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 ACTIVIA
Project Visual Recognition of Function and Intention
Researcher (PI) Ivan Laptev
Host Institution (HI) INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE
Call Details Starting Grant (StG), PE6, ERC-2012-StG_20111012
Summary "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."
Summary
"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."
Max ERC Funding
1 497 420 €
Duration
Start date: 2013-01-01, End date: 2018-12-31
Project acronym ADAPT
Project Theory and Algorithms for Adaptive Particle Simulation
Researcher (PI) Stephane Redon
Host Institution (HI) INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE
Call Details Starting Grant (StG), PE6, ERC-2012-StG_20111012
Summary "During the twentieth century, the development of macroscopic engineering has been largely stimulated by progress in digital prototyping: cars, planes, boats, etc. are nowadays designed and tested on computers. Digital prototypes have progressively replaced actual ones, and effective computer-aided engineering tools have helped cut costs and reduce production cycles of these macroscopic systems.
The twenty-first century is most likely to see a similar development at the atomic scale. Indeed, the recent years have seen tremendous progress in nanotechnology - in particular in the ability to control matter at the atomic scale. Similar to what has happened with macroscopic engineering, powerful and generic computational tools will be needed to engineer complex nanosystems, through modeling and simulation. As a result, a major challenge is to develop efficient simulation methods and algorithms.
NANO-D, the INRIA research group I started in January 2008 in Grenoble, France, aims at developing
efficient computational methods for modeling and simulating complex nanosystems, both natural and artificial. In particular, NANO-D develops SAMSON, a software application which gathers all algorithms designed by the group and its collaborators (SAMSON: Software for Adaptive Modeling and Simulation Of Nanosystems).
In this project, I propose to develop a unified theory, and associated algorithms, for adaptive particle simulation. The proposed theory will avoid problems that plague current popular multi-scale or hybrid simulation approaches by simulating a single potential throughout the system, while allowing users to finely trade precision for computational speed.
I believe the full development of the adaptive particle simulation theory will have an important impact on current modeling and simulation practices, and will enable practical design of complex nanosystems on desktop computers, which should significantly boost the emergence of generic nano-engineering."
Summary
"During the twentieth century, the development of macroscopic engineering has been largely stimulated by progress in digital prototyping: cars, planes, boats, etc. are nowadays designed and tested on computers. Digital prototypes have progressively replaced actual ones, and effective computer-aided engineering tools have helped cut costs and reduce production cycles of these macroscopic systems.
The twenty-first century is most likely to see a similar development at the atomic scale. Indeed, the recent years have seen tremendous progress in nanotechnology - in particular in the ability to control matter at the atomic scale. Similar to what has happened with macroscopic engineering, powerful and generic computational tools will be needed to engineer complex nanosystems, through modeling and simulation. As a result, a major challenge is to develop efficient simulation methods and algorithms.
NANO-D, the INRIA research group I started in January 2008 in Grenoble, France, aims at developing
efficient computational methods for modeling and simulating complex nanosystems, both natural and artificial. In particular, NANO-D develops SAMSON, a software application which gathers all algorithms designed by the group and its collaborators (SAMSON: Software for Adaptive Modeling and Simulation Of Nanosystems).
In this project, I propose to develop a unified theory, and associated algorithms, for adaptive particle simulation. The proposed theory will avoid problems that plague current popular multi-scale or hybrid simulation approaches by simulating a single potential throughout the system, while allowing users to finely trade precision for computational speed.
I believe the full development of the adaptive particle simulation theory will have an important impact on current modeling and simulation practices, and will enable practical design of complex nanosystems on desktop computers, which should significantly boost the emergence of generic nano-engineering."
Max ERC Funding
1 476 882 €
Duration
Start date: 2012-09-01, End date: 2017-08-31
Project acronym ADDECCO
Project Adaptive Schemes for Deterministic and Stochastic Flow Problems
Researcher (PI) Remi Abgrall
Host Institution (HI) INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary 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.
Summary
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.
