Project acronym AMORE
Project A distributional MOdel of Reference to Entities
Researcher (PI) Gemma BOLEDA TORRENT
Host Institution (HI) UNIVERSIDAD POMPEU FABRA
Call Details Starting Grant (StG), SH4, ERC-2016-STG
Summary "When I asked my seven-year-old daughter ""Who is the boy in your class who was also new in school last year, like you?"", she instantly replied ""Daniel"", using the descriptive content in my utterance to identify an entity in the real world and refer to it. The ability to use language to refer to reality is crucial for humans, and yet it is very difficult to model. AMORE breaks new ground in Computational Linguistics, Linguistics, and Artificial Intelligence by developing a model of linguistic reference to entities implemented as a computational system that can learn its own representations from data.
This interdisciplinary project builds on two complementary semantic traditions: 1) Formal semantics, a symbolic approach that can delimit and track linguistic referents, but does not adequately match them with the descriptive content of linguistic expressions; 2) Distributional semantics, which can handle descriptive content but does not associate it to individuated referents. AMORE synthesizes the two approaches into a unified, scalable model of reference that operates with individuated referents and links them to referential expressions characterized by rich descriptive content. The model is a distributed (neural network) version of a formal semantic framework that is furthermore able to integrate perceptual (visual) and linguistic information about entities. We test it extensively in referential tasks that require matching noun phrases (“the Medicine student”, “the white cat”) with entity representations extracted from text and images.
AMORE advances our scientific understanding of language and its computational modeling, and contributes to the far-reaching debate between symbolic and distributed approaches to cognition with an integrative proposal. I am in a privileged position to carry out this integration, since I have contributed top research in both distributional and formal semantics.
"
Summary
"When I asked my seven-year-old daughter ""Who is the boy in your class who was also new in school last year, like you?"", she instantly replied ""Daniel"", using the descriptive content in my utterance to identify an entity in the real world and refer to it. The ability to use language to refer to reality is crucial for humans, and yet it is very difficult to model. AMORE breaks new ground in Computational Linguistics, Linguistics, and Artificial Intelligence by developing a model of linguistic reference to entities implemented as a computational system that can learn its own representations from data.
This interdisciplinary project builds on two complementary semantic traditions: 1) Formal semantics, a symbolic approach that can delimit and track linguistic referents, but does not adequately match them with the descriptive content of linguistic expressions; 2) Distributional semantics, which can handle descriptive content but does not associate it to individuated referents. AMORE synthesizes the two approaches into a unified, scalable model of reference that operates with individuated referents and links them to referential expressions characterized by rich descriptive content. The model is a distributed (neural network) version of a formal semantic framework that is furthermore able to integrate perceptual (visual) and linguistic information about entities. We test it extensively in referential tasks that require matching noun phrases (“the Medicine student”, “the white cat”) with entity representations extracted from text and images.
AMORE advances our scientific understanding of language and its computational modeling, and contributes to the far-reaching debate between symbolic and distributed approaches to cognition with an integrative proposal. I am in a privileged position to carry out this integration, since I have contributed top research in both distributional and formal semantics.
"
Max ERC Funding
1 499 805 €
Duration
Start date: 2017-02-01, End date: 2022-01-31
Project acronym ANGEOM
Project Geometric analysis in the Euclidean space
Researcher (PI) Xavier Tolsa Domenech
Host Institution (HI) UNIVERSITAT AUTONOMA DE BARCELONA
Call Details Advanced Grant (AdG), PE1, ERC-2012-ADG_20120216
Summary "We propose to study different questions in the area of the so called geometric analysis. Most of the topics we are interested in deal with the connection between the behavior of singular integrals and the geometry of sets and measures. The study of this connection has been shown to be extremely helpful in the solution of certain long standing problems in the last years, such as the solution of the Painlev\'e problem or the obtaining of the optimal distortion bounds for quasiconformal mappings by Astala.
