Project acronym 2-3-AUT
Project Surfaces, 3-manifolds and automorphism groups
Researcher (PI) Nathalie Wahl
Host Institution (HI) KOBENHAVNS UNIVERSITET
Call Details Starting Grant (StG), PE1, ERC-2009-StG
Summary The scientific goal of the proposal is to answer central questions related to diffeomorphism groups of manifolds of dimension 2 and 3, and to their deformation invariant analogs, the mapping class groups. While the classification of surfaces has been known for more than a century, their automorphism groups have yet to be fully understood. Even less is known about diffeomorphisms of 3-manifolds despite much interest, and the objects here have only been classified recently, by the breakthrough work of Perelman on the Poincar\'e and geometrization conjectures. In dimension 2, I will focus on the relationship between mapping class groups and topological conformal field theories, with applications to Hochschild homology. In dimension 3, I propose to compute the stable homology of classifying spaces of diffeomorphism groups and mapping class groups, as well as study the homotopy type of the space of diffeomorphisms. I propose moreover to establish homological stability theorems in the wider context of automorphism groups and more general families of groups. The project combines breakthrough methods from homotopy theory with methods from differential and geometric topology. The research team will consist of 3 PhD students, and 4 postdocs, which I will lead.
Summary
The scientific goal of the proposal is to answer central questions related to diffeomorphism groups of manifolds of dimension 2 and 3, and to their deformation invariant analogs, the mapping class groups. While the classification of surfaces has been known for more than a century, their automorphism groups have yet to be fully understood. Even less is known about diffeomorphisms of 3-manifolds despite much interest, and the objects here have only been classified recently, by the breakthrough work of Perelman on the Poincar\'e and geometrization conjectures. In dimension 2, I will focus on the relationship between mapping class groups and topological conformal field theories, with applications to Hochschild homology. In dimension 3, I propose to compute the stable homology of classifying spaces of diffeomorphism groups and mapping class groups, as well as study the homotopy type of the space of diffeomorphisms. I propose moreover to establish homological stability theorems in the wider context of automorphism groups and more general families of groups. The project combines breakthrough methods from homotopy theory with methods from differential and geometric topology. The research team will consist of 3 PhD students, and 4 postdocs, which I will lead.
Max ERC Funding
724 992 €
Duration
Start date: 2009-11-01, End date: 2014-10-31
Project acronym ADAPTIVES
Project Algorithmic Development and Analysis of Pioneer Techniques for Imaging with waVES
Researcher (PI) Chrysoula Tsogka
Host Institution (HI) IDRYMA TECHNOLOGIAS KAI EREVNAS
Call Details Starting Grant (StG), PE1, ERC-2009-StG
Summary The proposed work concerns the theoretical and numerical development of robust and adaptive methodologies for broadband imaging in clutter. The word clutter expresses our uncertainty on the wave speed of the propagation medium. Our results are expected to have a strong impact in a wide range of applications, including underwater acoustics, exploration geophysics and ultrasound non-destructive testing. Our machinery is coherent interferometry (CINT), a state-of-the-art statistically stable imaging methodology, highly suitable for the development of imaging methods in clutter. We aim to extend CINT along two complementary directions: novel types of applications, and further mathematical and numerical development so as to assess and extend its range of applicability. CINT is designed for imaging with partially coherent array data recorded in richly scattering media. It uses statistical smoothing techniques to obtain results that are independent of the clutter realization. Quantifying the amount of smoothing needed is difficult, especially when there is no a priori knowledge about the propagation medium. We intend to address this question by coupling the imaging process with the estimation of the medium's large scale features. Our algorithms rely on the residual coherence in the data. When the coherent signal is too weak, the CINT results are unsatisfactory. We propose two ways for enhancing the resolution of CINT: filter the data prior to imaging (noise reduction) and waveform design (optimize the source distribution). Finally, we propose to extend the applicability of our imaging-in-clutter methodologies by investigating the possibility of utilizing ambient noise sources to perform passive sensor imaging, as well as by studying the imaging problem in random waveguides.
