Project acronym 1stProposal
Project An alternative development of analytic number theory and applications
Researcher (PI) ANDREW Granville
Host Institution (HI) UNIVERSITY COLLEGE LONDON
Country United Kingdom
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 AAMOT
Project Arithmetic of automorphic motives
Researcher (PI) Michael Harris
Host Institution (HI) INSTITUT DES HAUTES ETUDES SCIENTIFIQUES
Country France
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 ADAM
Project The Adaptive Auditory Mind
Researcher (PI) Shihab Shamma
Host Institution (HI) ECOLE NORMALE SUPERIEURE
Country France
Call Details Advanced Grant (AdG), SH4, ERC-2011-ADG_20110406
Summary Listening in realistic situations is an active process that engages perceptual and cognitive faculties, endowing speech with meaning, music with joy, and environmental sounds with emotion. Through hearing, humans and other animals navigate complex acoustic scenes, separate sound mixtures, and assess their behavioral relevance. These remarkable feats are currently beyond our understanding and exceed the capabilities of the most sophisticated audio engineering systems. The goal of the proposed research is to investigate experimentally a novel view of hearing, where active hearing emerges from a deep interplay between adaptive sensory processes and goal-directed cognition. Specifically, we shall explore the postulate that versatile perception is mediated by rapid-plasticity at the neuronal level. At the conjunction of sensory and cognitive processing, rapid-plasticity pervades all levels of auditory system, from the cochlea up to the auditory and prefrontal cortices. Exploiting fundamental statistical regularities of acoustics, it is what allows humans and other animal to deal so successfully with natural acoustic scenes where artificial systems fail. The project builds on the internationally recognized leadership of the PI in the fields of physiology and computational modeling, combined with the expertise of the Co-Investigator in psychophysics. Building on these highly complementary fields and several technical innovations, we hope to promote a novel view of auditory perception and cognition. We aim also to contribute significantly to translational research in the domain of signal processing for clinical hearing aids, given that many current limitations are not technological but rather conceptual. The project will finally result in the creation of laboratory facilities and an intellectual network unique in France and rare in all of Europe, combining cognitive, neural, and computational approaches to auditory neuroscience.
Summary
Listening in realistic situations is an active process that engages perceptual and cognitive faculties, endowing speech with meaning, music with joy, and environmental sounds with emotion. Through hearing, humans and other animals navigate complex acoustic scenes, separate sound mixtures, and assess their behavioral relevance. These remarkable feats are currently beyond our understanding and exceed the capabilities of the most sophisticated audio engineering systems. The goal of the proposed research is to investigate experimentally a novel view of hearing, where active hearing emerges from a deep interplay between adaptive sensory processes and goal-directed cognition. Specifically, we shall explore the postulate that versatile perception is mediated by rapid-plasticity at the neuronal level. At the conjunction of sensory and cognitive processing, rapid-plasticity pervades all levels of auditory system, from the cochlea up to the auditory and prefrontal cortices. Exploiting fundamental statistical regularities of acoustics, it is what allows humans and other animal to deal so successfully with natural acoustic scenes where artificial systems fail. The project builds on the internationally recognized leadership of the PI in the fields of physiology and computational modeling, combined with the expertise of the Co-Investigator in psychophysics. Building on these highly complementary fields and several technical innovations, we hope to promote a novel view of auditory perception and cognition. We aim also to contribute significantly to translational research in the domain of signal processing for clinical hearing aids, given that many current limitations are not technological but rather conceptual. The project will finally result in the creation of laboratory facilities and an intellectual network unique in France and rare in all of Europe, combining cognitive, neural, and computational approaches to auditory neuroscience.
Max ERC Funding
3 199 078 €
Duration
Start date: 2012-10-01, End date: 2018-09-30
Project acronym AFRIGOS
Project African Governance and Space: Transport Corridors, Border Towns and Port Cities in Transition
Researcher (PI) Paul Christopher Nugent
Host Institution (HI) THE UNIVERSITY OF EDINBURGH
Country United Kingdom
Call Details Advanced Grant (AdG), SH2, ERC-2014-ADG
Summary AFRIGOS investigates the process of 'respacing' Africa, a political drive towards regional and continental integration, on the one hand, and the re-casting of Africa's engagement with the global economy, on the other. This is reflected in unprecedented levels of investment in physical and communications infrastructure, and the outsourcing of key functions of Customs, Immigration and security agencies. AFRIGOS poses the question of how far respacing is genuinely forging institutions that are facilitating or obstructing the movement of people and goods; that are enabling or preventing urban and border spaces from being more effectively and responsively governed; and that take into account the needs of African populations whose livelihoods are rooted in mobility and informality. The principal research questions are approached through a comparative study of port cities, border towns and other strategic nodes situated along the busiest transport corridors in East, Central, West and Southern Africa. These represent sites of remarkable dynamism and cosmopolitanism, which reflects their role in connecting African urban centres to each other and to other global cities.