More specifically, we would like to study the relationship between the L^2 boundedness of singular integrals associated with Riesz and other related kernels, and rectifiability and other geometric notions. The so called David-Semmes problem is probably the main open problem in this area. Up to now, the techniques used to deal with this problem come from multiscale analysis and involve ideas from Littlewood-Paley theory and quantitative techniques of rectifiability. We propose to apply new ideas that combine variational arguments with other techniques which have connections with mass transportation. Further, we think that it is worth to explore in more detail the connection among mass transportation, singular integrals, and uniform rectifiability.
We are also interested in the field of quasiconformal mappings. We plan to study a problem regarding the quasiconformal distortion of quasicircles. This problem consists in proving that the bounds obtained recently by S. Smirnov on the dimension of K-quasicircles are optimal. We want to apply techniques from quantitative geometric measure theory to deal with this question.
Another question that we intend to explore lies in the interplay of harmonic analysis, geometric measure theory and partial differential equations. This concerns an old problem on the unique continuation of harmonic functions at the boundary open C^1 or Lipschitz domain. All the results known by now deal with smoother Dini domains."
Summary
"We propose to study different questions in the area of the so called geometric analysis. Most of the topics we are interested in deal with the connection between the behavior of singular integrals and the geometry of sets and measures. The study of this connection has been shown to be extremely helpful in the solution of certain long standing problems in the last years, such as the solution of the Painlev\'e problem or the obtaining of the optimal distortion bounds for quasiconformal mappings by Astala.
More specifically, we would like to study the relationship between the L^2 boundedness of singular integrals associated with Riesz and other related kernels, and rectifiability and other geometric notions. The so called David-Semmes problem is probably the main open problem in this area. Up to now, the techniques used to deal with this problem come from multiscale analysis and involve ideas from Littlewood-Paley theory and quantitative techniques of rectifiability. We propose to apply new ideas that combine variational arguments with other techniques which have connections with mass transportation. Further, we think that it is worth to explore in more detail the connection among mass transportation, singular integrals, and uniform rectifiability.
We are also interested in the field of quasiconformal mappings. We plan to study a problem regarding the quasiconformal distortion of quasicircles. This problem consists in proving that the bounds obtained recently by S. Smirnov on the dimension of K-quasicircles are optimal. We want to apply techniques from quantitative geometric measure theory to deal with this question.
Another question that we intend to explore lies in the interplay of harmonic analysis, geometric measure theory and partial differential equations. This concerns an old problem on the unique continuation of harmonic functions at the boundary open C^1 or Lipschitz domain. All the results known by now deal with smoother Dini domains."
Max ERC Funding
1 105 930 €
Duration
Start date: 2013-05-01, End date: 2018-04-30
Project acronym BILITERACY
Project Bi-literacy: Learning to read in L1 and in L2
Researcher (PI) Manuel Francisco Carreiras Valiña
Host Institution (HI) BCBL BASQUE CENTER ON COGNITION BRAIN AND LANGUAGE
Call Details Advanced Grant (AdG), SH4, ERC-2011-ADG_20110406
Summary Learning to read is probably one of the most exciting discoveries in our life. Using a longitudinal approach, the research proposed examines how the human brain responds to two major challenges: (a) the instantiation a complex cognitive function for which there is no genetic blueprint (learning to read in a first language, L1), and (b) the accommodation to new statistical regularities when learning to read in a second language (L2). The aim of the present research project is to identify the neural substrates of the reading process and its constituent cognitive components, with specific attention to individual differences and reading disabilities; as well as to investigate the relationship between specific cognitive functions and the changes in neural activity that take place in the course of learning to read in L1 and in L2. The project will employ a longitudinal design. We will recruit children before they learn to read in L1 and in L2 and track reading development with both cognitive and neuroimaging measures over 24 months. The findings from this project will provide a deeper understanding of (a) how general neurocognitive factors and language specific factors underlie individual differences – and reading disabilities– in reading acquisition in L1 and in L2; (b) how the neuro-cognitive circuitry changes and brain mechanisms synchronize while instantiating reading in L1 and in L2; (c) what the limitations and the extent of brain plasticity are in young readers. An interdisciplinary and multi-methodological approach is one of the keys to success of the present project, along with strong theory-driven investigation. By combining both we will generate breakthroughs to advance our understanding of how literacy in L1 and in L2 is acquired and mastered. The research proposed will also lay the foundations for more applied investigations of best practice in teaching reading in first and subsequent languages, and devising intervention methods for reading disabilities.
