the aim of this proposal is to build a research team with the interdisciplinary skills necessary to successfully exploit the latest observational datasets, interpret them within the context of the latest theoretical predictions, and thereby attempt to construct a fully consistent framework describing high-redshift galaxy evolution.

1 176 273 €

Start date: 2012-12-01, End date: 2016-11-30

The purpose of the project is to develop methods for computing with the rigid and crystalline cohomology of varieties over finite fields. The project will focus on two main problems. First, the fast computation of the Galois action. Second, the effective computation of the cycle class map, and the inverse problem of explicitly recovering algebraic cycles from Galois-invariant cohomology classes (c.f. the Tate conjecture). Research on the first problem would be a natural extension of on-going work of the Prinicipal Investigator and others. By contrast the second problem is entirely new, at least in the context of computational number theory. The overall goal of the project is to provide methods and software which will extend the range of application of computational number theory within the mathematical sciences.

750 000 €

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

The discovery of extrasolar planets - i.e. planets orbiting other stars - has fundamentally transformed our understanding of planets, solar systems and our place in the Milky Way. Recent discoveries have shown that planets between 1-2 R are the most abundant in our galaxy, so called super-Earths. Yet, they are entirely absent from our own solar system. Their nature, chemistry, formation histories or climate remain very much a mystery. Estimates of their densities suggest a variety of possible planet types and formation/evolution scenarios but current degeneracies cannot be broken with mass/radius measures alone. Spectroscopy of their atmospheres can provide vital insight. Recently, the first atmosphere around a super-Earth, 55 Cnc e, was discovered, showcasing that these worlds are far more complex than simple densities allow us to constrain. To achieve a more fundamental understanding, we need to move away from the status quo of treating individual planets as case-studies and analysing data ‘by hand’. A globally encompassing, self-consistent and self-calibrating approach is required. Here, I propose to move the field a significant step towards this goal with the ExoAI (Exoplanet Artificial Intelligence) framework. ExoAI will use state-of-the-art neural networks and Bayesian atmospheric retrieval algorithms applied to big-data. Given all available data of an instrument, ExoAI will autonomously learn the best calibration strategy, intelligently recognise spectral features and provide a full quantitative atmospheric model for every planet observed. This uniformly derived catalogue of super-Earth atmospheric models, will move us on from the individual case-studies and allow us to study the larger picture. We will constrain the underlying processes of planet formation/migration and bulk chemistries of super-Earths. The algorithm and the catalogue of atmospheric and instrument models will be made freely available to the community.

1 500 000 €

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

"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

The increasing demand for environmentally friendly, healthier, and better performing formulated products means that the process industry needs more than ever predictive models of formulation performance for rapid, effective, and sustainable screening of new products. Processing flows and end use produce deformations that are extreme compared to what is accessible with existing experimental methods. As a consequence, the effects of extreme deformation are often overlooked without justification. Extreme deformation of structured fluids and soft materials is an unexplored dynamic regime where unexpected phenomena may emerge. New flow-induced microstructures can arise due to periodic forcing that is much faster than the relaxation timescale of the system, leading to collective behaviors and large transient stresses. The goal of this research is to introduce a radically innovative approach to explore and characterize the regime of extreme deformation of structured fluids and interfaces. By combining cutting-edge techniques including acoustofluidics, microfluidics, and high-speed imaging, I will perform pioneering high-precision measurements of macroscopic stresses and evolution of the microstructure. I will also explore strategies to exploit the phenomena emerging upon extreme deformation (collapse under ultrafast compression, yielding) for new processes and for adding new functionality to formulated products. These experimental results, complemented by discrete particle simulations and continuum-scale modeling, will provide new insights that will lay the foundations of the new field of ultrafast soft matter. Ultimately the results of this research program will guide the development of predictive tools that can tackle the time scales of realistic flow conditions for applications to virtual screening of new formulations.

1 499 186 €

Start date: 2015-05-01, End date: 2020-04-30

"This proposal sits at the interface of analytic number theory and selected topics, viewed through the prism of Diophantine equations defining higher-dimensional algebraic varieties. A core part of the proposal involves using analytic methods (such as complex analysis, Fourier analysis and additive combinatorics) to tackle a range of problems about Diophantine equations. These include such basic questions as precisely when families of equations admit integer or rational solutions and, furthermore, how ``dense'' these solutions are when they exist. In the reverse direction, a significant component of the proposal is dedicated to established problems in number theory (such as stable cohomology of moduli spaces and uniform spectral gaps for arithmetic lattices) which can be tackled via the successful analysis of intermediary Diophantine equations."

