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 2D-4-CO2
Project DESIGNING 2D NANOSHEETS FOR CO2 REDUCTION AND INTEGRATION INTO vdW HETEROSTRUCTURES FOR ARTIFICIAL PHOTOSYNTHESIS
Researcher (PI) Damien VOIRY
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), PE8, ERC-2018-STG
Summary CO2 reduction reaction (CO2RR) holds great promise for conversion of the green-house gas carbon dioxide into chemical fuels. The absence of catalytic materials demonstrating high performance and high selectivity currently hampers practical demonstration. CO2RR is also limited by the low solubility of CO2 in the electrolyte solution and therefore electrocatalytic reactions in gas phase using gas diffusion electrodes would be preferred. 2D materials have recently emerged as a novel class of electrocatalytic materials thanks to their rich structures and electronic properties. The synthesis of novel 2D catalysts and their implementation into photocatalytic systems would be a major step towards the development of devices for storing solar energy in the form of chemical fuels. With 2D-4-CO2, I propose to: 1) develop novel class of CO2RR catalysts based on conducting 2D nanosheets and 2) demonstrate photocatalytic conversion of CO2 into chemical fuels using structure engineered gas diffusion electrodes made of 2D conducting catalysts. To reach this goal, the first objective of 2D-4-CO2 is to provide guidelines for the development of novel cutting-edge 2D catalysts towards CO2 conversion into chemical fuel. This will be possible by using a multidisciplinary approach based on 2D materials engineering, advanced methods of characterization and novel designs of gas diffusion electrodes for the reduction of CO2 in gas phase. The second objective is to develop practical photocatalytic systems using van der Waals (vdW) heterostructures for the efficient conversion of CO2 into chemical fuels. vdW heterostructures will consist in rational designs of 2D materials and 2D-like materials deposited by atomic layer deposition in order to achieve highly efficient light conversion and prolonged stability. This project will not only enable a deeper understanding of the CO2RR but it will also provide practical strategies for large-scale application of CO2RR for solar fuel production.
Summary
CO2 reduction reaction (CO2RR) holds great promise for conversion of the green-house gas carbon dioxide into chemical fuels. The absence of catalytic materials demonstrating high performance and high selectivity currently hampers practical demonstration. CO2RR is also limited by the low solubility of CO2 in the electrolyte solution and therefore electrocatalytic reactions in gas phase using gas diffusion electrodes would be preferred. 2D materials have recently emerged as a novel class of electrocatalytic materials thanks to their rich structures and electronic properties. The synthesis of novel 2D catalysts and their implementation into photocatalytic systems would be a major step towards the development of devices for storing solar energy in the form of chemical fuels. With 2D-4-CO2, I propose to: 1) develop novel class of CO2RR catalysts based on conducting 2D nanosheets and 2) demonstrate photocatalytic conversion of CO2 into chemical fuels using structure engineered gas diffusion electrodes made of 2D conducting catalysts. To reach this goal, the first objective of 2D-4-CO2 is to provide guidelines for the development of novel cutting-edge 2D catalysts towards CO2 conversion into chemical fuel. This will be possible by using a multidisciplinary approach based on 2D materials engineering, advanced methods of characterization and novel designs of gas diffusion electrodes for the reduction of CO2 in gas phase. The second objective is to develop practical photocatalytic systems using van der Waals (vdW) heterostructures for the efficient conversion of CO2 into chemical fuels. vdW heterostructures will consist in rational designs of 2D materials and 2D-like materials deposited by atomic layer deposition in order to achieve highly efficient light conversion and prolonged stability. This project will not only enable a deeper understanding of the CO2RR but it will also provide practical strategies for large-scale application of CO2RR for solar fuel production.