Summary
Learning to read is probably one of the most exciting discoveries in our life. Using a longitudinal approach, the research proposed examines how the human brain responds to two major challenges: (a) the instantiation a complex cognitive function for which there is no genetic blueprint (learning to read in a first language, L1), and (b) the accommodation to new statistical regularities when learning to read in a second language (L2). The aim of the present research project is to identify the neural substrates of the reading process and its constituent cognitive components, with specific attention to individual differences and reading disabilities; as well as to investigate the relationship between specific cognitive functions and the changes in neural activity that take place in the course of learning to read in L1 and in L2. The project will employ a longitudinal design. We will recruit children before they learn to read in L1 and in L2 and track reading development with both cognitive and neuroimaging measures over 24 months. The findings from this project will provide a deeper understanding of (a) how general neurocognitive factors and language specific factors underlie individual differences – and reading disabilities– in reading acquisition in L1 and in L2; (b) how the neuro-cognitive circuitry changes and brain mechanisms synchronize while instantiating reading in L1 and in L2; (c) what the limitations and the extent of brain plasticity are in young readers. An interdisciplinary and multi-methodological approach is one of the keys to success of the present project, along with strong theory-driven investigation. By combining both we will generate breakthroughs to advance our understanding of how literacy in L1 and in L2 is acquired and mastered. The research proposed will also lay the foundations for more applied investigations of best practice in teaching reading in first and subsequent languages, and devising intervention methods for reading disabilities.
Max ERC Funding
2 487 000 €
Duration
Start date: 2012-05-01, End date: 2017-04-30
Project acronym BIOCON
Project Biological origins of linguistic constraints
Researcher (PI) Juan Manuel Toro
Host Institution (HI) UNIVERSIDAD POMPEU FABRA
Call Details Starting Grant (StG), SH4, ERC-2012-StG_20111124
Summary The linguistic capacity to express and comprehend an unlimited number of ideas when combining a limited number of elements has only been observed in humans. Nevertheless, research has not fully identified the components of language that make it uniquely human and that allow infants to grasp the complexity of linguistic structure in an apparently effortless manner. Research on comparative cognition suggests humans and other species share powerful learning mechanisms and basic perceptual abilities we use for language processing. But humans display remarkable linguistic abilities that other animals do not possess. Understanding the interplay between general mechanisms shared across species and more specialized ones dedicated to the speech signal is at the heart of current debates in human language acquisition. This is a highly relevant issue for researchers in the fields of Psychology, Linguistics, Biology, Philosophy and Cognitive Neuroscience. By conducting experiments across several populations (human adults and infants) and species (human and nonhuman animals), and using a wide array of experimental techniques, the present proposal hopes to shed some light on the origins of shared biological constraints that guide more specialized mechanisms in the search for linguistic structure. More specifically, we hope to understand how general perceptual and cognitive mechanisms likely present in other animals constrain the way humans tackle the task of language acquisition. Our hypothesis is that differences between humans and other species are not the result of humans being able to process increasingly complex structures that are the hallmark of language. Rather, differences might be due to humans and other animals focusing on different cues present in the signal to extract relevant information. This research will hint at what is uniquely human and what is shared across different animals species.
