Project acronym 1stProposal
Project An alternative development of analytic number theory and applications
Researcher (PI) ANDREW Granville
Host Institution (HI) UNIVERSITY COLLEGE LONDON
Call Details Advanced Grant (AdG), PE1, ERC-2014-ADG
Summary The traditional (Riemann) approach to analytic number theory uses the zeros of zeta functions. This requires the associated multiplicative function, say f(n), to have special enough properties that the associated Dirichlet series may be analytically continued. In this proposal we continue to develop an approach which requires less of the multiplicative function, linking the original question with the mean value of f. Such techniques have been around for a long time but have generally been regarded as “ad hoc”. In this project we aim to show that one can develop a coherent approach to the whole subject, not only reproving all of the old results, but also many new ones that appear inaccessible to traditional methods.
Our first goal is to complete a monograph yielding a reworking of all the classical theory using these new methods and then to push forward in new directions. The most important is to extend these techniques to GL(n) L-functions, which we hope will now be feasible having found the correct framework in which to proceed. Since we rarely know how to analytically continue such L-functions this could be of great benefit to the subject.
We are developing the large sieve so that it can be used for individual moduli, and will determine a strong form of that. Also a new method to give asymptotics for mean values, when they are not too small.
We wish to incorporate techniques of analytic number theory into our theory, for example recent advances on mean values of Dirichlet polynomials. Also the recent breakthroughs on the sieve suggest strong links that need further exploration.
Additive combinatorics yields important results in many areas. There are strong analogies between its results, and those for multiplicative functions, especially in large value spectrum theory, and its applications. We hope to develop these further.
Much of this is joint work with K Soundararajan of Stanford University.
Summary
The traditional (Riemann) approach to analytic number theory uses the zeros of zeta functions. This requires the associated multiplicative function, say f(n), to have special enough properties that the associated Dirichlet series may be analytically continued. In this proposal we continue to develop an approach which requires less of the multiplicative function, linking the original question with the mean value of f. Such techniques have been around for a long time but have generally been regarded as “ad hoc”. In this project we aim to show that one can develop a coherent approach to the whole subject, not only reproving all of the old results, but also many new ones that appear inaccessible to traditional methods.
Our first goal is to complete a monograph yielding a reworking of all the classical theory using these new methods and then to push forward in new directions. The most important is to extend these techniques to GL(n) L-functions, which we hope will now be feasible having found the correct framework in which to proceed. Since we rarely know how to analytically continue such L-functions this could be of great benefit to the subject.
We are developing the large sieve so that it can be used for individual moduli, and will determine a strong form of that. Also a new method to give asymptotics for mean values, when they are not too small.
We wish to incorporate techniques of analytic number theory into our theory, for example recent advances on mean values of Dirichlet polynomials. Also the recent breakthroughs on the sieve suggest strong links that need further exploration.
Additive combinatorics yields important results in many areas. There are strong analogies between its results, and those for multiplicative functions, especially in large value spectrum theory, and its applications. We hope to develop these further.
Much of this is joint work with K Soundararajan of Stanford University.
Max ERC Funding
2 011 742 €
Duration
Start date: 2015-08-01, End date: 2020-07-31
Project acronym AAA
Project Adaptive Actin Architectures
Researcher (PI) Laurent Blanchoin
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Advanced Grant (AdG), LS3, ERC-2016-ADG
Summary Although we have extensive knowledge of many important processes in cell biology, including information on many of the molecules involved and the physical interactions among them, we still do not understand most of the dynamical features that are the essence of living systems. This is particularly true for the actin cytoskeleton, a major component of the internal architecture of eukaryotic cells. In living cells, actin networks constantly assemble and disassemble filaments while maintaining an apparent stable structure, suggesting a perfect balance between the two processes. Such behaviors are called “dynamic steady states”. They confer upon actin networks a high degree of plasticity allowing them to adapt in response to external changes and enable cells to adjust to their environments. Despite their fundamental importance in the regulation of cell physiology, the basic mechanisms that control the coordinated dynamics of co-existing actin networks are poorly understood. In the AAA project, first, we will characterize the parameters that allow the coupling among co-existing actin networks at steady state. In vitro reconstituted systems will be used to control the actin nucleation patterns, the closed volume of the reaction chamber and the physical interaction of the networks. We hope to unravel the mechanism allowing the global coherence of a dynamic actin cytoskeleton. Second, we will use our unique capacity to perform dynamic micropatterning, to add or remove actin nucleation sites in real time, in order to investigate the ability of dynamic networks to adapt to changes and the role of coupled network dynamics in this emergent property. In this part, in vitro experiments will be complemented by the analysis of actin network remodeling in living cells. In the end, our project will provide a comprehensive understanding of how the adaptive response of the cytoskeleton derives from the complex interplay between its biochemical, structural and mechanical properties.
