Project acronym 1stProposal
Project An alternative development of analytic number theory and applications
Researcher (PI) ANDREW Granville
Host Institution (HI) UNIVERSITY COLLEGE LONDON
Call Details Advanced Grant (AdG), PE1, ERC-2014-ADG
Summary The traditional (Riemann) approach to analytic number theory uses the zeros of zeta functions. This requires the associated multiplicative function, say f(n), to have special enough properties that the associated Dirichlet series may be analytically continued. In this proposal we continue to develop an approach which requires less of the multiplicative function, linking the original question with the mean value of f. Such techniques have been around for a long time but have generally been regarded as “ad hoc”. In this project we aim to show that one can develop a coherent approach to the whole subject, not only reproving all of the old results, but also many new ones that appear inaccessible to traditional methods.
Our first goal is to complete a monograph yielding a reworking of all the classical theory using these new methods and then to push forward in new directions. The most important is to extend these techniques to GL(n) L-functions, which we hope will now be feasible having found the correct framework in which to proceed. Since we rarely know how to analytically continue such L-functions this could be of great benefit to the subject.
We are developing the large sieve so that it can be used for individual moduli, and will determine a strong form of that. Also a new method to give asymptotics for mean values, when they are not too small.
We wish to incorporate techniques of analytic number theory into our theory, for example recent advances on mean values of Dirichlet polynomials. Also the recent breakthroughs on the sieve suggest strong links that need further exploration.
Additive combinatorics yields important results in many areas. There are strong analogies between its results, and those for multiplicative functions, especially in large value spectrum theory, and its applications. We hope to develop these further.
Much of this is joint work with K Soundararajan of Stanford University.
Summary
The traditional (Riemann) approach to analytic number theory uses the zeros of zeta functions. This requires the associated multiplicative function, say f(n), to have special enough properties that the associated Dirichlet series may be analytically continued. In this proposal we continue to develop an approach which requires less of the multiplicative function, linking the original question with the mean value of f. Such techniques have been around for a long time but have generally been regarded as “ad hoc”. In this project we aim to show that one can develop a coherent approach to the whole subject, not only reproving all of the old results, but also many new ones that appear inaccessible to traditional methods.
Our first goal is to complete a monograph yielding a reworking of all the classical theory using these new methods and then to push forward in new directions. The most important is to extend these techniques to GL(n) L-functions, which we hope will now be feasible having found the correct framework in which to proceed. Since we rarely know how to analytically continue such L-functions this could be of great benefit to the subject.
We are developing the large sieve so that it can be used for individual moduli, and will determine a strong form of that. Also a new method to give asymptotics for mean values, when they are not too small.
We wish to incorporate techniques of analytic number theory into our theory, for example recent advances on mean values of Dirichlet polynomials. Also the recent breakthroughs on the sieve suggest strong links that need further exploration.
Additive combinatorics yields important results in many areas. There are strong analogies between its results, and those for multiplicative functions, especially in large value spectrum theory, and its applications. We hope to develop these further.
Much of this is joint work with K Soundararajan of Stanford University.
Max ERC Funding
2 011 742 €
Duration
Start date: 2015-08-01, End date: 2020-07-31
Project acronym 2DQP
Project Two-dimensional quantum photonics
Researcher (PI) Brian David GERARDOT
Host Institution (HI) HERIOT-WATT UNIVERSITY
Call Details Consolidator Grant (CoG), PE3, ERC-2016-COG
Summary Quantum optics, the study of how discrete packets of light (photons) and matter interact, has led to the development of remarkable new technologies which exploit the bizarre properties of quantum mechanics. These quantum technologies are primed to revolutionize the fields of communication, information processing, and metrology in the coming years. Similar to contemporary technologies, the future quantum machinery will likely consist of a semiconductor platform to create and process the quantum information. However, to date the demanding requirements on a quantum photonic platform have yet to be satisfied with conventional bulk (three-dimensional) semiconductors.