Summary
The linguistic capacity to express and comprehend an unlimited number of ideas when combining a limited number of elements has only been observed in humans. Nevertheless, research has not fully identified the components of language that make it uniquely human and that allow infants to grasp the complexity of linguistic structure in an apparently effortless manner. Research on comparative cognition suggests humans and other species share powerful learning mechanisms and basic perceptual abilities we use for language processing. But humans display remarkable linguistic abilities that other animals do not possess. Understanding the interplay between general mechanisms shared across species and more specialized ones dedicated to the speech signal is at the heart of current debates in human language acquisition. This is a highly relevant issue for researchers in the fields of Psychology, Linguistics, Biology, Philosophy and Cognitive Neuroscience. By conducting experiments across several populations (human adults and infants) and species (human and nonhuman animals), and using a wide array of experimental techniques, the present proposal hopes to shed some light on the origins of shared biological constraints that guide more specialized mechanisms in the search for linguistic structure. More specifically, we hope to understand how general perceptual and cognitive mechanisms likely present in other animals constrain the way humans tackle the task of language acquisition. Our hypothesis is that differences between humans and other species are not the result of humans being able to process increasingly complex structures that are the hallmark of language. Rather, differences might be due to humans and other animals focusing on different cues present in the signal to extract relevant information. This research will hint at what is uniquely human and what is shared across different animals species.
Max ERC Funding
1 305 973 €
Duration
Start date: 2013-01-01, End date: 2018-12-31
Project acronym BSD
Project Euler systems and the conjectures of Birch and Swinnerton-Dyer, Bloch and Kato
Researcher (PI) Victor Rotger cerdà
Host Institution (HI) UNIVERSITAT POLITECNICA DE CATALUNYA
Call Details Consolidator Grant (CoG), PE1, ERC-2015-CoG
Summary In order to celebrate mathematics in the new millennium, the Clay Mathematics Institute established seven $1.000.000 Prize Problems. One of these is the conjecture of Birch and Swinnerton-Dyer (BSD), widely open since the 1960's. The main object of this proposal is developing innovative and unconventional strategies for proving groundbreaking results towards the resolution of this problem and their generalizations by Bloch and Kato (BK).
Breakthroughs on BSD were achieved by Coates-Wiles, Gross, Zagier and Kolyvagin, and Kato. Since then, there have been nearly no new ideas on how to tackle BSD. Only very recently, three independent revolutionary approaches have seen the light: the works of (1) the Fields medalist Bhargava, (2) Skinner and Urban, and (3) myself and my collaborators. In spite of that, our knowledge of BSD is rather poor. In my proposal I suggest innovating strategies for approaching new horizons in BSD and BK that I aim to develop with the team of PhD and postdoctoral researchers that the CoG may allow me to consolidate. The results I plan to prove represent a departure from the achievements obtained with my coauthors during the past years:
I. BSD over totally real number fields. I plan to prove new ground-breaking instances of BSD in rank 0 for elliptic curves over totally real number fields, generalizing the theorem of Kato (by providing a new proof) and covering many new scenarios that have never been considered before.
II. BSD in rank r=2. Most of the literature on BSD applies when r=0 or 1. I expect to prove p-adic versions of the theorems of Gross-Zagier and Kolyvagin in rank 2.
III. Darmon's 2000 conjecture on Stark-Heegner points. I plan to prove Darmon’s striking conjecture announced at the ICM2000 by recasting it in terms of special values of p-adic L-functions.
Summary
In order to celebrate mathematics in the new millennium, the Clay Mathematics Institute established seven $1.000.000 Prize Problems. One of these is the conjecture of Birch and Swinnerton-Dyer (BSD), widely open since the 1960's. The main object of this proposal is developing innovative and unconventional strategies for proving groundbreaking results towards the resolution of this problem and their generalizations by Bloch and Kato (BK).