Summary
Although we have extensive knowledge of many important processes in cell biology, including information on many of the molecules involved and the physical interactions among them, we still do not understand most of the dynamical features that are the essence of living systems. This is particularly true for the actin cytoskeleton, a major component of the internal architecture of eukaryotic cells. In living cells, actin networks constantly assemble and disassemble filaments while maintaining an apparent stable structure, suggesting a perfect balance between the two processes. Such behaviors are called “dynamic steady states”. They confer upon actin networks a high degree of plasticity allowing them to adapt in response to external changes and enable cells to adjust to their environments. Despite their fundamental importance in the regulation of cell physiology, the basic mechanisms that control the coordinated dynamics of co-existing actin networks are poorly understood. In the AAA project, first, we will characterize the parameters that allow the coupling among co-existing actin networks at steady state. In vitro reconstituted systems will be used to control the actin nucleation patterns, the closed volume of the reaction chamber and the physical interaction of the networks. We hope to unravel the mechanism allowing the global coherence of a dynamic actin cytoskeleton. Second, we will use our unique capacity to perform dynamic micropatterning, to add or remove actin nucleation sites in real time, in order to investigate the ability of dynamic networks to adapt to changes and the role of coupled network dynamics in this emergent property. In this part, in vitro experiments will be complemented by the analysis of actin network remodeling in living cells. In the end, our project will provide a comprehensive understanding of how the adaptive response of the cytoskeleton derives from the complex interplay between its biochemical, structural and mechanical properties.
Max ERC Funding
2 349 898 €
Duration
Start date: 2017-09-01, End date: 2022-08-31
Project acronym AAMOT
Project Arithmetic of automorphic motives
Researcher (PI) Michael Harris
Host Institution (HI) INSTITUT DES HAUTES ETUDES SCIENTIFIQUES
Call Details Advanced Grant (AdG), PE1, ERC-2011-ADG_20110209
Summary 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.
Summary
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.
Max ERC Funding
1 491 348 €
Duration
Start date: 2012-06-01, End date: 2018-05-31
Project acronym ACTOMYOSIN RING
Project Understanding Cytokinetic Actomyosin Ring Assembly Through Genetic Code Expansion, Click Chemistry, DNA origami, and in vitro Reconstitution
Researcher (PI) Mohan Balasubramanian
Host Institution (HI) THE UNIVERSITY OF WARWICK
Call Details Advanced Grant (AdG), LS3, ERC-2014-ADG
Summary The mechanism of cell division is conserved in many eukaryotes, from yeast to man. A contractile ring of filamentous actin and myosin II motors generates the force to bisect a mother cell into two daughters. The actomyosin ring is among the most complex cellular machines, comprising over 150 proteins. Understanding how these proteins organize themselves into a functional ring with appropriate contractile properties remains one of the great challenges in cell biology. Efforts to generate a comprehensive understanding of the mechanism of actomyosin ring assembly have been hampered by the lack of structural information on the arrangement of actin, myosin II, and actin modulators in the ring in its native state. Fundamental questions such as how actin filaments are assembled and organized into a ring remain actively debated. This project will investigate key issues pertaining to cytokinesis in the fission yeast Schizosaccharomyces pombe, which divides employing an actomyosin based contractile ring, using the methods of genetics, biochemistry, cellular imaging, DNA origami, genetic code expansion, and click chemistry. Specifically, we will (1) attempt to visualize actin filament assembly in live cells expressing fluorescent actin generated through synthetic biological approaches, including genetic code expansion and click chemistry (2) decipher actin filament polarity in the actomyosin ring using total internal reflection fluorescence microscopy of labelled dimeric and multimeric myosins V and VI generated through DNA origami approaches (3) address when, where, and how actin filaments for cytokinesis are assembled and organized into a ring and (4) reconstitute actin filament and functional actomyosin ring assembly in permeabilized spheroplasts and in supported bilayers. Success in the project will provide major insight into the mechanism of actomyosin ring assembly and illuminate principles behind cytoskeletal self-organization.