Max ERC Funding
1 499 931 €
Duration
Start date: 2019-01-01, End date: 2023-12-31
Project acronym 3D-FABRIC
Project 3D Flow Analysis in Bijels Reconfigured for Interfacial Catalysis
Researcher (PI) Martin F. HAASE
Host Institution (HI) UNIVERSITEIT UTRECHT
Call Details Starting Grant (StG), PE8, ERC-2018-STG
Summary The objective of this proposal is to determine the unknown criteria for convective cross-flow in bicontinuous interfacially jammed emulsion gels (bijels). Based on this, we will answer the question: Can continuously operated interfacial catalysis be realized in bijel cross-flow reactors? Demonstrating this potential will introduce a broadly applicable chemical technology, replacing wasteful chemical processes that require organic solvents. We will achieve our objective in three steps:
(a) Control over bijel structure and properties. Bijels will be formed with a selection of functional inorganic colloidal particles. Nanoparticle surface modifications will be developed and extensively characterized. General principles for the parameters determining bijel structures and properties will be established based on confocal and electron microscopy characterization. These principles will enable unprecedented control over bijel formation and will allow for designing desired properties.
(b) Convective flow in bijels. The mechanical strength of bijels will be tailored and measured. With mechanically robust bijels, the influence of size and organization of oil/water channels on convective mass transfer in bijels will be investigated. To this end, a bijel mass transfer apparatus fabricated by 3d-printing of bijel fibers and soft photolithography will be introduced. In conjunction with the following objective, the analysis of convective flows in bijels will facilitate a thorough description of their structure/function relationships.
(c) Biphasic chemical reactions in STrIPS bijel cross-flow reactors. First, continuous extraction in bijels will be realized. Next, conditions to carry out continuously-operated, phase transfer catalysis of well-known model reactions in bijels will be determined. Both processes will be characterized in-situ and in 3-dimensions by confocal microscopy of fluorescent phase transfer reactions in transparent bijels.
Summary
The objective of this proposal is to determine the unknown criteria for convective cross-flow in bicontinuous interfacially jammed emulsion gels (bijels). Based on this, we will answer the question: Can continuously operated interfacial catalysis be realized in bijel cross-flow reactors? Demonstrating this potential will introduce a broadly applicable chemical technology, replacing wasteful chemical processes that require organic solvents. We will achieve our objective in three steps:
(a) Control over bijel structure and properties. Bijels will be formed with a selection of functional inorganic colloidal particles. Nanoparticle surface modifications will be developed and extensively characterized. General principles for the parameters determining bijel structures and properties will be established based on confocal and electron microscopy characterization. These principles will enable unprecedented control over bijel formation and will allow for designing desired properties.
(b) Convective flow in bijels. The mechanical strength of bijels will be tailored and measured. With mechanically robust bijels, the influence of size and organization of oil/water channels on convective mass transfer in bijels will be investigated. To this end, a bijel mass transfer apparatus fabricated by 3d-printing of bijel fibers and soft photolithography will be introduced. In conjunction with the following objective, the analysis of convective flows in bijels will facilitate a thorough description of their structure/function relationships.
(c) Biphasic chemical reactions in STrIPS bijel cross-flow reactors. First, continuous extraction in bijels will be realized. Next, conditions to carry out continuously-operated, phase transfer catalysis of well-known model reactions in bijels will be determined. Both processes will be characterized in-situ and in 3-dimensions by confocal microscopy of fluorescent phase transfer reactions in transparent bijels.
Max ERC Funding
1 905 000 €
Duration
Start date: 2019-06-01, End date: 2024-05-31
Project acronym 3D-PXM
Project 3D Piezoresponse X-ray Microscopy
Researcher (PI) Hugh SIMONS
Host Institution (HI) DANMARKS TEKNISKE UNIVERSITET
Call Details Starting Grant (StG), PE3, ERC-2018-STG
Summary Polar materials, such as piezoelectrics and ferroelectrics are essential to our modern life, yet they are mostly developed by trial-and-error. Their properties overwhelmingly depend on the defects within them, the majority of which are hidden in the bulk. The road to better materials is via mapping these defects, but our best tool for it – piezoresponse force microscopy (PFM) – is limited to surfaces. 3D-PXM aims to revolutionize our understanding by measuring the local structure-property correlations around individual defects buried deep in the bulk.
