Project acronym 2D-CHEM
Project Two-Dimensional Chemistry towards New Graphene Derivatives
Researcher (PI) Michal Otyepka
Host Institution (HI) UNIVERZITA PALACKEHO V OLOMOUCI
Call Details Consolidator Grant (CoG), PE5, ERC-2015-CoG
Summary The suite of graphene’s unique properties and applications can be enormously enhanced by its functionalization. As non-covalently functionalized graphenes do not target all graphene’s properties and may suffer from limited stability, covalent functionalization represents a promising way for controlling graphene’s properties. To date, only a few well-defined graphene derivatives have been introduced. Among them, fluorographene (FG) stands out as a prominent member because of its easy synthesis and high stability. Being a perfluorinated hydrocarbon, FG was believed to be as unreactive as the two-dimensional counterpart perfluoropolyethylene (Teflon®). However, our recent experiments showed that FG is not chemically inert and can be used as a viable precursor for synthesizing graphene derivatives. This surprising behavior indicates that common textbook grade knowledge cannot blindly be applied to the chemistry of 2D materials. Further, there might be specific rules behind the chemistry of 2D materials, forming a new chemical discipline we tentatively call 2D chemistry. The main aim of the project is to explore, identify and apply the rules of 2D chemistry starting from FG. Using the knowledge gained of 2D chemistry, we will attempt to control the chemistry of various 2D materials aimed at preparing stable graphene derivatives with designed properties, e.g., 1-3 eV band gap, fluorescent properties, sustainable magnetic ordering and dispersability in polar media. The new graphene derivatives will be applied in sensing, imaging, magnetic delivery and catalysis and new emerging applications arising from the synergistic phenomena are expected. We envisage that new applications will be opened up that benefit from the 2D scaffold and tailored properties of the synthesized derivatives. The derivatives will be used for the synthesis of 3D hybrid materials by covalent linking of the 2D sheets joined with other organic and inorganic molecules, nanomaterials or biomacromolecules.
Summary
The suite of graphene’s unique properties and applications can be enormously enhanced by its functionalization. As non-covalently functionalized graphenes do not target all graphene’s properties and may suffer from limited stability, covalent functionalization represents a promising way for controlling graphene’s properties. To date, only a few well-defined graphene derivatives have been introduced. Among them, fluorographene (FG) stands out as a prominent member because of its easy synthesis and high stability. Being a perfluorinated hydrocarbon, FG was believed to be as unreactive as the two-dimensional counterpart perfluoropolyethylene (Teflon®). However, our recent experiments showed that FG is not chemically inert and can be used as a viable precursor for synthesizing graphene derivatives. This surprising behavior indicates that common textbook grade knowledge cannot blindly be applied to the chemistry of 2D materials. Further, there might be specific rules behind the chemistry of 2D materials, forming a new chemical discipline we tentatively call 2D chemistry. The main aim of the project is to explore, identify and apply the rules of 2D chemistry starting from FG. Using the knowledge gained of 2D chemistry, we will attempt to control the chemistry of various 2D materials aimed at preparing stable graphene derivatives with designed properties, e.g., 1-3 eV band gap, fluorescent properties, sustainable magnetic ordering and dispersability in polar media. The new graphene derivatives will be applied in sensing, imaging, magnetic delivery and catalysis and new emerging applications arising from the synergistic phenomena are expected. We envisage that new applications will be opened up that benefit from the 2D scaffold and tailored properties of the synthesized derivatives. The derivatives will be used for the synthesis of 3D hybrid materials by covalent linking of the 2D sheets joined with other organic and inorganic molecules, nanomaterials or biomacromolecules.