Breakthroughs on BSD were achieved by Coates-Wiles, Gross, Zagier and Kolyvagin, and Kato. Since then, there have been nearly no new ideas on how to tackle BSD. Only very recently, three independent revolutionary approaches have seen the light: the works of (1) the Fields medalist Bhargava, (2) Skinner and Urban, and (3) myself and my collaborators. In spite of that, our knowledge of BSD is rather poor. In my proposal I suggest innovating strategies for approaching new horizons in BSD and BK that I aim to develop with the team of PhD and postdoctoral researchers that the CoG may allow me to consolidate. The results I plan to prove represent a departure from the achievements obtained with my coauthors during the past years:
I. BSD over totally real number fields. I plan to prove new ground-breaking instances of BSD in rank 0 for elliptic curves over totally real number fields, generalizing the theorem of Kato (by providing a new proof) and covering many new scenarios that have never been considered before.
II. BSD in rank r=2. Most of the literature on BSD applies when r=0 or 1. I expect to prove p-adic versions of the theorems of Gross-Zagier and Kolyvagin in rank 2.
III. Darmon's 2000 conjecture on Stark-Heegner points. I plan to prove Darmon’s striking conjecture announced at the ICM2000 by recasting it in terms of special values of p-adic L-functions.
Max ERC Funding
1 428 588 €
Duration
Start date: 2016-09-01, End date: 2021-08-31
Project acronym CDAC
Project "The role of consciousness in adaptive behavior: A combined empirical, computational and robot based approach"
Researcher (PI) Paulus Franciscus Maria Joseph Verschure
Host Institution (HI) UNIVERSIDAD POMPEU FABRA
Call Details Advanced Grant (AdG), SH4, ERC-2013-ADG
Summary "Understanding the nature of consciousness is one of the grand outstanding scientific challenges and two of its features stand out: consciousness is defined as the construction of one coherent scene but this scene is experienced with a delay relative to the action of the agent and not necessarily the cause of actions and thoughts. Did evolution render solutions to the challenge of survival that includes epiphenomenal processes? The Conscious Distributed Adaptive Control (CDAC) project aims at resolving this paradox by using a multi-disciplinary approach to show the functional role of consciousness in adaptive behaviour, to identify its underlying neuronal principles and to construct a neuromorphic robot based real-time conscious architecture. CDAC proposes that the shift from surviving in a physical world to one that is dominated by intentional agents requires radically different control architectures combining parallel and distributed control loops to assure real-time operation together with a second level of control that assures coherence through sequential coherent representation of self and the task domain, i.e. consciousness. This conscious scene is driving dedicated credit assignment and planning beyond the immediately given information. CDAC advances a comprehensive framework progressing beyond the state of the art and will be realized using system level models of a conscious architecture, detailed computational studies of its underlying neuronal substrate focusing, empirical validation with a humanoid robot and stroke patients and the advancement of beyond state of the art tools appropriate to the complexity of its objectives. The CDAC project directly addresses one of the main outstanding questions in science: the function and genesis of consciousness and will advance our understanding of mind and brain, provide radically new neurorehabilitation technologies and contribute to realizing a new generation of robots with advanced social competence."
Summary
"Understanding the nature of consciousness is one of the grand outstanding scientific challenges and two of its features stand out: consciousness is defined as the construction of one coherent scene but this scene is experienced with a delay relative to the action of the agent and not necessarily the cause of actions and thoughts. Did evolution render solutions to the challenge of survival that includes epiphenomenal processes? The Conscious Distributed Adaptive Control (CDAC) project aims at resolving this paradox by using a multi-disciplinary approach to show the functional role of consciousness in adaptive behaviour, to identify its underlying neuronal principles and to construct a neuromorphic robot based real-time conscious architecture. CDAC proposes that the shift from surviving in a physical world to one that is dominated by intentional agents requires radically different control architectures combining parallel and distributed control loops to assure real-time operation together with a second level of control that assures coherence through sequential coherent representation of self and the task domain, i.e. consciousness. This conscious scene is driving dedicated credit assignment and planning beyond the immediately given information. CDAC advances a comprehensive framework progressing beyond the state of the art and will be realized using system level models of a conscious architecture, detailed computational studies of its underlying neuronal substrate focusing, empirical validation with a humanoid robot and stroke patients and the advancement of beyond state of the art tools appropriate to the complexity of its objectives. The CDAC project directly addresses one of the main outstanding questions in science: the function and genesis of consciousness and will advance our understanding of mind and brain, provide radically new neurorehabilitation technologies and contribute to realizing a new generation of robots with advanced social competence."