AFRIGOS considers how governance 'assemblages' are forged at different scales and is explicitly comparative. It works through 5 connected Streams that address specific questions: 1. AGENDA-SETTING is concerned with policy (re-)formulation. 2. PERIPHERAL URBANISM examines governance in border towns and port cities. 3. BORDER WORKERS addresses everyday governance emerging through the interaction of officials and others who make their livelihoods from the border. 4. CONNECTIVE INFRASTRUCTURE looks as the transformative effects of new technologies. 5. PEOPLE & GOODS IN MOTION traces the passage of people and goods and the regimes of regulation to which they are subjected. AFRIGOS contributes to interdisciplinary research on borderland studies, multi-level governance and the everyday state.
Summary
AFRIGOS investigates the process of 'respacing' Africa, a political drive towards regional and continental integration, on the one hand, and the re-casting of Africa's engagement with the global economy, on the other. This is reflected in unprecedented levels of investment in physical and communications infrastructure, and the outsourcing of key functions of Customs, Immigration and security agencies. AFRIGOS poses the question of how far respacing is genuinely forging institutions that are facilitating or obstructing the movement of people and goods; that are enabling or preventing urban and border spaces from being more effectively and responsively governed; and that take into account the needs of African populations whose livelihoods are rooted in mobility and informality. The principal research questions are approached through a comparative study of port cities, border towns and other strategic nodes situated along the busiest transport corridors in East, Central, West and Southern Africa. These represent sites of remarkable dynamism and cosmopolitanism, which reflects their role in connecting African urban centres to each other and to other global cities.
AFRIGOS considers how governance 'assemblages' are forged at different scales and is explicitly comparative. It works through 5 connected Streams that address specific questions: 1. AGENDA-SETTING is concerned with policy (re-)formulation. 2. PERIPHERAL URBANISM examines governance in border towns and port cities. 3. BORDER WORKERS addresses everyday governance emerging through the interaction of officials and others who make their livelihoods from the border. 4. CONNECTIVE INFRASTRUCTURE looks as the transformative effects of new technologies. 5. PEOPLE & GOODS IN MOTION traces the passage of people and goods and the regimes of regulation to which they are subjected. AFRIGOS contributes to interdisciplinary research on borderland studies, multi-level governance and the everyday state.
Max ERC Funding
2 491 364 €
Duration
Start date: 2016-01-01, End date: 2021-12-31
Project acronym ALKAGE
Project Algebraic and Kähler geometry
Researcher (PI) Jean-Pierre, Raymond, Philippe Demailly
Host Institution (HI) UNIVERSITE GRENOBLE ALPES
Country France
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: 2021-08-31
Project acronym ALLEGRO
Project unrAvelLing sLow modE travelinG and tRaffic: with innOvative data to a new transportation and traffic theory for pedestrians and bicycles
Researcher (PI) Serge Hoogendoorn
Host Institution (HI) TECHNISCHE UNIVERSITEIT DELFT
Country Netherlands
Call Details Advanced Grant (AdG), SH3, ERC-2014-ADG
Summary A major challenge in contemporary traffic and transportation theory is having a comprehensive understanding of pedestrians and cyclists behaviour. This is notoriously hard to observe, since sensors providing abundant and detailed information about key variables characterising this behaviour have not been available until very recently. The behaviour is also far more complex than that of the much better understood fast mode. This is due to the many degrees of freedom in decision-making, the interactions among slow traffic participants that are more involved and far less guided by traffic rules and regulations than those between car-drivers, and the many fascinating but complex phenomena in slow traffic flows (self-organised patterns, turbulence, spontaneous phase transitions, herding, etc.) that are very hard to predict accurately.
With slow traffic modes gaining ground in terms of mode share in many cities, lack of empirical insights, behavioural theories, predictively valid analytical and simulation models, and tools to support planning, design, management and control is posing a major societal problem as well: examples of major accidents due to bad planning, organisation and management of events are manifold, as are locations where safety of slow modes is a serious issue due to interactions with fast modes.