Summary
The mechanism of cell division is conserved in many eukaryotes, from yeast to man. A contractile ring of filamentous actin and myosin II motors generates the force to bisect a mother cell into two daughters. The actomyosin ring is among the most complex cellular machines, comprising over 150 proteins. Understanding how these proteins organize themselves into a functional ring with appropriate contractile properties remains one of the great challenges in cell biology. Efforts to generate a comprehensive understanding of the mechanism of actomyosin ring assembly have been hampered by the lack of structural information on the arrangement of actin, myosin II, and actin modulators in the ring in its native state. Fundamental questions such as how actin filaments are assembled and organized into a ring remain actively debated. This project will investigate key issues pertaining to cytokinesis in the fission yeast Schizosaccharomyces pombe, which divides employing an actomyosin based contractile ring, using the methods of genetics, biochemistry, cellular imaging, DNA origami, genetic code expansion, and click chemistry. Specifically, we will (1) attempt to visualize actin filament assembly in live cells expressing fluorescent actin generated through synthetic biological approaches, including genetic code expansion and click chemistry (2) decipher actin filament polarity in the actomyosin ring using total internal reflection fluorescence microscopy of labelled dimeric and multimeric myosins V and VI generated through DNA origami approaches (3) address when, where, and how actin filaments for cytokinesis are assembled and organized into a ring and (4) reconstitute actin filament and functional actomyosin ring assembly in permeabilized spheroplasts and in supported bilayers. Success in the project will provide major insight into the mechanism of actomyosin ring assembly and illuminate principles behind cytoskeletal self-organization.
Max ERC Funding
2 863 705 €
Duration
Start date: 2015-11-01, End date: 2020-10-31
Project acronym ADORA
Project Asymptotic approach to spatial and dynamical organizations
Researcher (PI) Benoit PERTHAME
Host Institution (HI) SORBONNE UNIVERSITE
Call Details Advanced Grant (AdG), PE1, ERC-2016-ADG
Summary The understanding of spatial, social and dynamical organization of large numbers of agents is presently a fundamental issue in modern science. ADORA focuses on problems motivated by biology because, more than anywhere else, access to precise and many data has opened the route to novel and complex biomathematical models. The problems we address are written in terms of nonlinear partial differential equations. The flux-limited Keller-Segel system, the integrate-and-fire Fokker-Planck equation, kinetic equations with internal state, nonlocal parabolic equations and constrained Hamilton-Jacobi equations are among examples of the equations under investigation.
The role of mathematics is not only to understand the analytical structure of these new problems, but it is also to explain the qualitative behavior of solutions and to quantify their properties. The challenge arises here because these goals should be achieved through a hierarchy of scales. Indeed, the problems under consideration share the common feature that the large scale behavior cannot be understood precisely without access to a hierarchy of finer scales, down to the individual behavior and sometimes its molecular determinants.
Major difficulties arise because the numerous scales present in these equations have to be discovered and singularities appear in the asymptotic process which yields deep compactness obstructions. Our vision is that the complexity inherent to models of biology can be enlightened by mathematical analysis and a classification of the possible asymptotic regimes.