801 187 €

Start date: 2012-12-01, End date: 2017-11-30

"Modern astrophysics has pushed the observational frontier to a time a billion years after the Big Bang. Lying beyond this frontier is the period when the first stars and galaxies formed, whose light heated and ionized the Universe in the process known as reionization. Understanding this ""epoch of reionization"" would fill in a key missing period in our picture of the history of the Universe. Existing observational techniques have scratched the surface, but new observational techniques are required to truly understand this early period of galaxy formation. My work will lay the theoretical foundations for three novel probes of this period - 21 cm tomography, the 21 cm global signal, and line intensity mapping - that would enable three dimensional maps of the epoch of reionization. If realized through challenging radio-frequency observations, these techniques would transform our understanding of the first galaxies. Through this ERC starting grant, I will build the theoretical framework needed to predict and interpret observations of line emission from gas in and surrounding the first generation of galaxies. My team will aim to develop models of the interplay between radiation from the first galaxies and the heating, ionization, and illumination of hydrogen gas that lies in the space between galaxies. At the same time, we will build models of the formation and properties of the atomic and molecular gas that fills the space inside galaxies. By combining probes of this ""inner"" and ""outer"" space a complete nature of galaxy formation during the first billion years might be achieved. Analysis of sky averaged 21 cm observations will complement this with a broad overview of galaxies back to a few hundred million years after the big bang. This work will provide a clear theoretical road map to guide the design of next generation radio telescopes, such as the Square Kilometer Array, to achieve this ambitious goal."

1 495 220 €

Start date: 2015-04-01, End date: 2020-03-31

I propose to combine state-of-the-art observations of weak gravitational lensing and baryon acoustic oscillations to answer one fundamental question; is the accelerating expansion of our Universe caused by dark energy, or is it a manifestation of beyond-Einstein gravity theories, as might arise if the Universe has more dimensions? This frontier research will have a wide ranging impact as is it believed that understanding the dark energy phenomenon will revolutionize our understanding of Physics today. The observational task of detecting and analysing probes of dark energy is technically very challenging and may be subject to systematic limits. I detail how I will exploit synergies between the weak lensing and baryon acoustic oscillations techniques, showing that the physical systematics that effect each technique can be neatly resolved using complementary information from the alternative technique. With support from the ERC I will create an inter-disciplinary team well positioned to first solve many of the systematic problems associated with dark energy research and then apply those novel solutions to the dark energy analysis of three world-leading wide-field surveys that I currently co-investigate; CFHTLS, a recently completed 170 square degree ugriz survey, PanSTARRS-1, a soon to be started all-sky grizy survey and ADEPT, a space-based infra-red telescope for baryon acoustic oscillation studies proposed for NASA s Joint Dark Energy Mission. Using innovative 3D statistical analyses, optimised photometric redshifts and new combined lensing and galaxy clustering statistics, my ERC team will aim to control systematic errors to place joint constraints on the evolving nature of dark energy and test directly beyond-Einstein gravity.

1 258 797 €

Start date: 2010-04-01, End date: 2015-10-31

The freezing of colloids is an amazingly common phenomenon encountered in many natural and engineering processes such as the freezing of soils, food engineering or cryobiology. It can also be used as a bioinspired, versatile and environmentally-friendly processing route for bioinspired porous materials and composites exhibiting breakthroughs in functional properties. Yet, it is still a puzzling phenomenon with many unexplained features, due to the complexity of the system, the space and time scales at which the process should be investigated and the multidisciplinary approach required to completely apprehend it. The objective is to progress towards a deep understanding of the freezing of colloids through novel in situ observations approaches and mathematical modelling, to exert a better control on the processing route and achieve the full potential of this novel class of bioinspired materials. Materials will be processed and their structure/properties relationships investigated and optimized. This project offers a unique integration of approaches, competences and resources in materials science, chemistry, physics, mathematics and technological developments of observation techniques. For materials science only, the versatility of the process and its control could yield potential breakthroughs in numerous key applications of tremendous human, technological, environmental and economical importance such as catalysis, biomaterials or energy production, and open a whole new field of research. Far-reaching implications beyond materials science are expected, both from the developments in mathematics and physics, and from the implications of colloids freezing in many situations and fields of research.