Summary
The proposed work concerns the theoretical and numerical development of robust and adaptive methodologies for broadband imaging in clutter. The word clutter expresses our uncertainty on the wave speed of the propagation medium. Our results are expected to have a strong impact in a wide range of applications, including underwater acoustics, exploration geophysics and ultrasound non-destructive testing. Our machinery is coherent interferometry (CINT), a state-of-the-art statistically stable imaging methodology, highly suitable for the development of imaging methods in clutter. We aim to extend CINT along two complementary directions: novel types of applications, and further mathematical and numerical development so as to assess and extend its range of applicability. CINT is designed for imaging with partially coherent array data recorded in richly scattering media. It uses statistical smoothing techniques to obtain results that are independent of the clutter realization. Quantifying the amount of smoothing needed is difficult, especially when there is no a priori knowledge about the propagation medium. We intend to address this question by coupling the imaging process with the estimation of the medium's large scale features. Our algorithms rely on the residual coherence in the data. When the coherent signal is too weak, the CINT results are unsatisfactory. We propose two ways for enhancing the resolution of CINT: filter the data prior to imaging (noise reduction) and waveform design (optimize the source distribution). Finally, we propose to extend the applicability of our imaging-in-clutter methodologies by investigating the possibility of utilizing ambient noise sources to perform passive sensor imaging, as well as by studying the imaging problem in random waveguides.
Max ERC Funding
690 000 €
Duration
Start date: 2010-06-01, End date: 2015-11-30
Project acronym AMAREC
Project Amenability, Approximation and Reconstruction
Researcher (PI) Wilhelm WINTER
Host Institution (HI) WESTFAELISCHE WILHELMS-UNIVERSITAET MUENSTER
Call Details Advanced Grant (AdG), PE1, ERC-2018-ADG
Summary Algebras of operators on Hilbert spaces were originally introduced as the right framework for the mathematical description of quantum mechanics. In modern mathematics the scope has much broadened due to the highly versatile nature of operator algebras. They are particularly useful in the analysis of groups and their actions. Amenability is a finiteness property which occurs in many different contexts and which can be characterised in many different ways. We will analyse amenability in terms of approximation properties, in the frameworks of abstract C*-algebras, of topological dynamical systems, and of discrete groups. Such approximation properties will serve as bridging devices between these setups, and they will be used to systematically recover geometric information about the underlying structures. When passing from groups, and more generally from dynamical systems, to operator algebras, one loses information, but one gains new tools to isolate and analyse pertinent properties of the underlying structure. We will mostly be interested in the topological setting, and in the associated C*-algebras. Amenability of groups or of dynamical systems then translates into the completely positive approximation property. Systems of completely positive approximations store all the essential data about a C*-algebra, and sometimes one can arrange the systems so that one can directly read of such information. For transformation group C*-algebras, one can achieve this by using approximation properties of the underlying dynamics. To some extent one can even go back, and extract dynamical approximation properties from completely positive approximations of the C*-algebra. This interplay between approximation properties in topological dynamics and in noncommutative topology carries a surprisingly rich structure. It connects directly to the heart of the classification problem for nuclear C*-algebras on the one hand, and to central open questions on amenable dynamics on the other.
Summary
Algebras of operators on Hilbert spaces were originally introduced as the right framework for the mathematical description of quantum mechanics. In modern mathematics the scope has much broadened due to the highly versatile nature of operator algebras. They are particularly useful in the analysis of groups and their actions. Amenability is a finiteness property which occurs in many different contexts and which can be characterised in many different ways. We will analyse amenability in terms of approximation properties, in the frameworks of abstract C*-algebras, of topological dynamical systems, and of discrete groups. Such approximation properties will serve as bridging devices between these setups, and they will be used to systematically recover geometric information about the underlying structures. When passing from groups, and more generally from dynamical systems, to operator algebras, one loses information, but one gains new tools to isolate and analyse pertinent properties of the underlying structure. We will mostly be interested in the topological setting, and in the associated C*-algebras. Amenability of groups or of dynamical systems then translates into the completely positive approximation property. Systems of completely positive approximations store all the essential data about a C*-algebra, and sometimes one can arrange the systems so that one can directly read of such information. For transformation group C*-algebras, one can achieve this by using approximation properties of the underlying dynamics. To some extent one can even go back, and extract dynamical approximation properties from completely positive approximations of the C*-algebra. This interplay between approximation properties in topological dynamics and in noncommutative topology carries a surprisingly rich structure. It connects directly to the heart of the classification problem for nuclear C*-algebras on the one hand, and to central open questions on amenable dynamics on the other.