This is a completely new kind of microscopy enabling 3D maps of local strain and polarization (i.e. piezoresponse) with 10 nm resolution in mm-sized samples. It is novel, multi-scale and fast enough to capture defect dynamics in real time. Uniquely, it is a full-field method that uses a synthetic-aperture approach to improve both resolution and recover the image phase. This phase is then quantitatively correlated to local polarization and strain via a forward model. 3D-PXM combines advances in X-Ray optics, phase recovery and data analysis to create something transformative. In principle, it can achieve spatial resolution comparable to the best coherent X-Ray microscopy methods while being faster, used on larger samples, and without risk of radiation damage.
For the first time, this opens the door to solving how defects influence bulk properties under real-life conditions. 3D-PXM focuses on three types of defects prevalent in polar materials: grain boundaries, dislocations and polar nanoregions. Individually they address major gaps in the state-of-the-art, while together making great strides towards fully understanding defects. This understanding is expected to inform a new generation of multi-scale models that can account for a material’s full heterogeneity. These models are the first step towards abandoning our tradition of trial-and-error, and with this comes the potential for a new era of polar materials.
Summary
Polar materials, such as piezoelectrics and ferroelectrics are essential to our modern life, yet they are mostly developed by trial-and-error. Their properties overwhelmingly depend on the defects within them, the majority of which are hidden in the bulk. The road to better materials is via mapping these defects, but our best tool for it – piezoresponse force microscopy (PFM) – is limited to surfaces. 3D-PXM aims to revolutionize our understanding by measuring the local structure-property correlations around individual defects buried deep in the bulk.
This is a completely new kind of microscopy enabling 3D maps of local strain and polarization (i.e. piezoresponse) with 10 nm resolution in mm-sized samples. It is novel, multi-scale and fast enough to capture defect dynamics in real time. Uniquely, it is a full-field method that uses a synthetic-aperture approach to improve both resolution and recover the image phase. This phase is then quantitatively correlated to local polarization and strain via a forward model. 3D-PXM combines advances in X-Ray optics, phase recovery and data analysis to create something transformative. In principle, it can achieve spatial resolution comparable to the best coherent X-Ray microscopy methods while being faster, used on larger samples, and without risk of radiation damage.
For the first time, this opens the door to solving how defects influence bulk properties under real-life conditions. 3D-PXM focuses on three types of defects prevalent in polar materials: grain boundaries, dislocations and polar nanoregions. Individually they address major gaps in the state-of-the-art, while together making great strides towards fully understanding defects. This understanding is expected to inform a new generation of multi-scale models that can account for a material’s full heterogeneity. These models are the first step towards abandoning our tradition of trial-and-error, and with this comes the potential for a new era of polar materials.
Max ERC Funding
1 496 941 €
Duration
Start date: 2019-01-01, End date: 2023-12-31
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 AEROBIC
Project Assessing the Effects of Rising O2 on Biogeochemical Cycles: Integrated Laboratory Experiments and Numerical Simulations
Researcher (PI) Itay Halevy
Host Institution (HI) WEIZMANN INSTITUTE OF SCIENCE
Call Details Starting Grant (StG), PE10, ERC-2013-StG
Summary The rise of atmospheric O2 ~2,500 million years ago is one of the most profound transitions in Earth's history. Yet, despite its central role in shaping Earth's surface environment, the cause for the rise of O2 remains poorly understood. Tight coupling between the O2 cycle and the biogeochemical cycles of redox-active elements, such as C, Fe and S, implies radical changes in these cycles before, during and after the rise of O2. These changes, too, are incompletely understood, but have left valuable information encoded in the geological record. This information has been qualitatively interpreted, leaving many aspects of the rise of O2, including its causes and constraints on ocean chemistry before and after it, topics of ongoing research and debate. Here, I outline a research program to address this fundamental question in geochemical Earth systems evolution. The inherently interdisciplinary program uniquely integrates laboratory experiments, numerical models, geological observations, and geochemical analyses. Laboratory experiments and geological observations will constrain unknown parameters of the early biogeochemical cycles, and, in combination with field studies, will validate and refine the use of paleoenvironmental proxies. The insight gained will be used to develop detailed models of the coupled biogeochemical cycles, which will themselves be used to quantitatively understand the events surrounding the rise of O2, and to illuminate the dynamics of elemental cycles in the early oceans.