To surmount these well-known obstacles, a new paradigm in quantum photonics is required. Initiated by the recent discovery of single photon emitters in atomically flat (two-dimensional) semiconducting materials, 2DQP aims to be at the nucleus of a new approach by realizing quantum optics with ultra-stable (coherent) quantum states integrated into devices with electronic and photonic functionality. We will characterize, identify, engineer, and coherently manipulate localized quantum states in this two-dimensional quantum photonic platform. A vital component of 2DQP’s vision is to go beyond the fundamental science and achieve the ideal solid-state single photon device yielding perfect extraction - 100% efficiency - of on-demand indistinguishable single photons. Finally, we will exploit this ideal device to implement the critical building block for a photonic quantum computer.
Summary
Quantum optics, the study of how discrete packets of light (photons) and matter interact, has led to the development of remarkable new technologies which exploit the bizarre properties of quantum mechanics. These quantum technologies are primed to revolutionize the fields of communication, information processing, and metrology in the coming years. Similar to contemporary technologies, the future quantum machinery will likely consist of a semiconductor platform to create and process the quantum information. However, to date the demanding requirements on a quantum photonic platform have yet to be satisfied with conventional bulk (three-dimensional) semiconductors.
To surmount these well-known obstacles, a new paradigm in quantum photonics is required. Initiated by the recent discovery of single photon emitters in atomically flat (two-dimensional) semiconducting materials, 2DQP aims to be at the nucleus of a new approach by realizing quantum optics with ultra-stable (coherent) quantum states integrated into devices with electronic and photonic functionality. We will characterize, identify, engineer, and coherently manipulate localized quantum states in this two-dimensional quantum photonic platform. A vital component of 2DQP’s vision is to go beyond the fundamental science and achieve the ideal solid-state single photon device yielding perfect extraction - 100% efficiency - of on-demand indistinguishable single photons. Finally, we will exploit this ideal device to implement the critical building block for a photonic quantum computer.
Max ERC Funding
1 999 135 €
Duration
Start date: 2018-01-01, End date: 2022-12-31
Project acronym ABLASE
Project Advanced Bioderived and Biocompatible Lasers
Researcher (PI) Malte Christian Gather
Host Institution (HI) THE UNIVERSITY COURT OF THE UNIVERSITY OF ST ANDREWS
Call Details Starting Grant (StG), PE3, ERC-2014-STG
Summary Naturally occurring optical phenomena attract great attention and transform our ability to study biological processes, with “the discovery and development of the green fluorescent protein (GFP)” (Nobel Prize in Chemistry 2008) being a particularly successful example. Although found only in very few species in nature, most organisms can be genetically programmed to produce the brightly fluorescent GFP molecules. Combined with modern fluorescence detection schemes, this has led to entirely new ways of monitoring biological processes. The applicant now demonstrated a biological laser – a completely novel, living source of coherent light based on a single biological cell bioengineered to produce GFP. Such a laser is intrinsically biocompatible, thus offering unique properties not shared by any existing laser. However, the physical processes involved in lasing from GFP remain poorly understood and so far biological lasers rely on bulky, impractical external resonators for optical feedback. Within this project, the applicant and his team will develop for the first time an understanding of stimulated emission in GFP and related proteins and create an unprecedented stand-alone single-cell biolaser based on intracellular optical feedback. These lasers will be deployed as microscopic and biocompatible imaging probes, thus opening in vivo microscopy to dense wavelength-multiplexing and enabling unmatched sensing of biomolecules and mechanical pressure. The evolutionarily evolved nano-structure of GFP will also enable novel ways of studying strong light-matter coupling and will bio-inspire advances of synthetic emitters. The proposed project is inter-disciplinary by its very nature, bridging photonics, genetic engineering and material science. The applicant’s previous pioneering work and synergies with work on other lasers developed at the applicant’s host institution provide an exclusive competitive edge. ERC support would transform this into a truly novel field of research.