However an enormous effort is needed to uncover the equations intimate mathematical structures, and bring them at the level of conceptual understanding they deserve being given the applications motivating these questions which range from medical science or neuroscience to cell biology.
Summary
The understanding of spatial, social and dynamical organization of large numbers of agents is presently a fundamental issue in modern science. ADORA focuses on problems motivated by biology because, more than anywhere else, access to precise and many data has opened the route to novel and complex biomathematical models. The problems we address are written in terms of nonlinear partial differential equations. The flux-limited Keller-Segel system, the integrate-and-fire Fokker-Planck equation, kinetic equations with internal state, nonlocal parabolic equations and constrained Hamilton-Jacobi equations are among examples of the equations under investigation.
The role of mathematics is not only to understand the analytical structure of these new problems, but it is also to explain the qualitative behavior of solutions and to quantify their properties. The challenge arises here because these goals should be achieved through a hierarchy of scales. Indeed, the problems under consideration share the common feature that the large scale behavior cannot be understood precisely without access to a hierarchy of finer scales, down to the individual behavior and sometimes its molecular determinants.
Major difficulties arise because the numerous scales present in these equations have to be discovered and singularities appear in the asymptotic process which yields deep compactness obstructions. Our vision is that the complexity inherent to models of biology can be enlightened by mathematical analysis and a classification of the possible asymptotic regimes.
However an enormous effort is needed to uncover the equations intimate mathematical structures, and bring them at the level of conceptual understanding they deserve being given the applications motivating these questions which range from medical science or neuroscience to cell biology.
Max ERC Funding
2 192 500 €
Duration
Start date: 2017-09-01, End date: 2022-08-31
Project acronym ALKAGE
Project Algebraic and Kähler geometry
Researcher (PI) Jean-Pierre, Raymond, Philippe Demailly
Host Institution (HI) UNIVERSITE GRENOBLE ALPES
Call Details Advanced Grant (AdG), PE1, ERC-2014-ADG
Summary The purpose of this project is to study basic questions in algebraic and Kähler geometry. It is well known that the structure of projective or Kähler manifolds is governed by positivity or negativity properties of the curvature tensor. However, many fundamental problems are still wide open. Since the mid 1980's, I have developed a large number of key concepts and results that have led to important progress in transcendental algebraic geometry. Let me mention the discovery of holomorphic Morse inequalities, systematic applications of L² estimates with singular hermitian metrics, and a much improved understanding of Monge-Ampère equations and of singularities of plurisuharmonic functions. My first goal will be to investigate the Green-Griffiths-Lang conjecture asserting that an entire curve drawn in a variety of general type is algebraically degenerate. The subject is intimately related to important questions concerning Diophantine equations, especially higher dimensional generalizations of Faltings' theorem - the so-called Vojta program. One can rely here on a breakthrough I made in 2010, showing that all such entire curves must satisfy algebraic differential equations. A second closely related area of research of this project is the analysis of the structure of projective or compact Kähler manifolds. It can be seen as a generalization of the classification theory of surfaces by Kodaira, and of the more recent results for dimension 3 (Kawamata, Kollár, Mori, Shokurov, ...) to other dimensions. My plan is to combine powerful recent results obtained on the duality of positive cohomology cones with an analysis of the instability of the tangent bundle, i.e. of the Harder-Narasimhan filtration. On these ground-breaking questions, I intend to go much further and to enhance my national and international collaborations. These subjects already attract many young researchers and postdocs throughout the world, and the grant could be used to create even stronger interactions.