Max ERC Funding
1 831 103 €
Duration
Start date: 2016-06-01, End date: 2021-05-31
Project acronym 2D-PnictoChem
Project Chemistry and Interface Control of Novel 2D-Pnictogen Nanomaterials
Researcher (PI) Gonzalo ABELLAN SAEZ
Host Institution (HI) UNIVERSITAT DE VALENCIA
Call Details Starting Grant (StG), PE5, ERC-2018-STG
Summary 2D-PnictoChem aims at exploring the Chemistry of a novel class of graphene-like 2D layered
elemental materials of group 15, the pnictogens: P, As, Sb, and Bi. In the last few years, these materials
have taken the field of Materials Science by storm since they can outperform and/or complement graphene
properties. Their strongly layer-dependent unique properties range from semiconducting to metallic,
including high carrier mobilities, tunable bandgaps, strong spin-orbit coupling or transparency. However,
the Chemistry of pnictogens is still in its infancy, remaining largely unexplored. This is the niche that
2D-PnictoChem aims to fill. By mastering the interface chemistry, we will develop the assembly of 2Dpnictogens
in complex hybrid heterostructures for the first time. Success will rely on a cross-disciplinary
approach combining both Inorganic- and Organic Chemistry with Solid-state Physics, including: 1)
Synthetizing and exfoliating high quality ultra-thin layer pnictogens, providing reliable access down to
the monolayer limit. 2) Achieving their chemical functionalization via both non-covalent and covalent
approaches in order to tailor at will their properties, decipher reactivity patterns and enable controlled
doping avenues. 3) Developing hybrid architectures through a precise chemical control of the interface,
in order to promote unprecedented access to novel heterostructures. 4) Exploring novel applications
concepts achieving outstanding performances. These are all priorities in the European Union agenda
aimed at securing an affordable, clean energy future by developing more efficient hybrid systems for
batteries, electronic devices or applications in catalysis. The opportunity is unique to reduce Europe’s
dependence on external technology and the PI’s background is ideally suited to tackle these objectives,
counting as well on a multidisciplinary team of international collaborators.
Summary
2D-PnictoChem aims at exploring the Chemistry of a novel class of graphene-like 2D layered
elemental materials of group 15, the pnictogens: P, As, Sb, and Bi. In the last few years, these materials
have taken the field of Materials Science by storm since they can outperform and/or complement graphene
properties. Their strongly layer-dependent unique properties range from semiconducting to metallic,
including high carrier mobilities, tunable bandgaps, strong spin-orbit coupling or transparency. However,
the Chemistry of pnictogens is still in its infancy, remaining largely unexplored. This is the niche that
2D-PnictoChem aims to fill. By mastering the interface chemistry, we will develop the assembly of 2Dpnictogens
in complex hybrid heterostructures for the first time. Success will rely on a cross-disciplinary
approach combining both Inorganic- and Organic Chemistry with Solid-state Physics, including: 1)
Synthetizing and exfoliating high quality ultra-thin layer pnictogens, providing reliable access down to
the monolayer limit. 2) Achieving their chemical functionalization via both non-covalent and covalent
approaches in order to tailor at will their properties, decipher reactivity patterns and enable controlled
doping avenues. 3) Developing hybrid architectures through a precise chemical control of the interface,
in order to promote unprecedented access to novel heterostructures. 4) Exploring novel applications
concepts achieving outstanding performances. These are all priorities in the European Union agenda
aimed at securing an affordable, clean energy future by developing more efficient hybrid systems for
batteries, electronic devices or applications in catalysis. The opportunity is unique to reduce Europe’s
dependence on external technology and the PI’s background is ideally suited to tackle these objectives,
counting as well on a multidisciplinary team of international collaborators.
Max ERC Funding
1 499 419 €
Duration
Start date: 2018-11-01, End date: 2023-10-31
Project acronym 4DBIOSERS
Project Four-Dimensional Monitoring of Tumour Growth by Surface Enhanced Raman Scattering
Researcher (PI) Luis LIZ-MARZAN
Host Institution (HI) ASOCIACION CENTRO DE INVESTIGACION COOPERATIVA EN BIOMATERIALES- CIC biomaGUNE
Call Details Advanced Grant (AdG), PE5, ERC-2017-ADG
Summary Optical bioimaging is limited by visible light penetration depth and stability of fluorescent dyes over extended periods of time. Surface enhanced Raman scattering (SERS) offers the possibility to overcome these drawbacks, through SERS-encoded nanoparticle tags, which can be excited with near-IR light (within the biological transparency window), providing high intensity, stable, multiplexed signals. SERS can also be used to monitor relevant bioanalytes within cells and tissues, during the development of diseases, such as tumours. In 4DBIOSERS we shall combine both capabilities of SERS, to go well beyond the current state of the art, by building three-dimensional scaffolds that support tissue (tumour) growth within a controlled environment, so that not only the fate of each (SERS-labelled) cell within the tumour can be monitored in real time (thus adding a fourth dimension to SERS bioimaging), but also recording the release of tumour metabolites and other indicators of cellular activity. Although 4DBIOSERS can be applied to a variety of diseases, we shall focus on cancer, melanoma and breast cancer in particular, as these are readily accessible by optical methods. We aim at acquiring a better understanding of tumour growth and dynamics, while avoiding animal experimentation. 3D printing will be used to generate hybrid scaffolds where tumour and healthy cells will be co-incubated to simulate a more realistic environment, thus going well beyond the potential of 2D cell cultures. Each cell type will be encoded with ultra-bright SERS tags, so that real-time monitoring can be achieved by confocal SERS microscopy. Tumour development will be correlated with simultaneous detection of various cancer biomarkers, during standard conditions and upon addition of selected drugs. The scope of 4DBIOSERS is multidisciplinary, as it involves the design of high-end nanocomposites, development of 3D cell culture models and optimization of emerging SERS tomography methods.