Summary
Naturally occurring optical phenomena attract great attention and transform our ability to study biological processes, with “the discovery and development of the green fluorescent protein (GFP)” (Nobel Prize in Chemistry 2008) being a particularly successful example. Although found only in very few species in nature, most organisms can be genetically programmed to produce the brightly fluorescent GFP molecules. Combined with modern fluorescence detection schemes, this has led to entirely new ways of monitoring biological processes. The applicant now demonstrated a biological laser – a completely novel, living source of coherent light based on a single biological cell bioengineered to produce GFP. Such a laser is intrinsically biocompatible, thus offering unique properties not shared by any existing laser. However, the physical processes involved in lasing from GFP remain poorly understood and so far biological lasers rely on bulky, impractical external resonators for optical feedback. Within this project, the applicant and his team will develop for the first time an understanding of stimulated emission in GFP and related proteins and create an unprecedented stand-alone single-cell biolaser based on intracellular optical feedback. These lasers will be deployed as microscopic and biocompatible imaging probes, thus opening in vivo microscopy to dense wavelength-multiplexing and enabling unmatched sensing of biomolecules and mechanical pressure. The evolutionarily evolved nano-structure of GFP will also enable novel ways of studying strong light-matter coupling and will bio-inspire advances of synthetic emitters. The proposed project is inter-disciplinary by its very nature, bridging photonics, genetic engineering and material science. The applicant’s previous pioneering work and synergies with work on other lasers developed at the applicant’s host institution provide an exclusive competitive edge. ERC support would transform this into a truly novel field of research.
Max ERC Funding
1 499 875 €
Duration
Start date: 2015-06-01, End date: 2020-05-31
Project acronym ACCORD
Project Algorithms for Complex Collective Decisions on Structured Domains
Researcher (PI) Edith Elkind
Host Institution (HI) THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Call Details Starting Grant (StG), PE6, ERC-2014-STG
Summary Algorithms for Complex Collective Decisions on Structured Domains.
The aim of this proposal is to substantially advance the field of Computational Social Choice, by developing new tools and methodologies that can be used for making complex group decisions in rich and structured environments. We consider settings where each member of a decision-making body has preferences over a finite set of alternatives, and the goal is to synthesise a collective preference over these alternatives, which may take the form of a partial order over the set of alternatives with a predefined structure: examples include selecting a fixed-size set of alternatives, a ranking of the alternatives, a winner and up to two runner-ups, etc. We will formulate desiderata that apply to such preference aggregation procedures, design specific procedures that satisfy as many of these desiderata as possible, and develop efficient algorithms for computing them. As the latter step may be infeasible on general preference domains, we will focus on identifying the least restrictive domains that enable efficient computation, and use real-life preference data to verify whether the associated restrictions are likely to be satisfied in realistic preference aggregation scenarios. Also, we will determine whether our preference aggregation procedures are computationally resistant to malicious behavior. To lower the cognitive burden on the decision-makers, we will extend our procedures to accept partial rankings as inputs. Finally, to further contribute towards bridging the gap between theory and practice of collective decision making, we will provide open-source software implementations of our procedures, and reach out to the potential users to obtain feedback on their practical applicability.
Summary
Algorithms for Complex Collective Decisions on Structured Domains.
The aim of this proposal is to substantially advance the field of Computational Social Choice, by developing new tools and methodologies that can be used for making complex group decisions in rich and structured environments. We consider settings where each member of a decision-making body has preferences over a finite set of alternatives, and the goal is to synthesise a collective preference over these alternatives, which may take the form of a partial order over the set of alternatives with a predefined structure: examples include selecting a fixed-size set of alternatives, a ranking of the alternatives, a winner and up to two runner-ups, etc. We will formulate desiderata that apply to such preference aggregation procedures, design specific procedures that satisfy as many of these desiderata as possible, and develop efficient algorithms for computing them. As the latter step may be infeasible on general preference domains, we will focus on identifying the least restrictive domains that enable efficient computation, and use real-life preference data to verify whether the associated restrictions are likely to be satisfied in realistic preference aggregation scenarios. Also, we will determine whether our preference aggregation procedures are computationally resistant to malicious behavior. To lower the cognitive burden on the decision-makers, we will extend our procedures to accept partial rankings as inputs. Finally, to further contribute towards bridging the gap between theory and practice of collective decision making, we will provide open-source software implementations of our procedures, and reach out to the potential users to obtain feedback on their practical applicability.
