ERC FUNDED PROJECTS

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

1 491 348 €

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

"Computer vision is concerned with the automated interpretation of images and video streams. Today's research is (mostly) aimed at answering queries such as ""Is this a picture of a dog?"", (classification) or sometimes ""Find the dog in this photo"" (detection). While categorisation and detection are useful for many tasks, inferring correct class labels is not the final answer to visual recognition. The categories and locations of objects do not provide direct understanding of their function i.e., how things work, what they can be used for, or how they can act and react. Such an understanding, however, would be highly desirable to answer currently unsolvable queries such as ""Am I in danger?"" or ""What can happen in this scene?"". Solving such queries is the aim of this proposal. My goal is to uncover the functional properties of objects and the purpose of actions by addressing visual recognition from a different and yet unexplored perspective. The main novelty of this proposal is to leverage observations of people, i.e., their actions and interactions to automatically learn the use, the purpose and the function of objects and scenes from visual data. The project is timely as it builds upon the two key recent technological advances: (a) the immense progress in visual recognition of objects, scenes and human actions achieved in the last ten years, as well as (b) the emergence of a massive amount of public image and video data now available to train visual models. ACTIVIA addresses fundamental research issues in automated interpretation of dynamic visual scenes, but its results are expected to serve as a basis for ground-breaking technological advances in practical applications. The recognition of functional properties and intentions as explored in this project will directly support high-impact applications such as detection of abnormal events, which are likely to revolutionise today's approaches to crime protection, hazard prevention, elderly care, and many others."

1 497 420 €

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

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

1 432 769 €

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

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

A massive and ever growing amount of digital image and video content is available today, on sites such as Flickr and YouTube, in audiovisual archives such as those of BBC and INA, and in personal collections. In most cases, it comes with additional information, such as text, audio or other metadata, that forms a rather sparse and noisy, yet rich and diverse source of annotation, ideally suited to emerging weakly supervised and active machine learning technology. The ALLEGRO project will take visual recognition to the next level by using this largely untapped source of data to automatically learn visual models. The main research objective of our project is the development of new algorithms and computer software capable of autonomously exploring evolving data collections, selecting the relevant information, and determining the visual models most appropriate for different object, scene, and activity categories. An emphasis will be put on learning visual models from video, a particularly rich source of information, and on the representation of human activities, one of today's most challenging problems in computer vision. Although this project addresses fundamental research issues, it is expected to result in significant advances in high-impact applications that range from visual mining of the Web and automated annotation and organization of family photo and video albums to large-scale information retrieval in television archives.

2 493 322 €

Start date: 2013-04-01, End date: 2019-03-31

Acute Myeloid Leukemia (AML), the most common leukemia diagnosed in adults, represents the paradigm of resistance to front-line therapies in hematology. Indeed, AML is so genetically complex that only few targeted therapies are currently tested in this disease and chemotherapy remains the only standard treatment for AML since the past four decades. Despite an initial sustained remission achieved by chemotherapeutic agents, almost all patients relapse with a chemoresistant minimal residual disease (MRD). The goal of my proposal is to characterize the still poorly understood biological mechanisms underlying persistence and emergence of MRD. MRD is the consequence of the re-expansion of leukemia-initiating cells that are intrinsically more resistant to chemotherapy. This cell fraction may be stochastically more prone to survive front-line therapy regardless of their mutational status (the stochastic model), or genetically predetermined to resist by virtue of a collection of chemoprotective mutations (the mutational model). I have already generated in mice, by consecutive rounds of chemotherapy, a stochastic MLL-AF9-driven chemoresistance model that I examined by RNA-sequencing. I will pursue the comprehensive cell autonomous and cell non-autonomous characterization of this chemoresistant AML disease using whole-exome and ChIP-sequencing. To establish a mutationally-induced chemoresistant mouse model, I will conduct an innovative in vivo screen using pooled mutant open reading frame and shRNA libraries in order to predict which combinations of mutations, among those already known in AML, actively promote chemoresistance. Finally, by combining genomic profiling and in vivo shRNA screening experiments, I will decipher the molecular mechanisms and identify the functional effectors of these two modes of resistance. Ultimately, I will then be able to firmly establish the fundamental relevance of the stochastic and/or the mutational model of chemoresistance for MRD genesis.