Max ERC Funding
1 596 017 €
Duration
Start date: 2019-10-01, End date: 2024-09-30
Project acronym ARGO
Project The Quest of the Argonautes - from Myth to Reality
Researcher (PI) JOHN VAN DER OOST
Host Institution (HI) WAGENINGEN UNIVERSITY
Call Details Advanced Grant (AdG), LS1, ERC-2018-ADG
Summary Argonaute nucleases are key players of the eukaryotic RNA interference (RNAi) system. Using small RNA guides, these Argonaute (Ago) proteins specifically target complementary RNA molecules, resulting in regulation of a wide range of crucial processes, including chromosome organization, gene expression and anti-virus defence. Since 2010, my research team has studied closely-related prokaryotic Argonaute (pAgo) variants. This has revealed spectacular mechanistic variations: several thermophilic pAgos catalyse DNA-guided cleavage of double stranded DNA, but only at elevated temperatures. Interestingly, a recently discovered mesophilic Argonaute (CbAgo) can generate double strand DNA breaks at moderate temperatures, providing an excellent basis for this ARGO project. In addition, genome analysis has revealed many distantly-related Argonaute variants, often with unique domain architectures. Hence, the currently known Argonaute homologs are just the tip of the iceberg, and the stage is set for making a big leap in the exploration of the Argonaute family. Initially we will dissect the molecular basis of functional and mechanistic features of uncharacterized natural Argonaute variants, both in eukaryotes (the presence of an Ago-like subunit in the Mediator complex, strongly suggests a regulatory role of an elusive non-coding RNA ligand) and in prokaryotes (selected Ago variants possess distinct domains indicating novel functionalities). After their thorough biochemical characterization, I aim at engineering the functionality of the aforementioned CbAgo through an integrated rational & random approach, i.e. by tinkering of domains, and by an unprecedented in vitro laboratory evolution approach. Eventually, natural & synthetic Argonautes will be selected for their exploitation, and used for developing original genome editing applications (from silencing to base editing). Embarking on this ambitious ARGO expedition will lead us to many exciting discoveries.
Summary
Argonaute nucleases are key players of the eukaryotic RNA interference (RNAi) system. Using small RNA guides, these Argonaute (Ago) proteins specifically target complementary RNA molecules, resulting in regulation of a wide range of crucial processes, including chromosome organization, gene expression and anti-virus defence. Since 2010, my research team has studied closely-related prokaryotic Argonaute (pAgo) variants. This has revealed spectacular mechanistic variations: several thermophilic pAgos catalyse DNA-guided cleavage of double stranded DNA, but only at elevated temperatures. Interestingly, a recently discovered mesophilic Argonaute (CbAgo) can generate double strand DNA breaks at moderate temperatures, providing an excellent basis for this ARGO project. In addition, genome analysis has revealed many distantly-related Argonaute variants, often with unique domain architectures. Hence, the currently known Argonaute homologs are just the tip of the iceberg, and the stage is set for making a big leap in the exploration of the Argonaute family. Initially we will dissect the molecular basis of functional and mechanistic features of uncharacterized natural Argonaute variants, both in eukaryotes (the presence of an Ago-like subunit in the Mediator complex, strongly suggests a regulatory role of an elusive non-coding RNA ligand) and in prokaryotes (selected Ago variants possess distinct domains indicating novel functionalities). After their thorough biochemical characterization, I aim at engineering the functionality of the aforementioned CbAgo through an integrated rational & random approach, i.e. by tinkering of domains, and by an unprecedented in vitro laboratory evolution approach. Eventually, natural & synthetic Argonautes will be selected for their exploitation, and used for developing original genome editing applications (from silencing to base editing). Embarking on this ambitious ARGO expedition will lead us to many exciting discoveries.