Summary
The purpose of this project is to study basic questions in algebraic and Kähler geometry. It is well known that the structure of projective or Kähler manifolds is governed by positivity or negativity properties of the curvature tensor. However, many fundamental problems are still wide open. Since the mid 1980's, I have developed a large number of key concepts and results that have led to important progress in transcendental algebraic geometry. Let me mention the discovery of holomorphic Morse inequalities, systematic applications of L² estimates with singular hermitian metrics, and a much improved understanding of Monge-Ampère equations and of singularities of plurisuharmonic functions. My first goal will be to investigate the Green-Griffiths-Lang conjecture asserting that an entire curve drawn in a variety of general type is algebraically degenerate. The subject is intimately related to important questions concerning Diophantine equations, especially higher dimensional generalizations of Faltings' theorem - the so-called Vojta program. One can rely here on a breakthrough I made in 2010, showing that all such entire curves must satisfy algebraic differential equations. A second closely related area of research of this project is the analysis of the structure of projective or compact Kähler manifolds. It can be seen as a generalization of the classification theory of surfaces by Kodaira, and of the more recent results for dimension 3 (Kawamata, Kollár, Mori, Shokurov, ...) to other dimensions. My plan is to combine powerful recent results obtained on the duality of positive cohomology cones with an analysis of the instability of the tangent bundle, i.e. of the Harder-Narasimhan filtration. On these ground-breaking questions, I intend to go much further and to enhance my national and international collaborations. These subjects already attract many young researchers and postdocs throughout the world, and the grant could be used to create even stronger interactions.
Max ERC Funding
1 809 345 €
Duration
Start date: 2015-09-01, End date: 2020-08-31
Project acronym ALPROS
Project Artificial Life-like Processive Systems
Researcher (PI) Roeland Johannes Maria Nolte
Host Institution (HI) STICHTING KATHOLIEKE UNIVERSITEIT
Call Details Advanced Grant (AdG), PE5, ERC-2011-ADG_20110209
Summary Toroidal processive enzymes (e.g. enzymes/proteins that are able to thread onto biopolymers and to perform stepwise reactions along the polymer chain) are among the most fascinating tools involved in the clockwork machinery of life. Processive catalysis is ubiquitous in Nature, viz. DNA polymerases, endo- and exo-nucleases and; it plays a crucial role in numerous events of the cell’s life, including most of the replication, transmission, and expression and repair processes of the genetic information. In the case of DNA polymerases the protein catalyst encircles the DNA and whilst moving along it, make copies of high fidelity. Although numerous works have been reported in relation with the synthesis of natural enzymes' analogues, very few efforts have been paid in comparison to mimic these processive properties. It is the goal of this proposal to rectify this oversight and unravel the essential components of Nature’s polymer catalysts. The individual projects are designed to specifically target the essential aspects of processive catalysis, i.e. rate of motion, rate of catalysis, and transfer of information. One project is aimed at extending the research into a processive catalytic system that is more suitable for industrial application. Two projects involve more farsighted studies and are designed to push the research way beyond the current boundaries into the area of Turing machines and bio-rotaxane catalysts which can modify DNA in a non-natural process. The vision of this proposal is to open up the field of ‘processive catalysis’ and invigorate the next generation of chemists to develop information transfer and toroidal processive catalysts. The construction of synthetic analogues of processive enzymes could open a gate toward a large range of applications, ranging from intelligent tailoring of polymers to information storage and processing.
Summary
Toroidal processive enzymes (e.g. enzymes/proteins that are able to thread onto biopolymers and to perform stepwise reactions along the polymer chain) are among the most fascinating tools involved in the clockwork machinery of life. Processive catalysis is ubiquitous in Nature, viz. DNA polymerases, endo- and exo-nucleases and; it plays a crucial role in numerous events of the cell’s life, including most of the replication, transmission, and expression and repair processes of the genetic information. In the case of DNA polymerases the protein catalyst encircles the DNA and whilst moving along it, make copies of high fidelity. Although numerous works have been reported in relation with the synthesis of natural enzymes' analogues, very few efforts have been paid in comparison to mimic these processive properties. It is the goal of this proposal to rectify this oversight and unravel the essential components of Nature’s polymer catalysts. The individual projects are designed to specifically target the essential aspects of processive catalysis, i.e. rate of motion, rate of catalysis, and transfer of information. One project is aimed at extending the research into a processive catalytic system that is more suitable for industrial application. Two projects involve more farsighted studies and are designed to push the research way beyond the current boundaries into the area of Turing machines and bio-rotaxane catalysts which can modify DNA in a non-natural process. The vision of this proposal is to open up the field of ‘processive catalysis’ and invigorate the next generation of chemists to develop information transfer and toroidal processive catalysts. The construction of synthetic analogues of processive enzymes could open a gate toward a large range of applications, ranging from intelligent tailoring of polymers to information storage and processing.