Max ERC Funding
1 432 769 €
Duration
Start date: 2008-12-01, End date: 2013-11-30
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 ALFA
Project Shaping a European Scientific Scene : Alfonsine Astronomy
Researcher (PI) Matthieu Husson
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Consolidator Grant (CoG), SH6, ERC-2016-COG
Summary Alfonsine astronomy is arguably among the first European scientific achievements. It shaped a scene for actors like Regiomontanus or Copernicus. There is however little detailed historical analysis encompassing its development in its full breadth. ALFA addresses this issue by studying tables, instruments, mathematical and theoretical texts in a methodologically innovative way relying on approaches from the history of manuscript cultures, history of mathematics, and history of astronomy.
ALFA integrates these approaches not only to benefit from different perspectives but also to build new questions from their interactions. For instance the analysis of mathematical practices in astral sciences manuscripts induces new ways to analyse the documents and to think about astronomical questions.
Relying on these approaches the main objectives of ALFA are thus to:
- Retrace the development of the corpus of Alfonsine texts from its origin in the second half of the 13th century to the end of the 15th century by following, on the manuscript level, the milieus fostering it;
- Analyse the Alfonsine astronomers’ practices, their relations to mathematics, to the natural world, to proofs and justification, their intellectual context and audiences;
- Build a meaningful narrative showing how astronomers in different milieus with diverse practices shaped, also from Arabic materials, an original scientific scene in Europe.
ALFA will shed new light on the intellectual history of the late medieval period as a whole and produce a better understanding of its relations to related scientific periods in Europe and beyond. It will also produce methodological breakthroughs impacting the ways history of knowledge is practiced outside the field of ancient and medieval sciences. Efforts will be devoted to bring these results not only to the relevant scholarly communities but also to a wider audience as a resource in the public debates around science, knowledge and culture.
Summary
Alfonsine astronomy is arguably among the first European scientific achievements. It shaped a scene for actors like Regiomontanus or Copernicus. There is however little detailed historical analysis encompassing its development in its full breadth. ALFA addresses this issue by studying tables, instruments, mathematical and theoretical texts in a methodologically innovative way relying on approaches from the history of manuscript cultures, history of mathematics, and history of astronomy.
ALFA integrates these approaches not only to benefit from different perspectives but also to build new questions from their interactions. For instance the analysis of mathematical practices in astral sciences manuscripts induces new ways to analyse the documents and to think about astronomical questions.
Relying on these approaches the main objectives of ALFA are thus to:
- Retrace the development of the corpus of Alfonsine texts from its origin in the second half of the 13th century to the end of the 15th century by following, on the manuscript level, the milieus fostering it;
- Analyse the Alfonsine astronomers’ practices, their relations to mathematics, to the natural world, to proofs and justification, their intellectual context and audiences;
- Build a meaningful narrative showing how astronomers in different milieus with diverse practices shaped, also from Arabic materials, an original scientific scene in Europe.
ALFA will shed new light on the intellectual history of the late medieval period as a whole and produce a better understanding of its relations to related scientific periods in Europe and beyond. It will also produce methodological breakthroughs impacting the ways history of knowledge is practiced outside the field of ancient and medieval sciences. Efforts will be devoted to bring these results not only to the relevant scholarly communities but also to a wider audience as a resource in the public debates around science, knowledge and culture.
Max ERC Funding
1 871 250 €
Duration
Start date: 2017-09-01, End date: 2022-08-31
Project acronym AlgTateGro
Project Constructing line bundles on algebraic varieties --around conjectures of Tate and Grothendieck
Researcher (PI) François CHARLES
Host Institution (HI) UNIVERSITE PARIS-SUD
Call Details Starting Grant (StG), PE1, ERC-2016-STG
Summary 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.
Summary
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.
Max ERC Funding
1 222 329 €
Duration
Start date: 2016-12-01, End date: 2021-11-30
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 ALLEGRO
Project Active large-scale learning for visual recognition
Researcher (PI) Cordelia Schmid
Host Institution (HI) INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE
Call Details Advanced Grant (AdG), PE6, ERC-2012-ADG_20120216
Summary 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.
Summary
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.
Max ERC Funding
2 493 322 €
Duration
Start date: 2013-04-01, End date: 2019-03-31