Max ERC Funding
2 177 158 €
Duration
Start date: 2019-07-01, End date: 2024-06-30
Project acronym BeyondA1
Project Set theory beyond the first uncountable cardinal
Researcher (PI) Assaf Shmuel Rinot
Host Institution (HI) BAR ILAN UNIVERSITY
Call Details Starting Grant (StG), PE1, ERC-2018-STG
Summary We propose to establish a research group that will unveil the combinatorial nature of the second uncountable cardinal. This includes its Ramsey-theoretic, order-theoretic, graph-theoretic and topological features. Among others, we will be directly addressing fundamental problems due to Erdos, Rado, Galvin, and Shelah.
While some of these problems are old and well-known, an unexpected series of breakthroughs from the last three years suggest that now is a promising point in time to carry out such a project. Indeed, through a short period, four previously unattainable problems concerning the second uncountable cardinal were successfully tackled: Aspero on a club-guessing problem of Shelah, Krueger on the club-isomorphism problem for Aronszajn trees, Neeman on the isomorphism problem for dense sets of reals, and the PI on the Souslin problem. Each of these results was obtained through the development of a completely new technical framework, and these frameworks could now pave the way for the solution of some major open questions.
A goal of the highest risk in this project is the discovery of a consistent (possibly, parameterized) forcing axiom that will (preferably, simultaneously) provide structure theorems for stationary sets, linearly ordered sets, trees, graphs, and partition relations, as well as the refutation of various forms of club-guessing principles, all at the level of the second uncountable cardinal. In comparison, at the level of the first uncountable cardinal, a forcing axiom due to Foreman, Magidor and Shelah achieves exactly that.
To approach our goals, the proposed project is divided into four core areas: Uncountable trees, Ramsey theory on ordinals, Club-guessing principles, and Forcing Axioms. There is a rich bilateral interaction between any pair of the four different cores, but the proposed division will allow an efficient allocation of manpower, and will increase the chances of parallel success.
Summary
We propose to establish a research group that will unveil the combinatorial nature of the second uncountable cardinal. This includes its Ramsey-theoretic, order-theoretic, graph-theoretic and topological features. Among others, we will be directly addressing fundamental problems due to Erdos, Rado, Galvin, and Shelah.
While some of these problems are old and well-known, an unexpected series of breakthroughs from the last three years suggest that now is a promising point in time to carry out such a project. Indeed, through a short period, four previously unattainable problems concerning the second uncountable cardinal were successfully tackled: Aspero on a club-guessing problem of Shelah, Krueger on the club-isomorphism problem for Aronszajn trees, Neeman on the isomorphism problem for dense sets of reals, and the PI on the Souslin problem. Each of these results was obtained through the development of a completely new technical framework, and these frameworks could now pave the way for the solution of some major open questions.
A goal of the highest risk in this project is the discovery of a consistent (possibly, parameterized) forcing axiom that will (preferably, simultaneously) provide structure theorems for stationary sets, linearly ordered sets, trees, graphs, and partition relations, as well as the refutation of various forms of club-guessing principles, all at the level of the second uncountable cardinal. In comparison, at the level of the first uncountable cardinal, a forcing axiom due to Foreman, Magidor and Shelah achieves exactly that.
To approach our goals, the proposed project is divided into four core areas: Uncountable trees, Ramsey theory on ordinals, Club-guessing principles, and Forcing Axioms. There is a rich bilateral interaction between any pair of the four different cores, but the proposed division will allow an efficient allocation of manpower, and will increase the chances of parallel success.