Max ERC Funding
1 395 933 €
Duration
Start date: 2015-07-01, End date: 2020-06-30
Project acronym ACrossWire
Project A Cross-Correlated Approach to Engineering Nitride Nanowires
Researcher (PI) Hannah Jane JOYCE
Host Institution (HI) THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE
Call Details Starting Grant (StG), PE7, ERC-2016-STG
Summary Nanowires based on group III–nitride semiconductors exhibit outstanding potential for emerging applications in energy-efficient lighting, optoelectronics and solar energy harvesting. Nitride nanowires, tailored at the nanoscale, should overcome many of the challenges facing conventional planar nitride materials, and also add extraordinary new functionality to these materials. However, progress towards III–nitride nanowire devices has been hampered by the challenges in quantifying nanowire electrical properties using conventional contact-based measurements. Without reliable electrical transport data, it is extremely difficult to optimise nanowire growth and device design. This project aims to overcome this problem through an unconventional approach: advanced contact-free electrical measurements. Contact-free measurements, growth studies, and device studies will be cross-correlated to provide unprecedented insight into the growth mechanisms that govern nanowire electronic properties and ultimately dictate device performance. A key contact-free technique at the heart of this proposal is ultrafast terahertz conductivity spectroscopy: an advanced technique ideal for probing nanowire electrical properties. We will develop new methods to enable the full suite of contact-free (including terahertz, photoluminescence and cathodoluminescence measurements) and contact-based measurements to be performed with high spatial resolution on the same nanowires. This will provide accurate, comprehensive and cross-correlated feedback to guide growth studies and expedite the targeted development of nanowires with specified functionality. We will apply this powerful approach to tailor nanowires as photoelectrodes for solar photoelectrochemical water splitting. This is an application for which nitride nanowires have outstanding, yet unfulfilled, potential. This project will thus harness the true potential of nitride nanowires and bring them to the forefront of 21st century technology.
Summary
Nanowires based on group III–nitride semiconductors exhibit outstanding potential for emerging applications in energy-efficient lighting, optoelectronics and solar energy harvesting. Nitride nanowires, tailored at the nanoscale, should overcome many of the challenges facing conventional planar nitride materials, and also add extraordinary new functionality to these materials. However, progress towards III–nitride nanowire devices has been hampered by the challenges in quantifying nanowire electrical properties using conventional contact-based measurements. Without reliable electrical transport data, it is extremely difficult to optimise nanowire growth and device design. This project aims to overcome this problem through an unconventional approach: advanced contact-free electrical measurements. Contact-free measurements, growth studies, and device studies will be cross-correlated to provide unprecedented insight into the growth mechanisms that govern nanowire electronic properties and ultimately dictate device performance. A key contact-free technique at the heart of this proposal is ultrafast terahertz conductivity spectroscopy: an advanced technique ideal for probing nanowire electrical properties. We will develop new methods to enable the full suite of contact-free (including terahertz, photoluminescence and cathodoluminescence measurements) and contact-based measurements to be performed with high spatial resolution on the same nanowires. This will provide accurate, comprehensive and cross-correlated feedback to guide growth studies and expedite the targeted development of nanowires with specified functionality. We will apply this powerful approach to tailor nanowires as photoelectrodes for solar photoelectrochemical water splitting. This is an application for which nitride nanowires have outstanding, yet unfulfilled, potential. This project will thus harness the true potential of nitride nanowires and bring them to the forefront of 21st century technology.
Max ERC Funding
1 499 195 €
Duration
Start date: 2017-04-01, End date: 2022-03-31
Project acronym ADSNeSP
Project Active and Driven Systems: Nonequilibrium Statistical Physics
Researcher (PI) Michael Elmhirst CATES
Host Institution (HI) THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE
Call Details Advanced Grant (AdG), PE3, ERC-2016-ADG
Summary Active Matter systems, such as self-propelled colloids, violate time-reversal symmetry by producing entropy locally, typically converting fuel into mechanical motion at the particle scale. Other driven systems instead produce entropy because of global forcing by external fields, or boundary conditions that impose macroscopic fluxes (such as the momentum flux across a fluid sheared between moving parallel walls).