1 500 000 €

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

This proposal is devoted to the applications of a new hypoelliptic Dirac operator, whose analytic properties have been studied by Lebeau and myself. Its construction connects classical Hodge theory with the geodesic flow, and more generally any geometrically defined Hodge Laplacian with a dynamical system on the cotangent bundle. The proper description of this object can be given in analytic, index theoretic and probabilistic terms, which explains both its potential many applications, and also its complexity.

1 112 400 €

Start date: 2012-02-01, End date: 2017-01-31

"During the past twenty years, we have witnessed profound technological changes, summarised under the terms of digital revolution or entering the information age. It is evident that these technological changes will have a deep societal impact, and questions of privacy and security are primordial to ensure the survival of a free and open society. Cryptology is a main building block of any security solution, and at the heart of projects such as electronic identity and health cards, access control, digital content distribution or electronic voting, to mention only a few important applications. During the past decades, public-key cryptology has established itself as a research topic in computer science; tools of theoretical computer science are employed to “prove” the security of cryptographic primitives such as encryption or digital signatures and of more complex protocols. It is often forgotten, however, that all practically relevant public-key cryptosystems are rooted in pure mathematics, in particular, number theory and arithmetic geometry. In fact, the socalled security “proofs” are all conditional to the algorithmic untractability of certain number theoretic problems, such as factorisation of large integers or discrete logarithms in algebraic curves. Unfortunately, there is a large cultural gap between computer scientists using a black-box security reduction to a supposedly hard problem in algorithmic number theory and number theorists, who are often interested in solving small and easy instances of the same problem. The theoretical grounds on which current algorithmic number theory operates are actually rather shaky, and cryptologists are generally unaware of this fact. The central goal of ANTICS is to rebuild algorithmic number theory on the firm grounds of theoretical computer science."

1 453 507 €

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

Diabetes has become one of the most widespread metabolic disorders with epidemic dimensions affecting almost 6% of the world’s population. Despite modern treatments, the life expectancy of patients with Type 1 diabetes remains reduced as compared to healthy subjects. There is therefore a need for alternative therapies. Towards this aim, using the mouse, we recently demonstrated that the in vivo forced expression of a single factor in pancreatic alpha-cells is sufficient to induce a continuous regeneration of alpha-cells and their subsequent conversion into beta-like cells, such converted cells being capable of reversing the consequences of chemically-induced diabetes in vivo (Collombat et al. Cell, 2009). The PI and his team therefore propose to further decipher the mechanisms involved in this alpha-cell-mediated beta-cell regeneration process and determine whether this approach may be applied to adult animals and whether it would efficiently reverse Type 1 diabetes. Furthermore, a major effort will be made to verify whether our findings could be translated to human. Specifically, we will use a tri-partite approach to address the following issues: (1) Can the in vivo alpha-cell-mediated beta-cell regeneration be induced in adults mice? What would be the genetic determinants involved? (2) Can alpha-cell-mediated beta-cell regeneration reverse diabetes in the NOD Type 1 diabetes mouse model? (3) Can adult human alpha-cells be converted into beta-like cells? Together, these ambitious objectives will most certainly allow us to gain new insight into the mechanisms defining the identity and the reprogramming capabilities of mouse and human endocrine cells and may thereby open new avenues for the treatment of diabetes. Similarly, the determination of the molecular triggers implicated in the beta-cell regeneration observed in our diabetic mice may lead to exciting new findings, including the identification of “drugable” targets of importance for human diabetic patients.

1 500 000 €

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

"The vast majority of research in computer security is dedicated to the design of detection, protection, and prevention solutions. While these techniques play a critical role to increase the security and privacy of our digital infrastructure, it is enough to look at the news to understand that it is not a matter of ""if"" a computer system will be compromised, but only a matter of ""when"". It is a well known fact that there is no 100% secure system, and that there is no practical way to prevent attackers with enough resources from breaking into sensitive targets. Therefore, it is extremely important to develop automated techniques to timely and precisely analyze computer security incidents and compromised systems. Unfortunately, the area of incident response received very little research attention, and it is still largely considered an art more than a science because of its lack of a proper theoretical and scientific background. The objective of BITCRUMBS is to rethink the Incident Response (IR) field from its foundations by proposing a more scientific and comprehensive approach to the analysis of compromised systems. BITCRUMBS will achieve this goal in three steps: (1) by introducing a new systematic approach to precisely measure the effectiveness and accuracy of IR techniques and their resilience to evasion and forgery; (2) by designing and implementing new automated techniques to cope with advanced threats and the analysis of IoT devices; and (3) by proposing a novel forensics-by-design development methodology and a set of guidelines for the design of future systems and software. To provide the right context for these new techniques and show the impact of the project in different fields and scenarios, BITCRUMBS plans to address its objectives using real case studies borrowed from two different domains: traditional computer software, and embedded systems. "