Max ERC Funding
1 362 500 €
Duration
Start date: 2018-10-01, End date: 2023-09-30
Project acronym BIOMEMOS
Project Higher order structure and function of biomembranes
Researcher (PI) Poul Nissen
Host Institution (HI) AARHUS UNIVERSITET
Call Details Advanced Grant (AdG), LS1, ERC-2009-AdG
Summary The biomembrane is a prerequisite of life. It enables the cell to maintain a controlled environment and to establish electrochemical gradients as rapidly accessible energy stores. Biomembranes also provide scaffold for organisation and spatial definition of signal transmission in the cell. Crystal structures of membrane proteins are determined with an increasing pace. Along with functional studies integral studies of individual membrane proteins are now widely implemented. The BIOMEMOS proposal goes a step further and approaches the function of the biomembrane at the higher level of membrane protein complexes. Through a combination of X-ray crystallography, electrophysiology, general biochemistry, biophysics and bioinformatics and including also the application of single-particle cryo-EM and small-angle X-ray scattering, the structure and function of membrane protein complexes of key importance in life will be investigated. The specific targets for investigation in this proposal include: 1) higher-order complexes of P-type ATPase pumps such as signalling complexes of Na+,K+-ATPase, and 2) development of methods for structural studies of membrane protein complexes Based on my unique track record in structural studies of large, difficult structures (ribosomes and membrane proteins) in the setting of a thriving research community in structural biology and biomembrane research in Aarhus provides a critical momentum for a long-term activity. The activity will take advantage of the new possibilities offered by synchrotron sources in Europe. Furthermore, a single-particle cryo-EM research group formed on my initiative in Aarhus, and a well-established small-angle X-ray scattering community provides for an optimal setting through multiple cues in structural biology and functional studies
Summary
The biomembrane is a prerequisite of life. It enables the cell to maintain a controlled environment and to establish electrochemical gradients as rapidly accessible energy stores. Biomembranes also provide scaffold for organisation and spatial definition of signal transmission in the cell. Crystal structures of membrane proteins are determined with an increasing pace. Along with functional studies integral studies of individual membrane proteins are now widely implemented. The BIOMEMOS proposal goes a step further and approaches the function of the biomembrane at the higher level of membrane protein complexes. Through a combination of X-ray crystallography, electrophysiology, general biochemistry, biophysics and bioinformatics and including also the application of single-particle cryo-EM and small-angle X-ray scattering, the structure and function of membrane protein complexes of key importance in life will be investigated. The specific targets for investigation in this proposal include: 1) higher-order complexes of P-type ATPase pumps such as signalling complexes of Na+,K+-ATPase, and 2) development of methods for structural studies of membrane protein complexes Based on my unique track record in structural studies of large, difficult structures (ribosomes and membrane proteins) in the setting of a thriving research community in structural biology and biomembrane research in Aarhus provides a critical momentum for a long-term activity. The activity will take advantage of the new possibilities offered by synchrotron sources in Europe. Furthermore, a single-particle cryo-EM research group formed on my initiative in Aarhus, and a well-established small-angle X-ray scattering community provides for an optimal setting through multiple cues in structural biology and functional studies
Max ERC Funding
2 444 180 €
Duration
Start date: 2010-04-01, End date: 2015-03-31
Project acronym BrokenGenome
Project Breaking and rebuilding the genome: mechanistic rules for the dangerous game of sex.
Researcher (PI) Corentin CLAEYS BOUUAERT
Host Institution (HI) UNIVERSITE CATHOLIQUE DE LOUVAIN
Call Details Starting Grant (StG), LS1, ERC-2018-STG
Summary Sexual reproduction depends on the programmed induction of DNA double-strand breaks (DSBs) and their ensuing repair by homologous recombination. This complex process is essential for sexual reproduction because it ultimately allows the pairing and separation of homologous chromosomes during formation of haploid gametes. Although meiotic recombination has been investigated for decades, many of the underlying molecular processes remain unclear, largely due to the lack of biochemical studies. I have recently made important progress by, for the first time, successfully purifying proteins involved in two aspects of meiotic recombination: DSB formation and the final stage of formation of the crossovers that are a central raison-d’être of meiotic recombination. This has opened new avenues for future research that I intend to pursue in my own laboratory. Here, I propose a set of biochemical approaches, complemented by molecular genetics methods, to gain insights into four central problems: (i) How meiotic proteins collaborate to induce DSBs; (ii) How DSB proteins interact with components that form the axes of meiotic chromosomes; (iii) How proteins involved at later stages of recombination form crossovers; and (iv) How crossover proteins interact with components of synapsed chromosomes. For each problem, I will set up in vitro systems to probe the activities of the players involved, their interactions with DNA, and their assembly into macromolecular complexes. In addition, I propose to develop new methodology for identifying proteins that are associated with DNA that has undergone recombination-related DNA synthesis. My goal is to gain insights into the mechanisms that govern meiotic recombination. Importantly, these mechanisms are intimately linked not only to gamete formation, but also to the general recombination pathways that all cells use to maintain genome stability. In both contexts, our findings will be relevant to the development and avoidance of disease states.