Max ERC Funding
1 603 699 €
Duration
Start date: 2012-02-01, End date: 2017-01-31
Project acronym AMPLIPORE
Project Understanding negative gas adsorption in highly porous networks for the design of pressure amplifying materials
Researcher (PI) Stefan Kaskel
Host Institution (HI) TECHNISCHE UNIVERSITAET DRESDEN
Call Details Advanced Grant (AdG), PE5, ERC-2016-ADG
Summary Negative gas adsorption (NGA) is a new, counterintuitive and paradoxical phenomenon, for the first time
reported by my group in 2016: Normal solid materials with significant outer or inner surface area always
take up gas when the pressure in the surrounding reservoir is increased (adsorption). NGA networks instead
react at a certain point in the opposite direction: They release gas upon external pressure increase, leading to
an overall pressure amplification in a closed system. Comparable phenomena have never been reported
before. What is so exciting about NGA? We have a unique material in hand, that counteracts to an external
force by force amplification.
So far NGA has solely been observed in one of our new coordination polymers, featuring a colossal selfcompression
associated with a mesopore-to-micropore transformation. Gas pressure amplifying materials
could lead to important innovations in gas releasing rescue systems, pneumatic control systems (production,
transportation), micropumps, microfluidic devices, pneumatic actuators, and artificial lungs. A fundamental
understanding of the physical mechanisms, structures, and thermodynamic boundary conditions is an
essential prerequisite for any industrial application of this counterintuitive phenomenon.
Combining strong synthetic methodologies with advanced analytical techniques, AMPLIPORE will elucidate
the characteristic molecular and mesoscopic materials signatures as well as thermodynamic boundary
conditions of NGA phenomena. We will elaborate a generic NGA-materials concept to tailor the pressure
amplification and explore temperature and pressure ranges at which NGA can be applied. Developing tailormade
instrumentation for kinetic investigations of NGA will give fundamental insights into the intrinsic and
macroscopic dynamics of crystal-to-crystal transformations for applications in micropneumatic systems.
Summary
Negative gas adsorption (NGA) is a new, counterintuitive and paradoxical phenomenon, for the first time
reported by my group in 2016: Normal solid materials with significant outer or inner surface area always
take up gas when the pressure in the surrounding reservoir is increased (adsorption). NGA networks instead
react at a certain point in the opposite direction: They release gas upon external pressure increase, leading to
an overall pressure amplification in a closed system. Comparable phenomena have never been reported
before. What is so exciting about NGA? We have a unique material in hand, that counteracts to an external
force by force amplification.
So far NGA has solely been observed in one of our new coordination polymers, featuring a colossal selfcompression
associated with a mesopore-to-micropore transformation. Gas pressure amplifying materials
could lead to important innovations in gas releasing rescue systems, pneumatic control systems (production,
transportation), micropumps, microfluidic devices, pneumatic actuators, and artificial lungs. A fundamental
understanding of the physical mechanisms, structures, and thermodynamic boundary conditions is an
essential prerequisite for any industrial application of this counterintuitive phenomenon.
Combining strong synthetic methodologies with advanced analytical techniques, AMPLIPORE will elucidate
the characteristic molecular and mesoscopic materials signatures as well as thermodynamic boundary
conditions of NGA phenomena. We will elaborate a generic NGA-materials concept to tailor the pressure
amplification and explore temperature and pressure ranges at which NGA can be applied. Developing tailormade
instrumentation for kinetic investigations of NGA will give fundamental insights into the intrinsic and
macroscopic dynamics of crystal-to-crystal transformations for applications in micropneumatic systems.