1 991 504 €

Start date: 2018-04-01, End date: 2023-03-31

"Many physical models involve nonlinear dispersive problems, like wave or laser propagation, plasmas, ferromagnetism, etc. So far, the mathematical under- standing of these equations is rather poor. In particular, we know little about the detailed qualitative behavior of their solutions. Our point is that an apparent com- plexity hides universal properties of these models; investigating and uncovering such properties has started only recently. More than the equations themselves, these univer- sal properties are essential for physical modelisation. By considering several standard models such as the nonlinear Schrodinger, nonlinear wave, generalized KdV equations and related geometric problems, the goal of this pro- posal is to describe the generic global behavior of the solutions and the profiles which emerge either for large time or by concentration due to strong nonlinear effects, if pos- sible through a few relevant solutions (sometimes explicit solutions, like solitons). In order to do this, we have to elaborate different mathematical tools depending on the context and the specificity of the problems. Particular emphasis will be placed on - large time asymptotics for global solutions, decomposition of generic solutions into sums of decoupled solitons in non integrable situations, - description of critical phenomenon for blow up in the Hamiltonian situation, stable or generic behavior for blow up on critical dynamics, various relevant regularisations of the problem, - global existence for defocusing supercritical problems and blow up dynamics in the focusing cases. We believe that the PI and his team have the ability to tackle these problems at present. The proposal will open whole fields of investigation in Partial Differential Equations in the future, clarify and simplify our knowledge on the dynamical behavior of solutions of these problems and provide Physicists some new insight on these models."

2 079 798 €

Start date: 2012-04-01, End date: 2017-03-31

Tissue homeostasis requires coordinated barrier function in blood and lymphatic vessels. Opening of junctions between endothelial cells (ECs) lining blood vessels leads to tissue fluid accumulation that is drained by lymphatic vessels. A pathological increase in blood vessel permeability or lack or malfunction of lymphatic vessels leads to edema and associated defects in macromolecule and immune cell clearance. Unbalanced barrier function between blood and lymphatic vessels contributes to neurodegeneration, chronic inflammation, and cardiovascular disease. In this proposal, we seek to gain mechanistic understanding into coordination of barrier function between blood and lymphatic vessels, how this process is altered in disease models and how it can be manipulated for therapeutic purposes. We will focus on two critical barriers with diametrically opposing functions, the blood-brain barrier (BBB) and the lymphatic capillary barrier (LCB). ECs of the BBB form very tight junctions that restrict paracellular access to the brain. In contrast, open junctions of the LCB ensure uptake of extravasated fluid, macromolecules and immune cells, as well as lipid in the gut. We have identified novel effectors of BBB and LCB junctions and will determine their role in adult homeostasis and in disease models. Mouse genetic gain and loss of function approaches in combination with histological, ultrastructural, functional and molecular analysis will determine mechanisms underlying formation of tissue specific EC barriers. Deliverables include in vivo validated targets that could be used for i) opening the BBB on demand for drug delivery into the brain, and ii) to lower plasma lipid uptake via interfering with the LCB, with implications for prevention of obesity, cardiovascular disease and inflammation. These pioneering studies promise to open up new opportunities for research and treatment of neurovascular and cardiovascular disease.