Summary
Sexual reproduction depends on the programmed induction of DNA double-strand breaks (DSBs) and their ensuing repair by homologous recombination. This complex process is essential for sexual reproduction because it ultimately allows the pairing and separation of homologous chromosomes during formation of haploid gametes. Although meiotic recombination has been investigated for decades, many of the underlying molecular processes remain unclear, largely due to the lack of biochemical studies. I have recently made important progress by, for the first time, successfully purifying proteins involved in two aspects of meiotic recombination: DSB formation and the final stage of formation of the crossovers that are a central raison-d’être of meiotic recombination. This has opened new avenues for future research that I intend to pursue in my own laboratory. Here, I propose a set of biochemical approaches, complemented by molecular genetics methods, to gain insights into four central problems: (i) How meiotic proteins collaborate to induce DSBs; (ii) How DSB proteins interact with components that form the axes of meiotic chromosomes; (iii) How proteins involved at later stages of recombination form crossovers; and (iv) How crossover proteins interact with components of synapsed chromosomes. For each problem, I will set up in vitro systems to probe the activities of the players involved, their interactions with DNA, and their assembly into macromolecular complexes. In addition, I propose to develop new methodology for identifying proteins that are associated with DNA that has undergone recombination-related DNA synthesis. My goal is to gain insights into the mechanisms that govern meiotic recombination. Importantly, these mechanisms are intimately linked not only to gamete formation, but also to the general recombination pathways that all cells use to maintain genome stability. In both contexts, our findings will be relevant to the development and avoidance of disease states.
Max ERC Funding
1 499 075 €
Duration
Start date: 2019-07-01, End date: 2024-06-30
Project acronym CiliaTubulinCode
Project Self-organization of the cilium: the role of the tubulin code
Researcher (PI) Gaia PIGINO
Host Institution (HI) MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Call Details Consolidator Grant (CoG), LS1, ERC-2018-COG
Summary This project aims at understanding of the role of the tubulin code for self-organization of complex microtubule based structures. Cilia turn out to be the ideal structures for the proposed research.
A cilium is a sophisticated cellular machine that self-organizes from many protein complexes. It plays motility, sensory, and signaling roles in most eukaryotic cells, and its malfunction causes pathologies. The assembly of the cilium requires intraflagellar transport (IFT), a specialized bidirectional motility process that is mediated by adaptor proteins and direction specific molecular motors. Work from my lab shows that anterograde and retrograde IFT make exclusive use of the B-tubules and A-tubules, respectively. This insight answered a long standing question and shows that functional differentiation of tubules exists and is important for IFT.
Tubulin post-translational modifications (PTMs) contribute to a tubulin code, making microtubules suitable for specific functions. Mutation of tubulin-PTM enzymes can have dramatic effects on cilia function and assembly. However, we do not understand of the role of tubulin-PTMs in cilia. Therefore, I propose to address the hypotheses that the tubulin code contributes to regulating bidirectional IFT motility, and more generally, that the tubulin code is a key player in structuring complex cellular assembly processes in space and time.
This proposal aims at (i) understanding if tubulin-PTMs are necessary and/or sufficient to regulate the bidirectionality of IFT (ii) examining how the tubulin code regulates the assembly of cilia and (iii) generating a high-resolution atlas of tubulin-PTMs and their respective enzymes.
We will combine advanced techniques encompassing state-of-the-art cryo-electron tomography, biochemical imaging, fluorescent microscopy, and in vitro assays to achieve molecular and structural understanding of the role of the tubulin code in the self-organization of cilia and of microtubule based cellular structures.