This program is expected to yield novel, quantitative insight into these important events in Earth history and to have a major impact on our understanding of early ocean chemistry and the rise of O2. An ERC Starting Grant will enable me to use the excellent experimental and computational facilities at my disposal, to access the outstanding human resource at the Weizmann Institute of Science, and to address one of the major open questions in modern geochemistry.
Summary
The rise of atmospheric O2 ~2,500 million years ago is one of the most profound transitions in Earth's history. Yet, despite its central role in shaping Earth's surface environment, the cause for the rise of O2 remains poorly understood. Tight coupling between the O2 cycle and the biogeochemical cycles of redox-active elements, such as C, Fe and S, implies radical changes in these cycles before, during and after the rise of O2. These changes, too, are incompletely understood, but have left valuable information encoded in the geological record. This information has been qualitatively interpreted, leaving many aspects of the rise of O2, including its causes and constraints on ocean chemistry before and after it, topics of ongoing research and debate. Here, I outline a research program to address this fundamental question in geochemical Earth systems evolution. The inherently interdisciplinary program uniquely integrates laboratory experiments, numerical models, geological observations, and geochemical analyses. Laboratory experiments and geological observations will constrain unknown parameters of the early biogeochemical cycles, and, in combination with field studies, will validate and refine the use of paleoenvironmental proxies. The insight gained will be used to develop detailed models of the coupled biogeochemical cycles, which will themselves be used to quantitatively understand the events surrounding the rise of O2, and to illuminate the dynamics of elemental cycles in the early oceans.
This program is expected to yield novel, quantitative insight into these important events in Earth history and to have a major impact on our understanding of early ocean chemistry and the rise of O2. An ERC Starting Grant will enable me to use the excellent experimental and computational facilities at my disposal, to access the outstanding human resource at the Weizmann Institute of Science, and to address one of the major open questions in modern geochemistry.
Max ERC Funding
1 472 690 €
Duration
Start date: 2013-09-01, End date: 2018-08-31
Project acronym AFFINITY
Project Actuation of Ferromagnetic Fibre Networks to improve Implant Longevity
Researcher (PI) Athina Markaki
Host Institution (HI) THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE
Call Details Starting Grant (StG), PE8, ERC-2009-StG
Summary This proposal is for an exploratory study into a radical new approach to the problem of orthopaedic implant loosening. Such loosening commonly occurs because the joint between the implant and the surrounding bone is insufficiently strong and durable. It is a serious problem both for implants cemented to the bone and for those dependent on bone in-growth into a rough/porous implant surface. In the latter case, the main problem is commonly that bone in-growth is insufficiently rapid or deep for a strong bond to be established. The idea proposed in this work is that the implant should have a highly porous surface layer, made by bonding ferromagnetic fibres together, into which bone tissue growth would occur. During the post-operative period, application of a magnetic field will cause the fibre network to deform elastically, as individual fibres tend to align with the field. This will impose strains on the bone tissue as it grows into the fibre network. Such mechanical deformation is known to be highly beneficial in promoting bone growth, providing the associated strain lies in a certain range (~0.1%). Preliminary work, involving both model development and experimental studies on the effect of magnetic fields on fibre networks, has suggested that beneficial therapeutic effects can be induced using field strengths no greater than those already employed for diagnostic purposes. A comprehensive 5-year, highly inter-disciplinary programme is planned, encompassing processing, network architecture characterisation, magneto-mechanical response investigations, various modelling activities and systematic in vitro experimentation to establish whether magneto-mechanical Actuation of Ferromagnetic Fibre Networks shows promise as a new therapeutic approach to improve implant longevity.