2 499 969 €

Start date: 2019-07-01, End date: 2024-06-30

The security of modern web applications depends on a variety of critical components including cryptographic libraries, Transport Layer Security (TLS), browser security mechanisms, and single sign-on protocols. Although these components are widely used, their security guarantees remain poorly understood, leading to subtle bugs and frequent attacks. Rather than fixing one attack at a time, we advocate the use of formal security verification to identify and eliminate entire classes of vulnerabilities in one go. With the aid of my ERC starting grant, I have built a team that has already achieved landmark results in this direction. We built the first TLS implementation with a cryptographic proof of security. We discovered high-profile vulnerabilities such as the recent Triple Handshake and FREAK attacks, both of which triggered critical security updates to all major web browsers and TLS libraries. So far, our security theorems only apply to carefully-written standalone reference implementations. CIRCUS proposes to take on the next great challenge: verifying the end-to-end security of web applications running in mainstream software. The key idea is to identify the core security components of web browsers and servers and replace them by rigorously verified components that offer the same functionality but with robust security guarantees. Our goal is ambitious and there are many challenges to overcome, but we believe this is an opportune time for this proposal. In response to the Snowden reports, many cryptographic libraries and protocols are currently being audited and redesigned. Standards bodies and software developers are inviting researchers to help analyse their designs and code. Responding to their call requires a team of researchers who are willing to deal with the messy details of nascent standards and legacy code, and at the same time prove strong security theorems based on precise cryptographic assumptions. We are able, we are willing, and the time is now.

1 885 248 €

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

I am willing to solve several well-known models from combinatorics, probability theory and statistical mechanics: the Ising model on isoradial graphs, dimer models, spanning forests, random walks in cones, occupation time problems. Although completely unrelated a priori, these models have the common feature of being presumed “exactly solvable” models, for which surprising and spectacular formulas should exist for quantities of interest. This is captured by the title “Elliptic Combinatorics”, the wording elliptic referring to the use of special functions, in a broad sense: algebraic/differentially finite (or holonomic)/diagonals/(hyper)elliptic/ hypergeometric/etc. Besides the exciting nature of the models which we aim at solving, one main strength of our project lies in the variety of modern methods and fields that we cover: combinatorics, probability, algebra (representation theory), computer algebra, algebraic geometry, with a spectrum going from applied to pure mathematics. We propose in addition two major applications, in finance (Markovian order books) and in population biology (evolution of multitype populations). We plan to work in close collaborations with researchers from these fields, to eventually apply our results (study of extinction probabilities for self-incompatible flower populations, for instance).

1 242 400 €

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

A fundamental question in biology is how constraints drive phenotypic changes and the diversification of life. We know little about the role of these constraints on crop domestication, nor how artificial selection can escape them. CONSTRAINTS questions whether crop domestication has shifted ecophysiological and biophysical traits related to resource acquisition, use and partitioning, and how trade-offs between them have constrained domestication and can limit future improvements in both optimal and sub-optimal conditions. The project is based on three objectives: 1. revealing the existence (or lack) of generic resource-use domestication syndrome in crop science; 2. elucidating ecophysiological and biophysical trade-offs within crop science and delineating the envelope of constraints for artificial selection; 3. examining the shape of ecophysiological and biophysical trade-offs in crop species when grown in sub-optimal environmental conditions. This project will be investigated within and across crop species thanks to a core panel of 12 studied species (maize, sunflower, Japanese rice, sorghum, durum wheat, bread wheat, alfalfa, orchardgrass, silvergrass, pea, colza, vine) for which data and collections (ca. 1,300 genotypes total) are already available to the PI, and additional high throughput phenotyping using automatons. Additional species will be used for specific tasks: (i) a panel of 30 species for a comparative analysis of crop species and their wild progenitors; (ii) 400 worldwide accessions of Arabidopsis thaliana for a genome-wide association study of resource-use traits. Collectively, we will use a multiple-tool approach by using: field measurement, high-throughput phenotyping, common-garden experiment, comparative analysis using databases, modelling, genomics. The ground-breaking nature of the project holds in the nature of the questions asked and in the unique opportunity to transfer knowledge from ecology and evolutionary biology to crop species.

1 499 979 €

Start date: 2015-06-01, End date: 2020-05-31

Every year, software bugs cost hundreds of millions of euros to companies and administrations. Hence, software quality is a prevalent notion and interactive theorem provers based on type theory have shown their efficiency to prove correctness of important pieces of software like the C compiler of the CompCert project. One main interest of such theorem provers is the ability to extract directly the code from the proof. Unfortunately, their democratization suffers from a major drawback, the mismatch between equality in mathematics and in type theory. Thus, significant Coq developments have only been done by virtuosos playing with advanced concepts of computer science and mathematics. Recently, an extension of type theory with homotopical concepts such as univalence is gaining traction because it allows for the first time to marry together expected principles of equality. But the univalence principle has been treated so far as a new axiom which breaks one fundamental property of mechanized proofs: the ability to compute with programs that make use of this axiom. The main goal of the CoqHoTT project is to provide a new generation of proof assistants with a computational version of univalence and use them as a base to implement effective logical model transformation so that the power of the internal logic of the proof assistant needed to prove the correctness of a program can be decided and changed at compile time—according to a trade-off between efficiency and logical expressivity. Our approach is based on a radically new compilation phase technique into a core type theory to modularize the difficulty of finding a decidable type checking algorithm for homotopy type theory. The impact of the CoqHoTT project will be very strong. Even if Coq is already a success, this project will promote it as a major proof assistant, for both computer scientists and mathematicians. CoqHoTT will become an essential tool for program certification and formalization of mathematics.