Summary
This project aims at understanding of the role of the tubulin code for self-organization of complex microtubule based structures. Cilia turn out to be the ideal structures for the proposed research.
A cilium is a sophisticated cellular machine that self-organizes from many protein complexes. It plays motility, sensory, and signaling roles in most eukaryotic cells, and its malfunction causes pathologies. The assembly of the cilium requires intraflagellar transport (IFT), a specialized bidirectional motility process that is mediated by adaptor proteins and direction specific molecular motors. Work from my lab shows that anterograde and retrograde IFT make exclusive use of the B-tubules and A-tubules, respectively. This insight answered a long standing question and shows that functional differentiation of tubules exists and is important for IFT.
Tubulin post-translational modifications (PTMs) contribute to a tubulin code, making microtubules suitable for specific functions. Mutation of tubulin-PTM enzymes can have dramatic effects on cilia function and assembly. However, we do not understand of the role of tubulin-PTMs in cilia. Therefore, I propose to address the hypotheses that the tubulin code contributes to regulating bidirectional IFT motility, and more generally, that the tubulin code is a key player in structuring complex cellular assembly processes in space and time.
This proposal aims at (i) understanding if tubulin-PTMs are necessary and/or sufficient to regulate the bidirectionality of IFT (ii) examining how the tubulin code regulates the assembly of cilia and (iii) generating a high-resolution atlas of tubulin-PTMs and their respective enzymes.
We will combine advanced techniques encompassing state-of-the-art cryo-electron tomography, biochemical imaging, fluorescent microscopy, and in vitro assays to achieve molecular and structural understanding of the role of the tubulin code in the self-organization of cilia and of microtubule based cellular structures.
Max ERC Funding
1 986 406 €
Duration
Start date: 2019-03-01, End date: 2024-02-29
Project acronym COMBOS
Project Collective phenomena in quantum and classical many body systems
Researcher (PI) Alessandro Giuliani
Host Institution (HI) UNIVERSITA DEGLI STUDI ROMA TRE
Call Details Starting Grant (StG), PE1, ERC-2009-StG
Summary The collective behavior of quantum and classical many body systems such as ultracold atomic gases, nanowires, cuprates and micromagnets are currently subject of an intense experimental and theoretical research worldwide. Understanding the fascinating phenomena of Bose-Einstein condensation, Luttinger liquid vs non-Luttinger liquid behavior, high temperature superconductivity, and spontaneous formation of periodic patterns in magnetic systems, is an exciting challenge for theoreticians. Most of these phenomena are still far from being fully understood, even from a heuristic point of view. Unveiling the exotic properties of such systems by rigorous mathematical analysis is an important and difficult challenge for mathematical physics. In the last two decades, substantial progress has been made on various aspects of many-body theory, including Fermi liquids, Luttinger liquids, perturbed Ising models at criticality, bosonization, trapped Bose gases and spontaneous formation of periodic patterns. The techniques successfully employed in this field are diverse, and range from constructive renormalization group to functional variational estimates. In this research project we propose to investigate a number of statistical mechanics models by a combination of different mathematical methods. The objective is, on the one hand, to understand crossover phenomena, phase transitions and low-temperature states with broken symmetry, which are of interest in the theory of condensed matter and that we believe to be accessible to the currently available methods; on the other, to develop new techiques combining different and complementary methods, such as multiscale analysis and localization bounds, or reflection positivity and cluster expansion, which may be useful to further progress on important open problems, such as Bose-Einstein condensation, conformal invariance in non-integrable models, existence of magnetic or superconducting long range order.
