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 GFTIPFD
Project Geometric function theory, inverse problems and fluid dinamics
Researcher (PI) Daniel Faraco Hurtado
Host Institution (HI) UNIVERSIDAD AUTONOMA DE MADRID
Call Details Starting Grant (StG), PE1, ERC-2012-StG_20111012
Summary The project will strike for conquering frontier results in three capital areas in partial differential equations and mathematical analysis: Elliptic equations and systems, fluid dynamics and inverse problems.
I propose to tackle the central problems in these areas with a new perspective based on the theory of differential inclusions. A thorough study of oscillating div-curl couples in this framework will lead us to the long expected higher dimensional version of the Tartar conjecture. The corresponding analysis of differential inclusions for gradient fields will lead to new results respect to the existence, uniqueness and regularity theory on the so far intractable theory of higher dimensional Beltrami systems. Next we will concentrate in weak solutions to the classical non linear equations governing fluid dynamics. A reformulation of these equations as differential inclusions enables a much more rich theory of weak solutions than the classical one. With this new tool at hand,we will close several long standing questions about existence, uniqueness and contour dynamics. The third part of the project is devoted to inverse problems in p.d.e. The most famous inverse problem is Calderón conductivity problem which asks whether the Dirichlet to Neumann map of an elliptic equation determines the coefficients. The problem is still open in three or more dimensions but a new formulation as a differential inclusion will allow us to close the 1980 Calderón conjecture by constructing new invisible materials. In dimension n=2 the recent approach based on quasiconformal theory will lead to the first regularization scheme valid for discontinuous conductivities and first results for non linear equations. For the stationary Schrödinger equation I propose to exploit a fascinating connection with the convergence to initial data of the non elliptic time dependent Schrödinger equation.
Summary
The project will strike for conquering frontier results in three capital areas in partial differential equations and mathematical analysis: Elliptic equations and systems, fluid dynamics and inverse problems.
I propose to tackle the central problems in these areas with a new perspective based on the theory of differential inclusions. A thorough study of oscillating div-curl couples in this framework will lead us to the long expected higher dimensional version of the Tartar conjecture. The corresponding analysis of differential inclusions for gradient fields will lead to new results respect to the existence, uniqueness and regularity theory on the so far intractable theory of higher dimensional Beltrami systems. Next we will concentrate in weak solutions to the classical non linear equations governing fluid dynamics. A reformulation of these equations as differential inclusions enables a much more rich theory of weak solutions than the classical one. With this new tool at hand,we will close several long standing questions about existence, uniqueness and contour dynamics. The third part of the project is devoted to inverse problems in p.d.e. The most famous inverse problem is Calderón conductivity problem which asks whether the Dirichlet to Neumann map of an elliptic equation determines the coefficients. The problem is still open in three or more dimensions but a new formulation as a differential inclusion will allow us to close the 1980 Calderón conjecture by constructing new invisible materials. In dimension n=2 the recent approach based on quasiconformal theory will lead to the first regularization scheme valid for discontinuous conductivities and first results for non linear equations. For the stationary Schrödinger equation I propose to exploit a fascinating connection with the convergence to initial data of the non elliptic time dependent Schrödinger equation.
Max ERC Funding
1 121 400 €
Duration
Start date: 2012-10-01, End date: 2018-09-30
Project acronym NONCODEVOL
Project Evolutionary genomics of long, non-coding RNAs
Researcher (PI) Juan Antonio Gabaldón Estevan
Host Institution (HI) FUNDACIO CENTRE DE REGULACIO GENOMICA
Call Details Starting Grant (StG), LS2, ERC-2012-StG_20111109
Summary Recent genomics analyses have facilitated the discovery of a novel major class of stable transcripts, now called long non-coding RNAs (lncRNAs). A growing number of analyses have implicated lncRNAs in the regulation of gene expression, dosage compensation and imprinting, and there is increasing evidence suggesting the involvement of lncRNAs in various diseases such as cancer. Despite recent advances, however, the role of the large majority of lncRNAs remains unknown and there is current debate on what fraction of lncRNAs may just represent transcriptional noise. Moreover, despite a growing number of lncRNAs catalogues for diverse model species, we lack a proper understanding of how these molecules evolve across genomes. Evolutionary analyses of protein-coding genes have proved tremendously useful in elucidating functional relationships and in understanding how the processes in which they are involved are shaped during evolution. Similar insights may be expected from a proper evolutionary characterization of lncRNAs, although the lack of proper tools and basic knowledge of underlying evolutionary mechanisms are a sizable challenge. Here, I propose to combine state-of-the-art computational and sequencing techniques in order to elucidate what evolutionary mechanisms are shaping this enigmatic component of eukaryotic genomes.The first goal is to enable large-scale phylogenomic analyses of lncRNAs by developing, for these molecules, methodologies that are now standard in the evolutionary analysis of protein-coding genes. The second goal is to explore, at high levels of resolution, the evolutionary dynamics of lncRNAs across selected eukaryotic groups for which novel genome-wide data will be produced experimentally using recently developed sequencing techniques that enable obtaining genome-wide footprints of RNA secondary structure. Finally, this dataset will be used to test the impact on lncRNAs evolution of processes known to be important in protein-coding genes.