1 469 034 €

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

"Our main goal is to apply the powerful analytical tools that are now emerging from areas of more ""applicable"" parts of mathematics such as ergodic theory, random walks, harmonic analysis and additive combinatorics to some longstanding open problems in more theoretical parts of mathematics such as group theory and number theory. The recent work of Green and Tao about arithmetic progressions of prime numbers, or Margulis' celebrated solution of the Oppenheim Conjecture about integer values of quadratic forms are examples of the growing interpenetration of such seemingly unrelated fields. We have in mind an explicit set of problems: a uniform Tits alternative, the equidistribution of dense subgroups, the Andre-Oort conjecture, the spectral gap conjecture, the Lehmer problem. All these questions involve group theory in various forms (discrete subgroups of Lie groups, representation theory and spectral theory, locally symmetric spaces and Shimura varieties, dynamics on homogeneous spaces of arithmetic origin, Cayley graphs of large finite groups, etc) and have also a number theoretic flavor. Their striking common feature is that each of them enjoys some intimate relationship, whether by the foreseen methods to tackle it or by its consequences, with ergodic theory on the one hand and harmonic analysis and combinatorics on the other. We believe that the new methods being currently developed in those fields will bring crucial insights to the problems at hand. This proposed research builds on previous results obtained by the author and addresses some of the most challenging open problems in the field."

750 000 €

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

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

I intend to cross ressources of holomorphic curves techniques and traditional topological methods to study some fundamental questions in symplectic and contact geometry such as: - The Weinstein conjecture in dimension greater than 3. - The construction of new invariants for both smooth manifolds and Legendrian/contact manifolds, in particular, try to define an analogue of Heegaard Floer homology in dimension larger than 3. - The link, in dimension 3, between the geometry of the ambient manifold (especially hyperbolicity) and the dynamical/topological properties of its Reeb vector fields and contact structures. - The topological characterization of odd-dimensional manifolds admitting a contact structure. A crucial ingredient of my program is to understand the key role played by open book decompositions in dimensions larger than three. This program requires a huge amount of mathematical knowledges. My idea is to organize a team around Ghiggini, Laudenbach, Rollin, Sandon and myself, augmented by two post-docs and one PhD student funded by the project. This will give us the critical size to organize a very active working seminar and to have a worldwide attractivity and recognition. I also plan to invite one confirmed researcher every year (for 1-2 months), to organize one conference and one summer school, as well as several focused weeks.

887 600 €

Start date: 2012-01-01, End date: 2016-12-31

GeopolyConc will provide the necessary scientific basis for the prediction of the long-term durability performance of alkali-activated ‘geopolymer’ concretes. These materials can be synthesised from industrial by-products and widely-available natural resources, and provide the opportunity for a highly significant reduction in the environmental footprint of the global construction materials industry, as it expands to meet the infrastructure needs of 21st century society. Experimental and modelling approaches will be coupled to provide major advances in the state of the art in the science and engineering of geopolymer concretes. The key scientific focus areas will be: (a) the development of the first ever rigorous mathematical description of the factors influencing the transport properties of alkali-activated concretes, and (b) ground-breaking work in understanding and controlling the factors which lead to the onset of corrosion of steel reinforcing embedded in alkali-activated concretes. This project will generate confidence in geopolymer concrete durability, which is essential to the application of these materials in reducing EU and global CO2 emissions. The GeopolyConc project will also be integrated with leading multinational collaborative test programmes coordinated through a RILEM Technical Committee (TC DTA) which is chaired by the PI, providing a route to direct international utilisation of the project outcomes.

1 495 458 €

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

The Langlands program is a conjectural framework for understanding the deep relations between automorphic forms and arithmetic. It implies a parameterization of representations of Galois groups of (local or global) fields in terms of representations of (p-adic or adelic) reductive groups. While making progress in the Langlands program often means overcoming significant technical obstacles, new results can have concrete applications to number theory, the proof of Fermat's Last Theorem by Wiles being a key example. Recently, V. Lafforgue has made a striking breakthrough in the Langlands program over function fields, by constructing an `automorphic-to-Galois' Langlands correspondence. As a consequence, this should imply the existence of a local Langlands correspondence over equicharacteristic non-archimedean local fields. The goal of this proposal is to show the surjectivity of this local Langlands correspondence. My strategy will be global, and will involve solving global problems of strong independent interest. I intend to establish a research group to carry out the following objectives, in the setting of global function fields: I. Establish automorphy lifting theorems for Galois representations valued in the (Langlands) dual group of an arbitrary split reductive group. II. Establish cases of automorphic induction for arbitrary reductive groups. III. Prove potential automorphy theorems for Galois representations valued in the dual group of an arbitrary reductive group. IV. Establish cases of soluble base change and descent for automorphic representations of arbitrary reductive groups. I will then combine these results to obtain the desired surjectivity. This will be a milestone in our understanding of the Langlands correspondence for function fields.