Max ERC Funding
2 469 268 €
Duration
Start date: 2014-02-01, End date: 2019-01-31
Project acronym CDSIF
Project Contour dynamics and singularities in incompressible flows
Researcher (PI) Diego Cordoba
Host Institution (HI) AGENCIA ESTATAL CONSEJO SUPERIOR DEINVESTIGACIONES CIENTIFICAS
Call Details Starting Grant (StG), PE1, ERC-2007-StG
Summary The search of singularities in incompressible flows has become a major challenge in the area of non-linear partial differential equations and is relevant in applied mathematics, physics and engineering. The existence of such singularities would have important consequences for the understanding of turbulence. One way to make progress in this direction, is to study plausible scenarios for the singularities supported by experiments or numerical analysis. With the more sophisticated numerical tools now available, the subject has recently gained considerable momentum. The main goal of this project is to study analytically several incompressible fluid models. In particular solutions that involve the possible formation of singularities or quasi-singular structures.
Summary
The search of singularities in incompressible flows has become a major challenge in the area of non-linear partial differential equations and is relevant in applied mathematics, physics and engineering. The existence of such singularities would have important consequences for the understanding of turbulence. One way to make progress in this direction, is to study plausible scenarios for the singularities supported by experiments or numerical analysis. With the more sophisticated numerical tools now available, the subject has recently gained considerable momentum. The main goal of this project is to study analytically several incompressible fluid models. In particular solutions that involve the possible formation of singularities or quasi-singular structures.
Max ERC Funding
650 000 €
Duration
Start date: 2008-09-01, End date: 2013-08-31
Project acronym ChronHib
Project Chronologicon Hibernicum – A Probabilistic Chronological Framework for Dating Early Irish Language Developments and Literature
Researcher (PI) David Stifter
Host Institution (HI) NATIONAL UNIVERSITY OF IRELAND MAYNOOTH
Call Details Consolidator Grant (CoG), SH4, ERC-2014-CoG
Summary Early Medieval Irish literature (7th–10th centuries) is vast in extent and rich in genres, but owing to its mostly anonymous transmission, for most texts the precise time and circumstances of composition are unknown. Unless where texts contain historical references, the only clues for a rough chronological positioning of the texts are to be found in their linguistic peculiarities. Phonology, morphology, syntax and the lexicon of the Irish language changed considerably from Early Old Irish (7th c.) into Middle Irish (c. 10th–12th centuries). However, only the relative sequence of changes is well understood; for most sound changes very few narrow dates have been proposed so far.
It is the aim of Chronologicon Hibernicum to find a common solution for both problems: through the linguistic profiling of externally dated texts (esp. annalistic writing and sources with a clear historical anchorage) and through serialising the emerging linguistic and chronological data, progress will be made in assigning dates to the linguistic changes. Groundbreakingly, this will be done by using statistical methods for the seriation of the data, and for estimating dates using Bayesian inference.
The resultant information will then be used to find new dates for hitherto undated texts. On this basis, a much tighter chronological framework for the developments of the Early Medieval Irish language will be created. In a further step it will be possible to arrive at a better chronological description of medieval Irish literature as a whole, which will have repercussions on the study of the history and cultural and intellectual environment of medieval Ireland and on its connections with the wider world.
The data collected and analysed in this project will form the database Chronologicon Hibernicum which will serve as the authoritative guideline and reference point for the linguistic dating of Irish texts. In the future, the methodology will be transferable to other languages.