Summary
Recent genomics analyses have facilitated the discovery of a novel major class of stable transcripts, now called long non-coding RNAs (lncRNAs). A growing number of analyses have implicated lncRNAs in the regulation of gene expression, dosage compensation and imprinting, and there is increasing evidence suggesting the involvement of lncRNAs in various diseases such as cancer. Despite recent advances, however, the role of the large majority of lncRNAs remains unknown and there is current debate on what fraction of lncRNAs may just represent transcriptional noise. Moreover, despite a growing number of lncRNAs catalogues for diverse model species, we lack a proper understanding of how these molecules evolve across genomes. Evolutionary analyses of protein-coding genes have proved tremendously useful in elucidating functional relationships and in understanding how the processes in which they are involved are shaped during evolution. Similar insights may be expected from a proper evolutionary characterization of lncRNAs, although the lack of proper tools and basic knowledge of underlying evolutionary mechanisms are a sizable challenge. Here, I propose to combine state-of-the-art computational and sequencing techniques in order to elucidate what evolutionary mechanisms are shaping this enigmatic component of eukaryotic genomes.The first goal is to enable large-scale phylogenomic analyses of lncRNAs by developing, for these molecules, methodologies that are now standard in the evolutionary analysis of protein-coding genes. The second goal is to explore, at high levels of resolution, the evolutionary dynamics of lncRNAs across selected eukaryotic groups for which novel genome-wide data will be produced experimentally using recently developed sequencing techniques that enable obtaining genome-wide footprints of RNA secondary structure. Finally, this dataset will be used to test the impact on lncRNAs evolution of processes known to be important in protein-coding genes.
Max ERC Funding
1 302 113 €
Duration
Start date: 2013-01-01, End date: 2017-12-31
Project acronym PRIMATESVS
Project Identification and characterization of primate structural variation and an assessment of intra-specific patterns of selection and copy-number variation
Researcher (PI) Tomas Marques Bonet
Host Institution (HI) UNIVERSIDAD POMPEU FABRA
Call Details Starting Grant (StG), LS2, ERC-2010-StG_20091118
Summary Structural variation and copy-number variant regions (CNVs) (including segmental duplications) are usually underrepresented in genome analyses but are becoming a prominent feature in understanding the organization of genomes as well as many diseases. Large-scale comparative sequencing projects promised a golden era in the study of human evolution, however, many genome regions, especially these complicated regions, are clearly not solved.
Despite international efforts to characterize thousand of human genomes to understand the extent of structural variants in the human species, primates (our closest relatives) have somehow been forgotten. Yet, they are the ideal set of species to study the evolution of these features from both mechanistic and adaptive points of view. Most genome projects include only one individual as a reference but in order to understand the impact of structural variants in the evolution of every species we need to re-sequence multiple individuals of each species. We can only understand the origins of genomic variants and phenotypical differences among species if we can model variation within species and compare it to a proper perspective with the differences among species.
The object of this proposal is to discover the extent of genome structural polymorphism within the great ape species by generating next-generation sequencing datasets at high coverage from multiple individuals of diverse species and subspecies, characterizing structural variants and validating them experimentally. The results of these analyses will assess the rate of genome variation in primate evolution, characterize regional deletions and copy-number expansions as well as determine the patterns of selection acting upon them and whether the diversity of these segments is consistent with other forms of genetic variation among humans and great apes. In so doing, a fundamental insight will be provided into evolutionary variation of these regions among primates and into the mechanisms of disease-causing rearrangements with multiple repercussions in the understanding of evolution and human disease.
Summary
Structural variation and copy-number variant regions (CNVs) (including segmental duplications) are usually underrepresented in genome analyses but are becoming a prominent feature in understanding the organization of genomes as well as many diseases. Large-scale comparative sequencing projects promised a golden era in the study of human evolution, however, many genome regions, especially these complicated regions, are clearly not solved.
Despite international efforts to characterize thousand of human genomes to understand the extent of structural variants in the human species, primates (our closest relatives) have somehow been forgotten. Yet, they are the ideal set of species to study the evolution of these features from both mechanistic and adaptive points of view. Most genome projects include only one individual as a reference but in order to understand the impact of structural variants in the evolution of every species we need to re-sequence multiple individuals of each species. We can only understand the origins of genomic variants and phenotypical differences among species if we can model variation within species and compare it to a proper perspective with the differences among species.