Summary
The collective behavior of quantum and classical many body systems such as ultracold atomic gases, nanowires, cuprates and micromagnets are currently subject of an intense experimental and theoretical research worldwide. Understanding the fascinating phenomena of Bose-Einstein condensation, Luttinger liquid vs non-Luttinger liquid behavior, high temperature superconductivity, and spontaneous formation of periodic patterns in magnetic systems, is an exciting challenge for theoreticians. Most of these phenomena are still far from being fully understood, even from a heuristic point of view. Unveiling the exotic properties of such systems by rigorous mathematical analysis is an important and difficult challenge for mathematical physics. In the last two decades, substantial progress has been made on various aspects of many-body theory, including Fermi liquids, Luttinger liquids, perturbed Ising models at criticality, bosonization, trapped Bose gases and spontaneous formation of periodic patterns. The techniques successfully employed in this field are diverse, and range from constructive renormalization group to functional variational estimates. In this research project we propose to investigate a number of statistical mechanics models by a combination of different mathematical methods. The objective is, on the one hand, to understand crossover phenomena, phase transitions and low-temperature states with broken symmetry, which are of interest in the theory of condensed matter and that we believe to be accessible to the currently available methods; on the other, to develop new techiques combining different and complementary methods, such as multiscale analysis and localization bounds, or reflection positivity and cluster expansion, which may be useful to further progress on important open problems, such as Bose-Einstein condensation, conformal invariance in non-integrable models, existence of magnetic or superconducting long range order.
Max ERC Funding
650 000 €
Duration
Start date: 2010-01-01, End date: 2014-12-31
Project acronym CONLAWS
Project Hyperbolic Systems of Conservation Laws: singular limits, properties of solutions and control problems
Researcher (PI) Stefano Bianchini
Host Institution (HI) SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE
Call Details Starting Grant (StG), PE1, ERC-2009-StG
Summary The research program concerns various theoretic aspects of hyperbolic conservation laws. In first place we plan to study the existence and uniqueness of solutions to systems of equations of mathematical physics with physic viscosity. This is one of the main open problems within the theory of conservation laws in one space dimension, which cannot be tackled relying on the techniques developed in the case where the viscosity matrix is the identity. Furthermore, this represents a first step toward the analysis of more complex relaxation and kinetic models with a finite number of velocities as for Broadwell equation, or with a continuous distribution of velocities as for Boltzmann equation. A second research topic concerns the study of conservation laws with large data. Even in this case the basic model is provided by fluidodynamic equations. We wish to extend the results of existence, uniqueness and continuous dependence of solutions to the case of large (in BV or in L^infty) data, at least for the simplest systems of mathematical physics such as the isentropic gas dynamics. A third research topic that we wish to pursue concerns the analysis of fine properties of solutions to conservation laws. Many of such properties depend on the existence of one or more entropies of the system. In particular, we have in mind to study the regularity and the concentration of the dissipativity measure for an entropic solution of a system of conservation laws. Finally, we wish to continue the study of hyperbolic equations from the control theory point of view along two directions: (i) the analysis of controllability and asymptotic stabilizability properties; (ii) the study of optimal control problems related to hyperbolic systems.
Summary
The research program concerns various theoretic aspects of hyperbolic conservation laws. In first place we plan to study the existence and uniqueness of solutions to systems of equations of mathematical physics with physic viscosity. This is one of the main open problems within the theory of conservation laws in one space dimension, which cannot be tackled relying on the techniques developed in the case where the viscosity matrix is the identity. Furthermore, this represents a first step toward the analysis of more complex relaxation and kinetic models with a finite number of velocities as for Broadwell equation, or with a continuous distribution of velocities as for Boltzmann equation. A second research topic concerns the study of conservation laws with large data. Even in this case the basic model is provided by fluidodynamic equations. We wish to extend the results of existence, uniqueness and continuous dependence of solutions to the case of large (in BV or in L^infty) data, at least for the simplest systems of mathematical physics such as the isentropic gas dynamics. A third research topic that we wish to pursue concerns the analysis of fine properties of solutions to conservation laws. Many of such properties depend on the existence of one or more entropies of the system. In particular, we have in mind to study the regularity and the concentration of the dissipativity measure for an entropic solution of a system of conservation laws. Finally, we wish to continue the study of hyperbolic equations from the control theory point of view along two directions: (i) the analysis of controllability and asymptotic stabilizability properties; (ii) the study of optimal control problems related to hyperbolic systems.
Max ERC Funding
422 000 €
Duration
Start date: 2009-11-01, End date: 2013-10-31