Summary
This proposal is for an exploratory study into a radical new approach to the problem of orthopaedic implant loosening. Such loosening commonly occurs because the joint between the implant and the surrounding bone is insufficiently strong and durable. It is a serious problem both for implants cemented to the bone and for those dependent on bone in-growth into a rough/porous implant surface. In the latter case, the main problem is commonly that bone in-growth is insufficiently rapid or deep for a strong bond to be established. The idea proposed in this work is that the implant should have a highly porous surface layer, made by bonding ferromagnetic fibres together, into which bone tissue growth would occur. During the post-operative period, application of a magnetic field will cause the fibre network to deform elastically, as individual fibres tend to align with the field. This will impose strains on the bone tissue as it grows into the fibre network. Such mechanical deformation is known to be highly beneficial in promoting bone growth, providing the associated strain lies in a certain range (~0.1%). Preliminary work, involving both model development and experimental studies on the effect of magnetic fields on fibre networks, has suggested that beneficial therapeutic effects can be induced using field strengths no greater than those already employed for diagnostic purposes. A comprehensive 5-year, highly inter-disciplinary programme is planned, encompassing processing, network architecture characterisation, magneto-mechanical response investigations, various modelling activities and systematic in vitro experimentation to establish whether magneto-mechanical Actuation of Ferromagnetic Fibre Networks shows promise as a new therapeutic approach to improve implant longevity.
Max ERC Funding
1 442 756 €
Duration
Start date: 2010-01-01, End date: 2015-11-30
Project acronym AFRIVAL
Project African river basins: catchment-scale carbon fluxes and transformations
Researcher (PI) Steven Bouillon
Host Institution (HI) KATHOLIEKE UNIVERSITEIT LEUVEN
Call Details Starting Grant (StG), PE10, ERC-2009-StG
Summary This proposal wishes to fundamentally improve our understanding of the role of tropical freshwater ecosystems in carbon (C) cycling on the catchment scale. It uses an unprecedented combination of state-of-the-art proxies such as stable isotope, 14C and biomarker signatures to characterize organic matter, radiogenic isotope signatures to determine particle residence times, as well as field measurements of relevant biogeochemical processes. We focus on tropical systems since there is a striking lack of data on such systems, even though riverine C transport is thought to be disproportionately high in tropical areas. Furthermore, the presence of landscape-scale contrasts in vegetation (in particular, C3 vs. C4 plants) are an important asset in the use of stable isotopes as natural tracers of C cycling processes on this scale. Freshwater ecosystems are an important component in the global C cycle, and the primary link between terrestrial and marine ecosystems. Recent estimates indicate that ~2 Pg C y-1 (Pg=Petagram) enter freshwater systems, i.e., about twice the estimated global terrestrial C sink. More than half of this is thought to be remineralized before it reaches the coastal zone, and for the Amazon basin this has even been suggested to be ~90% of the lateral C inputs. The question how general these patterns are is a matter of debate, and assessing the mechanisms determining the degree of processing versus transport of organic carbon in lakes and river systems is critical to further constrain their role in the global C cycle. This proposal provides an interdisciplinary approach to describe and quantify catchment-scale C transport and cycling in tropical river basins. Besides conceptual and methodological advances, and a significant expansion of our dataset on C processes in such systems, new data gathered in this project are likely to provide exciting and novel hypotheses on the functioning of freshwater systems and their linkage to the terrestrial C budget.