This programme is geared towards establishing a comprehensive theory of slow mode traffic behaviour, considering the different behavioural levels relevant for understanding, reproducing and predicting slow mode traffic flows in cities. The levels deal with walking and cycling operations, activity scheduling and travel behaviour, and knowledge representation and learning. Major scientific breakthroughs are expected at each of these levels, in terms of theory and modelling, by using innovative (big) data collection and experimentation, analysis and fusion techniques, including social media data analytics, using augmented reality, and remote and crowd sensing.
Summary
A major challenge in contemporary traffic and transportation theory is having a comprehensive understanding of pedestrians and cyclists behaviour. This is notoriously hard to observe, since sensors providing abundant and detailed information about key variables characterising this behaviour have not been available until very recently. The behaviour is also far more complex than that of the much better understood fast mode. This is due to the many degrees of freedom in decision-making, the interactions among slow traffic participants that are more involved and far less guided by traffic rules and regulations than those between car-drivers, and the many fascinating but complex phenomena in slow traffic flows (self-organised patterns, turbulence, spontaneous phase transitions, herding, etc.) that are very hard to predict accurately.
With slow traffic modes gaining ground in terms of mode share in many cities, lack of empirical insights, behavioural theories, predictively valid analytical and simulation models, and tools to support planning, design, management and control is posing a major societal problem as well: examples of major accidents due to bad planning, organisation and management of events are manifold, as are locations where safety of slow modes is a serious issue due to interactions with fast modes.
This programme is geared towards establishing a comprehensive theory of slow mode traffic behaviour, considering the different behavioural levels relevant for understanding, reproducing and predicting slow mode traffic flows in cities. The levels deal with walking and cycling operations, activity scheduling and travel behaviour, and knowledge representation and learning. Major scientific breakthroughs are expected at each of these levels, in terms of theory and modelling, by using innovative (big) data collection and experimentation, analysis and fusion techniques, including social media data analytics, using augmented reality, and remote and crowd sensing.
Max ERC Funding
2 458 700 €
Duration
Start date: 2015-11-01, End date: 2020-10-31
Project acronym analysisdirac
Project The analysis of the Dirac operator: the hypoelliptic Laplacian and its applications
Researcher (PI) Jean-Michel Philippe Marie-Jose Bismut
Host Institution (HI) UNIVERSITE PARIS-SUD
Country France
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 ANALYTICAL SOCIOLOGY
Project Analytical Sociology: Theoretical Developments and Empirical Research
Researcher (PI) Mats Peter Hedstroem
Host Institution (HI) LINKOPINGS UNIVERSITET
Country Sweden
Call Details Advanced Grant (AdG), SH2, ERC-2012-ADG_20120411
Summary This proposal outlines a highly ambitious and path-breaking research program. Through a tightly integrated package of basic theoretical work, strategic empirical research projects, international workshops, and a large number of publications in leading journals, the research program seeks to move sociology in a more analytical direction.
One part of the research program focuses on the epistemological and methodological foundations of analytical sociology, an approach to sociological theory and research that currently receives considerable attention in the international scholarly community. This work will be organized around two core themes: (1) the principles of mechanism-based explanations and (2) the micro-macro link.
The empirical research analyzes in great detail the ethnic, gender, and socio-economic segregation of key interaction domains in Sweden using the approach of analytical sociology. The interaction domains focused upon are schools, workplaces and neighborhoods; domains where people spend a considerable part of their time, where much of the social interaction between people takes place, where identities are formed, and where important resources are distributed.
Large-scale longitudinal micro data on the entire Swedish population, unique longitudinal data on social networks within school classes, and various agent-based simulation techniques, are used to better understand the processes through which schools, workplaces and neighborhoods become segregated along various dimensions, how the domains interact with one another, and how the structure and extent of segregation affects diverse social and economic outcomes.
Summary
This proposal outlines a highly ambitious and path-breaking research program. Through a tightly integrated package of basic theoretical work, strategic empirical research projects, international workshops, and a large number of publications in leading journals, the research program seeks to move sociology in a more analytical direction.
One part of the research program focuses on the epistemological and methodological foundations of analytical sociology, an approach to sociological theory and research that currently receives considerable attention in the international scholarly community. This work will be organized around two core themes: (1) the principles of mechanism-based explanations and (2) the micro-macro link.
The empirical research analyzes in great detail the ethnic, gender, and socio-economic segregation of key interaction domains in Sweden using the approach of analytical sociology. The interaction domains focused upon are schools, workplaces and neighborhoods; domains where people spend a considerable part of their time, where much of the social interaction between people takes place, where identities are formed, and where important resources are distributed.