Summary
Optical bioimaging is limited by visible light penetration depth and stability of fluorescent dyes over extended periods of time. Surface enhanced Raman scattering (SERS) offers the possibility to overcome these drawbacks, through SERS-encoded nanoparticle tags, which can be excited with near-IR light (within the biological transparency window), providing high intensity, stable, multiplexed signals. SERS can also be used to monitor relevant bioanalytes within cells and tissues, during the development of diseases, such as tumours. In 4DBIOSERS we shall combine both capabilities of SERS, to go well beyond the current state of the art, by building three-dimensional scaffolds that support tissue (tumour) growth within a controlled environment, so that not only the fate of each (SERS-labelled) cell within the tumour can be monitored in real time (thus adding a fourth dimension to SERS bioimaging), but also recording the release of tumour metabolites and other indicators of cellular activity. Although 4DBIOSERS can be applied to a variety of diseases, we shall focus on cancer, melanoma and breast cancer in particular, as these are readily accessible by optical methods. We aim at acquiring a better understanding of tumour growth and dynamics, while avoiding animal experimentation. 3D printing will be used to generate hybrid scaffolds where tumour and healthy cells will be co-incubated to simulate a more realistic environment, thus going well beyond the potential of 2D cell cultures. Each cell type will be encoded with ultra-bright SERS tags, so that real-time monitoring can be achieved by confocal SERS microscopy. Tumour development will be correlated with simultaneous detection of various cancer biomarkers, during standard conditions and upon addition of selected drugs. The scope of 4DBIOSERS is multidisciplinary, as it involves the design of high-end nanocomposites, development of 3D cell culture models and optimization of emerging SERS tomography methods.
Max ERC Funding
2 410 771 €
Duration
Start date: 2018-10-01, End date: 2023-09-30
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 ADJUV-ANT VACCINES
Project Elucidating the Molecular Mechanisms of Synthetic Saponin Adjuvants and Development of Novel Self-Adjuvanting Vaccines
Researcher (PI) Alberto FERNANDEZ TEJADA
Host Institution (HI) ASOCIACION CENTRO DE INVESTIGACION COOPERATIVA EN BIOCIENCIAS
Call Details Starting Grant (StG), PE5, ERC-2016-STG
Summary The clinical success of anticancer and antiviral vaccines often requires the use of an adjuvant, a substance that helps stimulate the body’s immune response to the vaccine, making it work better. However, few adjuvants are sufficiently potent and non-toxic for clinical use; moreover, it is not really known how they work. Current vaccine approaches based on weak carbohydrate and glycopeptide antigens are not being particularly effective to induce the human immune system to mount an effective fight against cancer. Despite intensive research and several clinical trials, no such carbohydrate-based antitumor vaccine has yet been approved for public use. In this context, the proposed project has a double, ultimate goal based on applying chemistry to address the above clear gaps in the adjuvant-vaccine field. First, I will develop new improved adjuvants and novel chemical strategies towards more effective, self-adjuvanting synthetic vaccines. Second, I will probe deeply into the molecular mechanisms of the synthetic constructs by combining extensive immunological evaluations with molecular target identification and detailed conformational studies. Thus, the singularity of this multidisciplinary proposal stems from the integration of its main objectives and approaches connecting chemical synthesis and chemical/structural biology with cellular and molecular immunology. This ground-breaking project at the chemistry-biology frontier will allow me to establish my own independent research group and explore key unresolved mechanistic questions in the adjuvant/vaccine arena with extraordinary chemical precision. Therefore, with this transformative and timely research program I aim to (a) develop novel synthetic antitumor and antiviral vaccines with improved properties and efficacy for their prospective translation into the clinic and (b) gain new critical insights into the molecular basis and three-dimensional structure underlying the biological activity of these constructs.