1 498 290 €

Start date: 2015-06-01, End date: 2020-05-31

In the mammalian brain, the neocortex is the site where sensory information is integrated into complex cognitive functions. This is accomplished by the activity of both principal glutamatergic neurons and locally-projecting inhibitory GABAergic interneurons, interconnected in complex networks. Inhibitory neurons play several key roles in neocortical function. For example, they shape sensory receptive fields and drive several high frequency network oscillations. On the other hand, defects in their function can lead to devastating diseases, such as epilepsy and schizophrenia. Cortical interneurons represent a highly heterogeneous cell population. Understanding the specific role of each interneuron subtype within cortical microcircuits is still a crucial open question. We have examined properties of two major functional interneuron subclasses in neocortical layer V: fast-spiking (FS) and low-threshold spiking (LTS) cells. Our previous data indicate that each group expresses a novel form of self inhibition, namely autaptic inhibitory transmission in FS cells and an endocannabinoid-mediated slow self inhibition in LTS interneurons. In this proposal we will address three major questions relevant to self-inhibition of neocortical interneurons: 1) What is the role of FS cell autapses in coordinating fast network synchrony? 2) What are the molecular mechanisms underlying autaptic asynchronous release, prolonging FS cell self-inhibition by several seconds, and what is its relevance during physiological and pathological network activities? 3) What are the induction mechanisms, the molecular players involved and the functional roles within cortical microcircuits of the endocannabinoid-mediated long-lasting self-inhibition in LTS interneurons? Results of these experiments will lead to a better understanding of GABAergic interneuron regulation of neocortical excitability, relevant to both normal and pathological cortical function.

996 000 €

Start date: 2008-10-01, End date: 2014-03-31

The aim of this 5,5 years project is to create around the PI a research group on the control of systems modeled by partial differential equations at the Laboratory Jacques-Louis Lions of the UPMC and to develop with this group an intensive research activity focused on nonlinear phenomena. With the ERC grant, the PI plans to hire post-doc fellows and PhD students, to offer 1-to-3 months positions to confirmed researchers, a regular seminar and workshops. A lot is known on finite dimensional control systems and linear control systems modeled by partial differential equations. Much less is known for nonlinear control systems modeled by partial differential equations. In particular, in many important cases, one does not know how to use the classical iterated Lie brackets which are so useful to deal with nonlinear control systems in finite dimension. In this project, the PI plans to develop, with the research group, methods to deal with the problems of controllability and of stabilization for nonlinear systems modeled by partial differential equations, in the case where the nonlinearity plays a crucial role. This is for example the case where the linearized control system around the equilibrium of interest is not controllable or not stabilizable. This is also the case when the nonlinearity is too big at infinity and one looks for global results. This is also the case if the nonlinearity contains too many derivatives. The PI has already introduced some methods to deal with these cases, but a lot remains to be done. Indeed, many natural important and challenging problems are still open. Precise examples, often coming from physics, are given in this proposal.

1 403 100 €

Start date: 2011-05-01, End date: 2016-09-30

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

The field of software security analysis stands at a critical juncture. Applications have become too large for security experts to examine by hand, automated verification tools do not scale, and the risks of deploying insecure software are too great to tolerate anything less than mathematical proof. A radical shift of strategy is needed if programming and analysis techniques are to keep up in a networked world where increasing amounts of governmental and individual information are generated, manipulated, and accessed through web-based software applications. The basic tenet of this proposal is that the main roadblock to the security verification of a large program is not its size, but rather the lack of precise security specifications for the underlying libraries and security-critical application code. Since, large-scale software is often a collaborative effort, no single programmer knows all the design goals. Hence, this proposal advocates a collaborative specification and verification framework that helps teams of programmers write detailed security specifications incrementally and then verify that they are satisfied by the source program. The main scientific challenge is to develop new program verification techniques that can be applied collaboratively, incrementally, and modularly to application and library code written in mainstream programming languages. The validation of this approach will be through substantial case studies. Our aim is to produce the first verified open source cryptographic protocol library and the first web applications with formal proofs of security. The proposed project is bold and ambitious, but it is certainly feasible, and has the potential to change how software security is analyzed for years to come.