Nonequilibrium statistical physics (NeSP) is the basic toolbox for both classes of system. In recent years, much progress in NeSP has stemmed from bottom-up work on driven systems. This has provided a number of exactly solved benchmark models, and extended approximation techniques to address driven non-ergodic systems, such as sheared glasses. Meanwhile, work on fluctuation theorems and stochastic thermodynamics have created profound, model-independent insights into dynamics far from equilibrium.
More recently, the field of Active Matter has moved forward rapidly, leaving in its wake a series of generic and profound NeSP questions that now need answers: When is time-reversal symmetry, broken at the microscale, restored by coarse-graining? If it is restored, is an effective thermodynamic description is possible? How different is an active system's behaviour from a globally forced one?
ADSNeSP aims to distil from recent Active Matter research such fundamental questions; answer them first in the context of specific models and second in more general terms; and then, using the tools and insights gained, shed new light on longstanding problems in the wider class of driven systems.
I believe these new tools and insights will be substantial, because local activity takes systems far from equilibrium in a conceptually distinct direction from most types of global driving. By focusing on general principles and on simple models of activity, I seek to create a new vantage point that can inform, and potentially transform, wider areas of statistical physics.
Summary
Active Matter systems, such as self-propelled colloids, violate time-reversal symmetry by producing entropy locally, typically converting fuel into mechanical motion at the particle scale. Other driven systems instead produce entropy because of global forcing by external fields, or boundary conditions that impose macroscopic fluxes (such as the momentum flux across a fluid sheared between moving parallel walls).
Nonequilibrium statistical physics (NeSP) is the basic toolbox for both classes of system. In recent years, much progress in NeSP has stemmed from bottom-up work on driven systems. This has provided a number of exactly solved benchmark models, and extended approximation techniques to address driven non-ergodic systems, such as sheared glasses. Meanwhile, work on fluctuation theorems and stochastic thermodynamics have created profound, model-independent insights into dynamics far from equilibrium.
More recently, the field of Active Matter has moved forward rapidly, leaving in its wake a series of generic and profound NeSP questions that now need answers: When is time-reversal symmetry, broken at the microscale, restored by coarse-graining? If it is restored, is an effective thermodynamic description is possible? How different is an active system's behaviour from a globally forced one?
ADSNeSP aims to distil from recent Active Matter research such fundamental questions; answer them first in the context of specific models and second in more general terms; and then, using the tools and insights gained, shed new light on longstanding problems in the wider class of driven systems.
I believe these new tools and insights will be substantial, because local activity takes systems far from equilibrium in a conceptually distinct direction from most types of global driving. By focusing on general principles and on simple models of activity, I seek to create a new vantage point that can inform, and potentially transform, wider areas of statistical physics.
Max ERC Funding
2 043 630 €
Duration
Start date: 2017-10-01, End date: 2022-09-30
Project acronym AlCat
Project Bond activation and catalysis with low-valent aluminium
Researcher (PI) Michael James COWLEY
Host Institution (HI) THE UNIVERSITY OF EDINBURGH
Call Details Starting Grant (StG), PE5, ERC-2016-STG
Summary This project will develop the principles required to enable bond-modifying redox catalysis based on aluminium by preparing and studying new Al(I) compounds capable of reversible oxidative addition.
Catalytic processes are involved in the synthesis of 75 % of all industrially produced chemicals, but most catalysts involved are based on precious metals such as rhodium, palladium or platinum. These metals are expensive and their supply limited and unstable; there is a significant need to develop the chemistry of non-precious metals as alternatives. On toxicity and abundance alone, aluminium is an attractive candidate. Furthermore, recent work, including in our group, has demonstrated that Al(I) compounds can perform a key step in catalytic cycles - the oxidative addition of E-H bonds.
In order to realise the significant potential of Al(I) for transition-metal style catalysis we urgently need to:
- establish the principles governing oxidative addition and reductive elimination reactivity in aluminium systems.