Summary
This proposal wishes to fundamentally improve our understanding of the role of tropical freshwater ecosystems in carbon (C) cycling on the catchment scale. It uses an unprecedented combination of state-of-the-art proxies such as stable isotope, 14C and biomarker signatures to characterize organic matter, radiogenic isotope signatures to determine particle residence times, as well as field measurements of relevant biogeochemical processes. We focus on tropical systems since there is a striking lack of data on such systems, even though riverine C transport is thought to be disproportionately high in tropical areas. Furthermore, the presence of landscape-scale contrasts in vegetation (in particular, C3 vs. C4 plants) are an important asset in the use of stable isotopes as natural tracers of C cycling processes on this scale. Freshwater ecosystems are an important component in the global C cycle, and the primary link between terrestrial and marine ecosystems. Recent estimates indicate that ~2 Pg C y-1 (Pg=Petagram) enter freshwater systems, i.e., about twice the estimated global terrestrial C sink. More than half of this is thought to be remineralized before it reaches the coastal zone, and for the Amazon basin this has even been suggested to be ~90% of the lateral C inputs. The question how general these patterns are is a matter of debate, and assessing the mechanisms determining the degree of processing versus transport of organic carbon in lakes and river systems is critical to further constrain their role in the global C cycle. This proposal provides an interdisciplinary approach to describe and quantify catchment-scale C transport and cycling in tropical river basins. Besides conceptual and methodological advances, and a significant expansion of our dataset on C processes in such systems, new data gathered in this project are likely to provide exciting and novel hypotheses on the functioning of freshwater systems and their linkage to the terrestrial C budget.
Max ERC Funding
1 745 262 €
Duration
Start date: 2009-10-01, End date: 2014-09-30
Project acronym ANGULON
Project Angulon: physics and applications of a new quasiparticle
Researcher (PI) Mikhail Lemeshko
Host Institution (HI) INSTITUTE OF SCIENCE AND TECHNOLOGYAUSTRIA
Call Details Starting Grant (StG), PE3, ERC-2018-STG
Summary This project aims to develop a universal approach to angular momentum in quantum many-body systems based on the angulon quasiparticle recently discovered by the PI. We will establish a general theory of angulons in and out of equilibrium, and apply it to a variety of experimentally studied problems, ranging from chemical dynamics in solvents to solid-state systems (e.g. angular momentum transfer in the Einstein-de Haas effect and ultrafast magnetism).
The concept of angular momentum is ubiquitous across physics, whether one deals with nuclear collisions, chemical reactions, or formation of galaxies. In the microscopic world, quantum rotations are described by non-commuting operators. This makes the angular momentum theory extremely involved, even for systems consisting of only a few interacting particles, such as gas-phase atoms or molecules.
Furthermore, in most experiments the behavior of quantum particles is inevitably altered by a many-body environment of some kind. For example, molecular rotation – and therefore reactivity – depends on the presence of a solvent, electronic angular momentum in solids is coupled to lattice phonons, highly excited atomic levels can be perturbed by a surrounding ultracold gas. If approached in a brute-force fashion, understanding angular momentum in such systems is an impossible task, since a macroscopic number of particles is involved.
Recently, the PI and his team have shown that this challenge can be met by introducing a new quasiparticle – the angulon. In 2017, the PI has demonstrated the existence of angulons by comparing his theory with 20 years of measurements on molecules rotating in superfluids. Most importantly, the angulon concept allows one to gain analytical insights inaccessible to the state-of-the-art techniques of condensed matter and chemical physics. The angulon approach holds the promise of opening up a new interdisciplinary research area with applications reaching far beyond what is proposed here.
Summary
This project aims to develop a universal approach to angular momentum in quantum many-body systems based on the angulon quasiparticle recently discovered by the PI. We will establish a general theory of angulons in and out of equilibrium, and apply it to a variety of experimentally studied problems, ranging from chemical dynamics in solvents to solid-state systems (e.g. angular momentum transfer in the Einstein-de Haas effect and ultrafast magnetism).
The concept of angular momentum is ubiquitous across physics, whether one deals with nuclear collisions, chemical reactions, or formation of galaxies. In the microscopic world, quantum rotations are described by non-commuting operators. This makes the angular momentum theory extremely involved, even for systems consisting of only a few interacting particles, such as gas-phase atoms or molecules.
Furthermore, in most experiments the behavior of quantum particles is inevitably altered by a many-body environment of some kind. For example, molecular rotation – and therefore reactivity – depends on the presence of a solvent, electronic angular momentum in solids is coupled to lattice phonons, highly excited atomic levels can be perturbed by a surrounding ultracold gas. If approached in a brute-force fashion, understanding angular momentum in such systems is an impossible task, since a macroscopic number of particles is involved.