Summary
Early Medieval Irish literature (7th–10th centuries) is vast in extent and rich in genres, but owing to its mostly anonymous transmission, for most texts the precise time and circumstances of composition are unknown. Unless where texts contain historical references, the only clues for a rough chronological positioning of the texts are to be found in their linguistic peculiarities. Phonology, morphology, syntax and the lexicon of the Irish language changed considerably from Early Old Irish (7th c.) into Middle Irish (c. 10th–12th centuries). However, only the relative sequence of changes is well understood; for most sound changes very few narrow dates have been proposed so far.
It is the aim of Chronologicon Hibernicum to find a common solution for both problems: through the linguistic profiling of externally dated texts (esp. annalistic writing and sources with a clear historical anchorage) and through serialising the emerging linguistic and chronological data, progress will be made in assigning dates to the linguistic changes. Groundbreakingly, this will be done by using statistical methods for the seriation of the data, and for estimating dates using Bayesian inference.
The resultant information will then be used to find new dates for hitherto undated texts. On this basis, a much tighter chronological framework for the developments of the Early Medieval Irish language will be created. In a further step it will be possible to arrive at a better chronological description of medieval Irish literature as a whole, which will have repercussions on the study of the history and cultural and intellectual environment of medieval Ireland and on its connections with the wider world.
The data collected and analysed in this project will form the database Chronologicon Hibernicum which will serve as the authoritative guideline and reference point for the linguistic dating of Irish texts. In the future, the methodology will be transferable to other languages.
Max ERC Funding
1 804 230 €
Duration
Start date: 2015-09-01, End date: 2020-08-31
Project acronym CZOSQP
Project Noncommutative Calderón-Zygmund theory, operator space geometry and quantum probability
Researcher (PI) Javier Parcet Hernandez
Host Institution (HI) AGENCIA ESTATAL CONSEJO SUPERIOR DEINVESTIGACIONES CIENTIFICAS
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary Von Neumann's concept of quantization goes back to the foundations of quantum mechanics
and provides a noncommutative model of integration. Over the years, von Neumann algebras
have shown a profound structure and set the right framework for quantizing portions of algebra,
analysis, geometry and probability. A fundamental part of my research is devoted to develop a
very much expected Calderón-Zygmund theory for von Neumann algebras. The lack of natural
metrics partly justifies this long standing gap in the theory. Key new ingredients come from
recent results on noncommutative martingale inequalities, operator space theory and quantum
probability. This is an ambitious research project and applications include new estimates for
noncommutative Riesz transforms, Fourier and Schur multipliers on arbitrary discrete groups
or noncommutative ergodic theorems. Other related objectives of this project include Rubio
de Francia's conjecture on the almost everywhere convergence of Fourier series for matrix
valued functions or a formulation of Fefferman-Stein's maximal inequality for noncommutative
martingales. Reciprocally, I will also apply new techniques from quantum probability in
noncommutative Lp embedding theory and the local theory of operator spaces. I have already
obtained major results in this field, which might be useful towards a noncommutative form of
weighted harmonic analysis and new challenging results on quantum information theory.
Summary
Von Neumann's concept of quantization goes back to the foundations of quantum mechanics
and provides a noncommutative model of integration. Over the years, von Neumann algebras
have shown a profound structure and set the right framework for quantizing portions of algebra,
analysis, geometry and probability. A fundamental part of my research is devoted to develop a
very much expected Calderón-Zygmund theory for von Neumann algebras. The lack of natural
metrics partly justifies this long standing gap in the theory. Key new ingredients come from
recent results on noncommutative martingale inequalities, operator space theory and quantum
probability. This is an ambitious research project and applications include new estimates for
noncommutative Riesz transforms, Fourier and Schur multipliers on arbitrary discrete groups
or noncommutative ergodic theorems. Other related objectives of this project include Rubio
de Francia's conjecture on the almost everywhere convergence of Fourier series for matrix
valued functions or a formulation of Fefferman-Stein's maximal inequality for noncommutative
martingales. Reciprocally, I will also apply new techniques from quantum probability in
noncommutative Lp embedding theory and the local theory of operator spaces. I have already
obtained major results in this field, which might be useful towards a noncommutative form of
weighted harmonic analysis and new challenging results on quantum information theory.