Max ERC Funding
2 363 125 €
Duration
Start date: 2017-09-01, End date: 2022-08-31
Project acronym analysisdirac
Project The analysis of the Dirac operator: the hypoelliptic Laplacian and its applications
Researcher (PI) Jean-Michel Philippe Marie-José Bismut
Host Institution (HI) UNIVERSITE PARIS-SUD
Call Details Advanced Grant (AdG), PE1, ERC-2011-ADG_20110209
Summary 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.
Summary
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.
Max ERC Funding
1 112 400 €
Duration
Start date: 2012-02-01, End date: 2017-01-31
Project acronym ARPEMA
Project Anionic redox processes: A transformational approach for advanced energy materials
Researcher (PI) Jean-Marie Tarascon
Host Institution (HI) COLLEGE DE FRANCE
Call Details Advanced Grant (AdG), PE5, ERC-2014-ADG
Summary Redox chemistry provides the fundamental basis for numerous energy-related electrochemical devices, among which Li-ion batteries (LIB) have become the premier energy storage technology for portable electronics and vehicle electrification. Throughout its history, LIB technology has relied on cationic redox reactions as the sole source of energy storage capacity. This is no longer true. In 2013 we demonstrated that Li-driven reversible formation of (O2)n peroxo-groups in new layered oxides led to extraordinary increases in energy storage capacity. This finding, which is receiving worldwide attention, represents a transformational approach for creating advanced energy materials for not only energy storage, but also water splitting applications as both involve peroxo species. However, as is often the case with new discoveries, the fundamental science at work needs to be rationalized and understood. Specifically, what are the mechanisms for ion and electron transport in these Li-driven anionic redox reactions?
To address these seminal questions and to widen the spectrum of materials (transition metal and anion) showing anionic redox chemistry, we propose a comprehensive research program that combines experimental and computational methods. The experimental methods include structural and electrochemical analyses (both ex-situ and in-situ), and computational modeling will be based on first-principles DFT for identifying the fundamental processes that enable anionic redox activity. The knowledge gained from these studies, in combination with our expertise in inorganic synthesis, will enable us to design a new generation of Li-ion battery materials that exhibit substantial increases (20 -30%) in energy storage capacity, with additional impacts on the development of Na-ion batteries and the design of water splitting catalysts, with the feasibility to surpass current water splitting efficiencies via novel (O2)n-based electrocatalysts.
Summary
Redox chemistry provides the fundamental basis for numerous energy-related electrochemical devices, among which Li-ion batteries (LIB) have become the premier energy storage technology for portable electronics and vehicle electrification. Throughout its history, LIB technology has relied on cationic redox reactions as the sole source of energy storage capacity. This is no longer true. In 2013 we demonstrated that Li-driven reversible formation of (O2)n peroxo-groups in new layered oxides led to extraordinary increases in energy storage capacity. This finding, which is receiving worldwide attention, represents a transformational approach for creating advanced energy materials for not only energy storage, but also water splitting applications as both involve peroxo species. However, as is often the case with new discoveries, the fundamental science at work needs to be rationalized and understood. Specifically, what are the mechanisms for ion and electron transport in these Li-driven anionic redox reactions?
To address these seminal questions and to widen the spectrum of materials (transition metal and anion) showing anionic redox chemistry, we propose a comprehensive research program that combines experimental and computational methods. The experimental methods include structural and electrochemical analyses (both ex-situ and in-situ), and computational modeling will be based on first-principles DFT for identifying the fundamental processes that enable anionic redox activity. The knowledge gained from these studies, in combination with our expertise in inorganic synthesis, will enable us to design a new generation of Li-ion battery materials that exhibit substantial increases (20 -30%) in energy storage capacity, with additional impacts on the development of Na-ion batteries and the design of water splitting catalysts, with the feasibility to surpass current water splitting efficiencies via novel (O2)n-based electrocatalysts.
Max ERC Funding
2 249 196 €
Duration
Start date: 2015-10-01, End date: 2020-09-30