Large-scale longitudinal micro data on the entire Swedish population, unique longitudinal data on social networks within school classes, and various agent-based simulation techniques, are used to better understand the processes through which schools, workplaces and neighborhoods become segregated along various dimensions, how the domains interact with one another, and how the structure and extent of segregation affects diverse social and economic outcomes.
Max ERC Funding
1 745 098 €
Duration
Start date: 2013-03-01, End date: 2018-02-28
Project acronym ANGEOM
Project Geometric analysis in the Euclidean space
Researcher (PI) Xavier Tolsa Domenech
Host Institution (HI) UNIVERSIDAD AUTONOMA DE BARCELONA
Country Spain
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 Angiolnc
Project Endothelial long non-coding RNAs
Researcher (PI) Stefanie Dimmeler
Host Institution (HI) JOHANN WOLFGANG GOETHE-UNIVERSITAET FRANKFURT AM MAIN
Country Germany
Call Details Advanced Grant (AdG), LS4, ERC-2014-ADG
Summary Endothelial cells comprise the inner cellular cover of the vasculature, which delivers metabolites and oxygen to the tissue. Dysfunction of endothelial cells as it occurs during aging or metabolic syndromes can result in atherosclerosis, which can lead to myocardial infarction or stroke, whereas pathological angiogenesis contributes to tumor growth and diabetic retinopathy. Thus, endothelial cells play central roles in pathophysiological processes of many diseases including cardiovascular diseases and cancer. Many studies explored the regulation of endothelial cell functions by growth factors, but the impact of epigenetic mechanisms and particularly the role of novel non-coding RNAs is largely unknown. More than 70 % of the human genome encodes for non-coding RNAs (ncRNAs) and increasing evidence suggests that a significant portion of these ncRNAs are functionally active as RNA molecules. Angiolnc aims to explore the function of long ncRNAs (lncRNAs) and particular circular RNAs (circRNAs) in the endothelium. LncRNAs comprise a heterogenic class of RNAs with a length of > 200 nucleotides and circRNAs are generated by back splicing.
Angiolnc is based on the discovery of novel endothelial hypoxia-regulated lncRNAs and circRNAs by next generation sequencing. To begin to understand the potential functions of lncRNAs in the endothelium, we will study two lncRNAs, named Angiolnc1 und Angiolnc2, as prototypical examples of endothelial cell-enriched lncRNAs that are regulated by oxygen levels. We will further dissect the epigenetic mechanisms, by which these lncRNAs regulate endothelial cell function. In the second part of the application, we will determine the regulation and function of circRNAs, which may act as molecular sponges in the cytoplasm. Finally, we will study the function of identified lncRNAs and circRNAs in mouse models and measure their expression in human specimens in order to determine their role as therapeutic targets or diagnostic tools.
Summary
Endothelial cells comprise the inner cellular cover of the vasculature, which delivers metabolites and oxygen to the tissue. Dysfunction of endothelial cells as it occurs during aging or metabolic syndromes can result in atherosclerosis, which can lead to myocardial infarction or stroke, whereas pathological angiogenesis contributes to tumor growth and diabetic retinopathy. Thus, endothelial cells play central roles in pathophysiological processes of many diseases including cardiovascular diseases and cancer. Many studies explored the regulation of endothelial cell functions by growth factors, but the impact of epigenetic mechanisms and particularly the role of novel non-coding RNAs is largely unknown. More than 70 % of the human genome encodes for non-coding RNAs (ncRNAs) and increasing evidence suggests that a significant portion of these ncRNAs are functionally active as RNA molecules. Angiolnc aims to explore the function of long ncRNAs (lncRNAs) and particular circular RNAs (circRNAs) in the endothelium. LncRNAs comprise a heterogenic class of RNAs with a length of > 200 nucleotides and circRNAs are generated by back splicing.
Angiolnc is based on the discovery of novel endothelial hypoxia-regulated lncRNAs and circRNAs by next generation sequencing. To begin to understand the potential functions of lncRNAs in the endothelium, we will study two lncRNAs, named Angiolnc1 und Angiolnc2, as prototypical examples of endothelial cell-enriched lncRNAs that are regulated by oxygen levels. We will further dissect the epigenetic mechanisms, by which these lncRNAs regulate endothelial cell function. In the second part of the application, we will determine the regulation and function of circRNAs, which may act as molecular sponges in the cytoplasm. Finally, we will study the function of identified lncRNAs and circRNAs in mouse models and measure their expression in human specimens in order to determine their role as therapeutic targets or diagnostic tools.
Max ERC Funding
2 497 398 €
Duration
Start date: 2016-01-01, End date: 2021-06-30