Max ERC Funding
1 090 925 €
Duration
Start date: 2010-10-01, End date: 2015-09-30
Project acronym DYCON
Project Dynamic Control and Numerics of Partial Differential Equations
Researcher (PI) Enrique Zuazua
Host Institution (HI) FUNDACION DEUSTO
Call Details Advanced Grant (AdG), PE1, ERC-2015-AdG
Summary This project aims at making a breakthrough contribution in the broad area of Control of Partial Differential Equations (PDE) and their numerical approximation methods by addressing key unsolved issues appearing systematically in real-life applications.
To this end, we pursue three objectives: 1) to contribute with new key theoretical methods and results, 2) to develop the corresponding numerical tools, and 3) to build up new computational software, the DYCON-COMP computational platform, thereby bridging the gap to applications.
The field of PDEs, together with numerical approximation and simulation methods and control theory, have evolved significantly in the last decades in a cross-fertilization process, to address the challenging demands of industrial and cross-disciplinary applications such as, for instance, the management of natural resources, meteorology, aeronautics, oil industry, biomedicine, human and animal collective behaviour, etc. Despite these efforts, some of the key issues still remain unsolved, either because of a lack of analytical understanding, of the absence of efficient numerical solvers, or of a combination of both.
This project identifies and focuses on six key topics that play a central role in most of the processes arising in applications, but which are still poorly understood: control of parameter dependent problems; long time horizon control; control under constraints; inverse design of time-irreversible models; memory models and hybrid PDE/ODE models, and finite versus infinite-dimensional dynamical systems.
These topics cannot be handled by superposing the state of the art in the various disciplines, due to the unexpected interactive phenomena that may emerge, for instance, in the fine numerical approximation of control problems. The coordinated and focused effort that we aim at developing is timely and much needed in order to solve these issues and bridge the gap from modelling to control, computer simulations and applications.
Summary
This project aims at making a breakthrough contribution in the broad area of Control of Partial Differential Equations (PDE) and their numerical approximation methods by addressing key unsolved issues appearing systematically in real-life applications.
To this end, we pursue three objectives: 1) to contribute with new key theoretical methods and results, 2) to develop the corresponding numerical tools, and 3) to build up new computational software, the DYCON-COMP computational platform, thereby bridging the gap to applications.
The field of PDEs, together with numerical approximation and simulation methods and control theory, have evolved significantly in the last decades in a cross-fertilization process, to address the challenging demands of industrial and cross-disciplinary applications such as, for instance, the management of natural resources, meteorology, aeronautics, oil industry, biomedicine, human and animal collective behaviour, etc. Despite these efforts, some of the key issues still remain unsolved, either because of a lack of analytical understanding, of the absence of efficient numerical solvers, or of a combination of both.
This project identifies and focuses on six key topics that play a central role in most of the processes arising in applications, but which are still poorly understood: control of parameter dependent problems; long time horizon control; control under constraints; inverse design of time-irreversible models; memory models and hybrid PDE/ODE models, and finite versus infinite-dimensional dynamical systems.
These topics cannot be handled by superposing the state of the art in the various disciplines, due to the unexpected interactive phenomena that may emerge, for instance, in the fine numerical approximation of control problems. The coordinated and focused effort that we aim at developing is timely and much needed in order to solve these issues and bridge the gap from modelling to control, computer simulations and applications.
Max ERC Funding
2 065 125 €
Duration
Start date: 2016-10-01, End date: 2021-09-30