1 094 610 €

Start date: 2017-01-01, End date: 2021-12-31

The project is located between logic and mathematics, more precisely between model theory and group theory. There are extremely difficult questions arising about the model theory of groups, notably the question of the construction of new groups with prescribed algebraic properties and at the same time good model-theoretic properties. In particular, it is an important question, both in model theory and in group theory, to build new stable groups and eventually new nonalgebraic groups with a good dimension notion. The present project aims at filling these gaps. It is divided into three main directions. Firstly, it consists in the continuation of the classification of groups with a good dimension notion, notably groups of finite Morley rank or related notions. Secondly, it consists in a systematic inspection of the combinatorial and geometric group theory which can be applied to build new groups, keeping a control on their first order theory. Thirdly, and in connection to the previous difficult problem, it consists in a very systematic and general study of infinite permutation groups.

366 598 €

Start date: 2011-10-01, End date: 2013-12-31

"Over the past years, carbon nanomaterial such as graphene and carbon nanotubes (CNTs) have attracted the interest of scientists, because some of their properties are unlike any other engineering material. Individual graphene sheets and CNTs have shown a Youngs Modulus of 1 TPa and a tensile strength of 100 GPa, hereby exceeding steel at only a fraction of its weight. Further, they offer high currents carrying capacities of 10^9 A/cm², and thermal conductivities up to 3500 W/mK, exceeding diamond. Importantly, these off-the-chart properties are only valid for high quality individualized nanotubes or sheets. However, most engineering applications require the assembly of tens to millions of these nanoparticles into one device. Unfortunately, the mechanical and electronic figures of merit of such assembled materials typically drop by at least an order of magnitude in comparison to the constituent nanoparticles. In this ERC project, we aim at the development of new techniques to create structured assemblies of carbon nanoparticles. Herein we emphasize the importance of controlling hierarchical arrangement at different length scales in order to engineer the properties of the final device. The project will follow a methodical approach, bringing together different fields of expertise ranging from macro- and microscale manufacturing, to nanoscale material synthesis and mesoscale chemical surface modification. For instance, we will pursue combined top-down microfabrication and bottom-up self-assembly, accompanied with surface modification through hydrothermal processing. This research will impact scientific understanding of how nanotubes and nanosheets interact, and will create new hierarchical assembly techniques for nanomaterials. Further, this ERC project pursues applications with high societal impact, including energy storage and water filtration. Finally, HIENA will tie relations with EU’s rich CNT industry to disseminate its technologic achievements."

1 496 379 €

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

Due to their unique molecular structure carbon nanotubes can offer high electrical conductivity and superior current density. Both of these properties are sought after, especially for overhead power transmission lines where the extremely high axial strength of nanotubes would also be a bonus. In this research proposal single wall carbon nanotubes (nanometer size tubes made of rolled up graphene sheets) with desirable dimensions and controlled way of the graphene sheet rolled up into a tube (referred to as chirality), will be synthesized and spun into fibres using two unique methods, which were developed in Cambridge. These high performance carbon nanotube fibres will be explored as flexible, lightweight, highly efficient materials for use as wires for a variety of power transmission applications. The project will focus on achieving precise chirality control of carbon nanotubes through crystallographic manipulation of the catalyst particles using a recently-discovered in-house method. Tuning the molecular structure of individual nanotubes will achieve maximum uniformity and desired level of electrical conductivity. Next, carbon nanotube fibres will be spun using a unique process currently available only in Cambridge. The quality of fibres will be assessed, after which the fibres will be assembled into strands and cables. In the final stage, different polymeric coatings will be investigated as insulation for the wires and diverse geometries explored. There will be several fundamental benefits from the outcome of this research proposal. Demonstration of the chirality control of nanotubes, which is the “holy grail” in the field, would be important in itself, while application of the material as useful wires and cables will make it much more immediately useful

1 470 114 €

Start date: 2010-08-01, End date: 2015-07-31