The object of this proposal is to discover the extent of genome structural polymorphism within the great ape species by generating next-generation sequencing datasets at high coverage from multiple individuals of diverse species and subspecies, characterizing structural variants and validating them experimentally. The results of these analyses will assess the rate of genome variation in primate evolution, characterize regional deletions and copy-number expansions as well as determine the patterns of selection acting upon them and whether the diversity of these segments is consistent with other forms of genetic variation among humans and great apes. In so doing, a fundamental insight will be provided into evolutionary variation of these regions among primates and into the mechanisms of disease-causing rearrangements with multiple repercussions in the understanding of evolution and human disease.
Max ERC Funding
1 599 999 €
Duration
Start date: 2010-12-01, End date: 2014-11-30
Project acronym RIBOMYLOME
Project The Role of Non-coding RNA in Protein Networks and Neurodegenerative Diseases
Researcher (PI) Gian Gaetano Tartaglia
Host Institution (HI) FUNDACIO CENTRE DE REGULACIO GENOMICA
Call Details Starting Grant (StG), LS2, ERC-2012-StG_20111109
Summary "A major portion of the eukaryotic genome is occupied by DNA sequences whose transcripts do not code for proteins. This part of the genome is transcribed in a developmentally regulated manner and in response to external stimuli to produce large numbers of long non-coding RNAs (lncRNAs). From the beginning of transcription through splicing and translation, RNA molecules are associated with numerous RNA binding proteins that regulate their processing, stability, transport and translation. Both coding and non-coding RNAs and their associated binding proteins are involved in numerous cellular pathways. These pathways, which include RNA processing and the regulation of transcription and translation, are critical determinants of neuronal differentiation and plasticity. Alterations in these pathways have been identified to contribute to a wide variety of neurodegenerative diseases. Mutations in two RNA binding proteins involved in RNA splicing, the Tar DNA binding protein of 43kd (TDP-43) and Fused in Sarcoma (FUS), cause amyloid aggregation and are associated with Amyotrophic Lateral Sclerosis (ALS). My main interest is to understand the role played by RNA molecules in protein networks. Characterizing protein-RNA associations is key to unravel the complexity and functionality of mammalian genomes. In this project, I propose to study associations of lncRNAs with proteins involved in i) transcriptional regulation and epigenetics (such as polymerases, transcription factors and chromatin-modifiers) and ii) neurodegenerative diseases (such as Parkinson’s -synuclein, Alzheimer’s disease amyloid protein APP, TDP-43 and FUS). In particular, I will investigate if RNA molecules are involved in regulatory mechanisms that control protein production and prevent formation of toxic aggregates. In a multidisciplinary effort, I aim to discover protein-RNA interactions using advanced computational methods developed in my group and state of the art experimental techniques."
Summary
"A major portion of the eukaryotic genome is occupied by DNA sequences whose transcripts do not code for proteins. This part of the genome is transcribed in a developmentally regulated manner and in response to external stimuli to produce large numbers of long non-coding RNAs (lncRNAs). From the beginning of transcription through splicing and translation, RNA molecules are associated with numerous RNA binding proteins that regulate their processing, stability, transport and translation. Both coding and non-coding RNAs and their associated binding proteins are involved in numerous cellular pathways. These pathways, which include RNA processing and the regulation of transcription and translation, are critical determinants of neuronal differentiation and plasticity. Alterations in these pathways have been identified to contribute to a wide variety of neurodegenerative diseases. Mutations in two RNA binding proteins involved in RNA splicing, the Tar DNA binding protein of 43kd (TDP-43) and Fused in Sarcoma (FUS), cause amyloid aggregation and are associated with Amyotrophic Lateral Sclerosis (ALS). My main interest is to understand the role played by RNA molecules in protein networks. Characterizing protein-RNA associations is key to unravel the complexity and functionality of mammalian genomes. In this project, I propose to study associations of lncRNAs with proteins involved in i) transcriptional regulation and epigenetics (such as polymerases, transcription factors and chromatin-modifiers) and ii) neurodegenerative diseases (such as Parkinson’s -synuclein, Alzheimer’s disease amyloid protein APP, TDP-43 and FUS). In particular, I will investigate if RNA molecules are involved in regulatory mechanisms that control protein production and prevent formation of toxic aggregates. In a multidisciplinary effort, I aim to discover protein-RNA interactions using advanced computational methods developed in my group and state of the art experimental techniques."
Max ERC Funding
1 465 351 €
Duration
Start date: 2013-01-01, End date: 2017-12-31