Recently, the PI and his team have shown that this challenge can be met by introducing a new quasiparticle – the angulon. In 2017, the PI has demonstrated the existence of angulons by comparing his theory with 20 years of measurements on molecules rotating in superfluids. Most importantly, the angulon concept allows one to gain analytical insights inaccessible to the state-of-the-art techniques of condensed matter and chemical physics. The angulon approach holds the promise of opening up a new interdisciplinary research area with applications reaching far beyond what is proposed here.
Max ERC Funding
1 499 588 €
Duration
Start date: 2019-02-01, End date: 2024-01-31
Project acronym AQSER
Project Automorphic q-series and their application
Researcher (PI) Kathrin Bringmann
Host Institution (HI) UNIVERSITAET ZU KOELN
Call Details Starting Grant (StG), PE1, ERC-2013-StG
Summary This proposal aims to unravel mysteries at the frontier of number theory and other areas of mathematics and physics. The main focus will be to understand and exploit “modularity” of q-hypergeometric series. “Modular forms are functions on the complex plane that are inordinately symmetric.” (Mazur) The motivation comes from the wide-reaching applications of modularity in combinatorics, percolation, Lie theory, and physics (black holes).
The interplay between automorphic forms, q-series, and other areas of mathematics and physics is often two-sided. On the one hand, the other areas provide interesting examples of automorphic objects and predict their behavior. Sometimes these even motivate new classes of automorphic objects which have not been previously studied. On the other hand, knowing that certain generating functions are modular gives one access to deep theoretical tools to prove results in other areas. “Mathematics is a language, and we need that language to understand the physics of our universe.”(Ooguri) Understanding this interplay has attracted attention of researchers from a variety of areas. However, proofs of modularity of q-hypergeometric series currently fall far short of a comprehensive theory to describe the interplay between them and automorphic forms. A recent conjecture of W. Nahm relates the modularity of such series to K-theory. In this proposal I aim to fill this gap and provide a better understanding of this interplay by building a general structural framework enveloping these q-series. For this I will employ new kinds of automorphic objects and embed the functions of interest into bigger families
A successful outcome of the proposed research will open further horizons and also answer open questions, even those in other areas which were not addressed in this proposal; for example the new theory could be applied to better understand Donaldson invariants.
Summary
This proposal aims to unravel mysteries at the frontier of number theory and other areas of mathematics and physics. The main focus will be to understand and exploit “modularity” of q-hypergeometric series. “Modular forms are functions on the complex plane that are inordinately symmetric.” (Mazur) The motivation comes from the wide-reaching applications of modularity in combinatorics, percolation, Lie theory, and physics (black holes).
The interplay between automorphic forms, q-series, and other areas of mathematics and physics is often two-sided. On the one hand, the other areas provide interesting examples of automorphic objects and predict their behavior. Sometimes these even motivate new classes of automorphic objects which have not been previously studied. On the other hand, knowing that certain generating functions are modular gives one access to deep theoretical tools to prove results in other areas. “Mathematics is a language, and we need that language to understand the physics of our universe.”(Ooguri) Understanding this interplay has attracted attention of researchers from a variety of areas. However, proofs of modularity of q-hypergeometric series currently fall far short of a comprehensive theory to describe the interplay between them and automorphic forms. A recent conjecture of W. Nahm relates the modularity of such series to K-theory. In this proposal I aim to fill this gap and provide a better understanding of this interplay by building a general structural framework enveloping these q-series. For this I will employ new kinds of automorphic objects and embed the functions of interest into bigger families
A successful outcome of the proposed research will open further horizons and also answer open questions, even those in other areas which were not addressed in this proposal; for example the new theory could be applied to better understand Donaldson invariants.
Max ERC Funding
1 240 500 €
Duration
Start date: 2014-01-01, End date: 2019-04-30