- know how the reactivity of Al(I) compounds can be controlled by varying properties of ligand frameworks.
- understand the onward reactivity of oxidative addition products of Al(I) to enable applications in catalysis.
In this project we will:
- Study mechanisms of oxidative addition and reductive elimination of a range of synthetically relevant bonds at Al(I) centres, establishing the principles governing this fundamental reactivity.
- Develop new ligand frameworks to support of Al(I) centres and evaluate the effect of the ligand on oxidative addition/reductive elimination at Al centres.
- Investigate methods for Al-mediated functionalisation of organic compounds by exploring the reactivity of E-H oxidative addition products with unsaturated organic compounds.
Summary
This project will develop the principles required to enable bond-modifying redox catalysis based on aluminium by preparing and studying new Al(I) compounds capable of reversible oxidative addition.
Catalytic processes are involved in the synthesis of 75 % of all industrially produced chemicals, but most catalysts involved are based on precious metals such as rhodium, palladium or platinum. These metals are expensive and their supply limited and unstable; there is a significant need to develop the chemistry of non-precious metals as alternatives. On toxicity and abundance alone, aluminium is an attractive candidate. Furthermore, recent work, including in our group, has demonstrated that Al(I) compounds can perform a key step in catalytic cycles - the oxidative addition of E-H bonds.
In order to realise the significant potential of Al(I) for transition-metal style catalysis we urgently need to:
- establish the principles governing oxidative addition and reductive elimination reactivity in aluminium systems.
- know how the reactivity of Al(I) compounds can be controlled by varying properties of ligand frameworks.
- understand the onward reactivity of oxidative addition products of Al(I) to enable applications in catalysis.
In this project we will:
- Study mechanisms of oxidative addition and reductive elimination of a range of synthetically relevant bonds at Al(I) centres, establishing the principles governing this fundamental reactivity.
- Develop new ligand frameworks to support of Al(I) centres and evaluate the effect of the ligand on oxidative addition/reductive elimination at Al centres.
- Investigate methods for Al-mediated functionalisation of organic compounds by exploring the reactivity of E-H oxidative addition products with unsaturated organic compounds.
Max ERC Funding
1 493 679 €
Duration
Start date: 2017-03-01, End date: 2022-02-28
Project acronym ALEXANDRIA
Project Large-Scale Formal Proof for the Working Mathematician
Researcher (PI) Lawrence PAULSON
Host Institution (HI) THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE
Call Details Advanced Grant (AdG), PE6, ERC-2016-ADG
Summary Mathematical proofs have always been prone to error. Today, proofs can be hundreds of pages long and combine results from many specialisms, making them almost impossible to check. One solution is to deploy modern verification technology. Interactive theorem provers have demonstrated their potential as vehicles for formalising mathematics through achievements such as the verification of the Kepler Conjecture. Proofs done using such tools reach a high standard of correctness.
However, existing theorem provers are unsuitable for mathematics. Their formal proofs are unreadable. They struggle to do simple tasks, such as evaluating limits. They lack much basic mathematics, and the material they do have is difficult to locate and apply.
ALEXANDRIA will create a proof development environment attractive to working mathematicians, utilising the best technology available across computer science. Its focus will be the management and use of large-scale mathematical knowledge, both theorems and algorithms. The project will employ mathematicians to investigate the formalisation of mathematics in practice. Our already substantial formalised libraries will serve as the starting point. They will be extended and annotated to support sophisticated searches. Techniques will be borrowed from machine learning, information retrieval and natural language processing. Algorithms will be treated similarly: ALEXANDRIA will help users find and invoke the proof methods and algorithms appropriate for the task.
ALEXANDRIA will provide (1) comprehensive formal mathematical libraries; (2) search within libraries, and the mining of libraries for proof patterns; (3) automated support for the construction of large formal proofs; (4) sound and practical computer algebra tools.
ALEXANDRIA will be based on legible structured proofs. Formal proofs should be not mere code, but a machine-checkable form of communication between mathematicians.