1 406 726 €

Start date: 2010-11-01, End date: 2015-10-31

Multicore processors have now become mainstream for both general-purpose and embedded computing. Instead of working on improving the architecture of the next generation multicore, with the DAL project, we deliberately anticipate the next few generations of multicores. While multicores featuring 1000's of cores might become feasible around 2020, there are strong indications that sequential programming style will continue to be dominant. Even future mainstream parallel applications will exhibit large sequential sections. Amdahl's law indicates that high performance on these sequential sections is needed to enable overall high performance on the whole application. On many (most) applications, the effective performance of future computer systems using a 1000-core processor chip will significantly depend on their performance on both sequential code sections and single thread. We envision that, around 2020, the processor chips will feature a few complex cores and many (may be 1000's) simpler, more silicon and power effective cores. In the DAL research project, we will explore the microarchitecture techniques that will be needed to enable high performance on such heterogeneous processor chips. Very high performance will be required on both sequential sections -legacy sequential codes, sequential sections of parallel applications- and critical threads on parallel applications -e.g. the main thread controlling the application. Our research will focus on enhancing single process performance. On the microarchitecture side, we will explore both a radically new approach, the sequential accelerator, and more conventional processor architectures. We will also study how to exploit heterogeneous multicore architectures to enhance sequential thread performance.

2 398 542 €

Start date: 2011-04-01, End date: 2016-03-31

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

We propose to radically extend the frontiers of two major themes in computing, parallelism and dynamism, and develop a novel paradigm of computing: dynamic-parallelism. To this end, we will follow two lines of research. First, we will develop techniques for extracting efficiency and high performance from parallel programs written in high-level programming languages. Second, we will develop the dynamic-parallelism model, where computations can respond to a wide variety of dynamic changes to their data automatically and efficiently, by developing novel abstractions (calculi), high-level programming-language constructs, and compilation techniques. The research will culminate in a language that extends the C programming language with support for parallel and dynamic-parallel programming. The proposal is motivated by urgent needs driven by the advent of multicore chips, which is making parallelism mainstream, and the increasing ubiquity of software, which requires applications to operate on highly dynamic data. These advances demand parallel and highly dynamic software, which remains too difficult and labor intensive to develop. The urgency is further underlined by the increasing data and problem sizes---online data grows exponentially, doubling every few years---that require similarly powerful advances in performance. The proposal will achieve profound impact by dramatically simplifying the development of high-performing dynamic and dynamic-parallel software. As a result, programmer productivity and software quality including correctness, reliability, performance, and resource (e.g., time and energy) consumption will improve significantly. The proposal will not only open new research opportunities in parallel computing, programming languages, and compilers, but also in other fields where parallel and dynamic problems abound, e.g., algorithms, computational biology, geometry, graphics, machine learning, and software systems.

1 076 570 €

Start date: 2013-06-01, End date: 2018-05-31

We propose a program that aims at providing new developments and new applications of shifted symplectic and Poisson structures. It is formulated in the language and framework of derived algebraic geometry after Toën–Vezzosi and Lurie. On the foundational side, we will introduce the new notion of shifted symplectic groupoids and prove that they provide an alternative approach to shifted Poisson structures (as they were defined by the PI together with Tony Pantev, Bertrand Toën, Michel Vaquié and Gabriele Vezzosi). Along the way, we shall be able to prove several conjectures that have recently been formulated by the PI and other people. Applications are related to mathematical physics. For instance: - We will provide an interpretation of the Batalin–Vilkovisky formalism in terms of derived symplectic reduction. - We will show that the semi-classical topological field theories with values in derived Lagrangian correspondences that were previously introduced by the PI are actually fully extended topological field theories in the sense of Baez–Dolan and Lurie. - We will explain how one may use this formalism to rigorously construct a 2D topological field theory that has been discovered by Moore and Tachikawa. Quantization problems will also be discussed at the end of the proposal. This project proposal lies at the crossroads of algebraic geometry, mathematical physics (in its algebraic and geometric aspects) and higher algebra.

1 385 247 €

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