Summary
Mathematical proofs have always been prone to error. Today, proofs can be hundreds of pages long and combine results from many specialisms, making them almost impossible to check. One solution is to deploy modern verification technology. Interactive theorem provers have demonstrated their potential as vehicles for formalising mathematics through achievements such as the verification of the Kepler Conjecture. Proofs done using such tools reach a high standard of correctness.
However, existing theorem provers are unsuitable for mathematics. Their formal proofs are unreadable. They struggle to do simple tasks, such as evaluating limits. They lack much basic mathematics, and the material they do have is difficult to locate and apply.
ALEXANDRIA will create a proof development environment attractive to working mathematicians, utilising the best technology available across computer science. Its focus will be the management and use of large-scale mathematical knowledge, both theorems and algorithms. The project will employ mathematicians to investigate the formalisation of mathematics in practice. Our already substantial formalised libraries will serve as the starting point. They will be extended and annotated to support sophisticated searches. Techniques will be borrowed from machine learning, information retrieval and natural language processing. Algorithms will be treated similarly: ALEXANDRIA will help users find and invoke the proof methods and algorithms appropriate for the task.
ALEXANDRIA will provide (1) comprehensive formal mathematical libraries; (2) search within libraries, and the mining of libraries for proof patterns; (3) automated support for the construction of large formal proofs; (4) sound and practical computer algebra tools.
ALEXANDRIA will be based on legible structured proofs. Formal proofs should be not mere code, but a machine-checkable form of communication between mathematicians.
Max ERC Funding
2 430 140 €
Duration
Start date: 2017-09-01, End date: 2022-08-31
Project acronym ALKENoNE
Project Algal Lipids: the Key to Earth Now and aNcient Earth
Researcher (PI) Jaime Lynn Toney
Host Institution (HI) UNIVERSITY OF GLASGOW
Call Details Starting Grant (StG), PE10, ERC-2014-STG
Summary Alkenones are algal lipids that have been used for decades to reconstruct quantitative past sea surface temperature. Although alkenones are being discovered in an increasing number of lake sites worldwide, only two terrestrial temperature records have been reconstructed so far. The development of this research field is limited by the lack of interdisciplinary research that combines modern biological and ecological algal research with the organic geochemical techniques needed to develop a quantitative biomarker (or molecular fossil) for past lake temperatures. More research is needed for alkenones to become a widely used tool for reconstructing past terrestrial temperature change. The early career Principal Investigator has discovered a new lake alkenone-producing species of haptophyte algae that produces alkenones in high abundances both in the environment and in laboratory cultures. This makes the new species an ideal organism for developing a culture-based temperature calibration and exploring other potential environmental controls. In this project, alkenone production will be manipulated, and monitored using state-of-the-art photobioreactors with real-time detectors for cell density, light, and temperature. The latest algal culture and isolation techniques that are used in microalgal biofuel development will be applied to developing the lake temperature proxy. The objectives will be achieved through the analysis of 90 new Canadian lakes to develop a core-top temperature calibration across a large latitudinal and temperature gradient (Δ latitude = 5°, Δ spring surface temperature = 9°C). The results will be used to assess how regional palaeo-temperature (Uk37), palaeo-moisture (δDwax) and palaeo-evaporation (δDalgal) respond during times of past global warmth (e.g., Medieval Warm Period, 900-1200 AD) to find an accurate analogue for assessing future drought risk in the interior of Canada.
Summary
Alkenones are algal lipids that have been used for decades to reconstruct quantitative past sea surface temperature. Although alkenones are being discovered in an increasing number of lake sites worldwide, only two terrestrial temperature records have been reconstructed so far. The development of this research field is limited by the lack of interdisciplinary research that combines modern biological and ecological algal research with the organic geochemical techniques needed to develop a quantitative biomarker (or molecular fossil) for past lake temperatures. More research is needed for alkenones to become a widely used tool for reconstructing past terrestrial temperature change. The early career Principal Investigator has discovered a new lake alkenone-producing species of haptophyte algae that produces alkenones in high abundances both in the environment and in laboratory cultures. This makes the new species an ideal organism for developing a culture-based temperature calibration and exploring other potential environmental controls. In this project, alkenone production will be manipulated, and monitored using state-of-the-art photobioreactors with real-time detectors for cell density, light, and temperature. The latest algal culture and isolation techniques that are used in microalgal biofuel development will be applied to developing the lake temperature proxy. The objectives will be achieved through the analysis of 90 new Canadian lakes to develop a core-top temperature calibration across a large latitudinal and temperature gradient (Δ latitude = 5°, Δ spring surface temperature = 9°C). The results will be used to assess how regional palaeo-temperature (Uk37), palaeo-moisture (δDwax) and palaeo-evaporation (δDalgal) respond during times of past global warmth (e.g., Medieval Warm Period, 900-1200 AD) to find an accurate analogue for assessing future drought risk in the interior of Canada.
Max ERC Funding
940 883 €
Duration
Start date: 2015-04-01, End date: 2020-03-31
Project acronym AtoFun
Project Atomic Scale Defects: Structure and Function
Researcher (PI) Felix HOFMANN
Host Institution (HI) THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Call Details Starting Grant (StG), PE5, ERC-2016-STG
Summary Atomic scale defects play a key role in determining the behaviour of all crystalline materials, profoundly modifying mechanical, thermal and electrical properties. Many current technological applications make do with phenomenological descriptions of these effects; yet myriad intriguing questions about the fundamental link between defect structure and material function remain.
Transmission electron microscopy revolutionised the study of atomic scale defects by enabling their direct imaging. The novel coherent X-ray diffraction techniques developed in this project promise a similar advancement, making it possible to probe the strain fields that govern defect interactions in 3D with high spatial resolution (<10 nm). They will allow us to clarify the effect of impurities and retained gas on dislocation strain fields, shedding light on opportunities to engineer dislocation properties. The exceptional strain sensitivity of coherent diffraction will enable us to explore the fundamental mechanisms governing the behaviour of ion-implantation-induced point defects that are invisible to TEM. While we concentrate on dislocations and point defects, the new techniques will apply to all crystalline materials where defects are important. Our characterisation of defect structure will be combined with laser transient grating measurements of thermal transport changes due to specific defect populations. This unique multifaceted perspective of defect behaviour will transform our ability to devise modelling approaches linking defect structure to material function.
Our proof-of-concept results highlight the feasibility of this ambitious research project. It opens up a vast range of exciting possibilities to gain a deep, fundamental understanding of atomic scale defects and their effect on material function. This is an essential prerequisite for exploiting and engineering defects to enhance material properties.
Summary
Atomic scale defects play a key role in determining the behaviour of all crystalline materials, profoundly modifying mechanical, thermal and electrical properties. Many current technological applications make do with phenomenological descriptions of these effects; yet myriad intriguing questions about the fundamental link between defect structure and material function remain.
Transmission electron microscopy revolutionised the study of atomic scale defects by enabling their direct imaging. The novel coherent X-ray diffraction techniques developed in this project promise a similar advancement, making it possible to probe the strain fields that govern defect interactions in 3D with high spatial resolution (<10 nm). They will allow us to clarify the effect of impurities and retained gas on dislocation strain fields, shedding light on opportunities to engineer dislocation properties. The exceptional strain sensitivity of coherent diffraction will enable us to explore the fundamental mechanisms governing the behaviour of ion-implantation-induced point defects that are invisible to TEM. While we concentrate on dislocations and point defects, the new techniques will apply to all crystalline materials where defects are important. Our characterisation of defect structure will be combined with laser transient grating measurements of thermal transport changes due to specific defect populations. This unique multifaceted perspective of defect behaviour will transform our ability to devise modelling approaches linking defect structure to material function.
Our proof-of-concept results highlight the feasibility of this ambitious research project. It opens up a vast range of exciting possibilities to gain a deep, fundamental understanding of atomic scale defects and their effect on material function. This is an essential prerequisite for exploiting and engineering defects to enhance material properties.
Max ERC Funding
1 610 231 €
Duration
Start date: 2017-03-01, End date: 2022-02-28