Summary
The clinical success of anticancer and antiviral vaccines often requires the use of an adjuvant, a substance that helps stimulate the body’s immune response to the vaccine, making it work better. However, few adjuvants are sufficiently potent and non-toxic for clinical use; moreover, it is not really known how they work. Current vaccine approaches based on weak carbohydrate and glycopeptide antigens are not being particularly effective to induce the human immune system to mount an effective fight against cancer. Despite intensive research and several clinical trials, no such carbohydrate-based antitumor vaccine has yet been approved for public use. In this context, the proposed project has a double, ultimate goal based on applying chemistry to address the above clear gaps in the adjuvant-vaccine field. First, I will develop new improved adjuvants and novel chemical strategies towards more effective, self-adjuvanting synthetic vaccines. Second, I will probe deeply into the molecular mechanisms of the synthetic constructs by combining extensive immunological evaluations with molecular target identification and detailed conformational studies. Thus, the singularity of this multidisciplinary proposal stems from the integration of its main objectives and approaches connecting chemical synthesis and chemical/structural biology with cellular and molecular immunology. This ground-breaking project at the chemistry-biology frontier will allow me to establish my own independent research group and explore key unresolved mechanistic questions in the adjuvant/vaccine arena with extraordinary chemical precision. Therefore, with this transformative and timely research program I aim to (a) develop novel synthetic antitumor and antiviral vaccines with improved properties and efficacy for their prospective translation into the clinic and (b) gain new critical insights into the molecular basis and three-dimensional structure underlying the biological activity of these constructs.
Max ERC Funding
1 499 219 €
Duration
Start date: 2017-03-01, End date: 2022-02-28
Project acronym AGALT
Project Asymptotic Geometric Analysis and Learning Theory
Researcher (PI) Shahar Mendelson
Host Institution (HI) TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Call Details Starting Grant (StG), PE1, ERC-2007-StG
Summary In a typical learning problem one tries to approximate an unknown function by a function from a given class using random data, sampled according to an unknown measure. In this project we will be interested in parameters that govern the complexity of a learning problem. It turns out that this complexity is determined by the geometry of certain sets in high dimension that are connected to the given class (random coordinate projections of the class). Thus, one has to understand the structure of these sets as a function of the dimension - which is given by the cardinality of the random sample. The resulting analysis leads to many theoretical questions in Asymptotic Geometric Analysis, Probability (most notably, Empirical Processes Theory) and Combinatorics, which are of independent interest beyond the application to Learning Theory. Our main goal is to describe the role of various complexity parameters involved in a learning problem, to analyze the connections between them and to investigate the way they determine the geometry of the relevant high dimensional sets. Some of the questions we intend to tackle are well known open problems and making progress towards their solution will have a significant theoretical impact. Moreover, this project should lead to a more complete theory of learning and is likely to have some practical impact, for example, in the design of more efficient learning algorithms.
Summary
In a typical learning problem one tries to approximate an unknown function by a function from a given class using random data, sampled according to an unknown measure. In this project we will be interested in parameters that govern the complexity of a learning problem. It turns out that this complexity is determined by the geometry of certain sets in high dimension that are connected to the given class (random coordinate projections of the class). Thus, one has to understand the structure of these sets as a function of the dimension - which is given by the cardinality of the random sample. The resulting analysis leads to many theoretical questions in Asymptotic Geometric Analysis, Probability (most notably, Empirical Processes Theory) and Combinatorics, which are of independent interest beyond the application to Learning Theory. Our main goal is to describe the role of various complexity parameters involved in a learning problem, to analyze the connections between them and to investigate the way they determine the geometry of the relevant high dimensional sets. Some of the questions we intend to tackle are well known open problems and making progress towards their solution will have a significant theoretical impact. Moreover, this project should lead to a more complete theory of learning and is likely to have some practical impact, for example, in the design of more efficient learning algorithms.
Max ERC Funding
750 000 €
Duration
Start date: 2009-03-01, End date: 2014-02-28
Project acronym ANGEOM
Project Geometric analysis in the Euclidean space
Researcher (PI) Xavier Tolsa Domenech
Host Institution (HI) UNIVERSITAT AUTONOMA DE BARCELONA
Call Details Advanced Grant (AdG), PE1, ERC-2012-ADG_20120216
Summary "We propose to study different questions in the area of the so called geometric analysis. Most of the topics we are interested in deal with the connection between the behavior of singular integrals and the geometry of sets and measures. The study of this connection has been shown to be extremely helpful in the solution of certain long standing problems in the last years, such as the solution of the Painlev\'e problem or the obtaining of the optimal distortion bounds for quasiconformal mappings by Astala.
More specifically, we would like to study the relationship between the L^2 boundedness of singular integrals associated with Riesz and other related kernels, and rectifiability and other geometric notions. The so called David-Semmes problem is probably the main open problem in this area. Up to now, the techniques used to deal with this problem come from multiscale analysis and involve ideas from Littlewood-Paley theory and quantitative techniques of rectifiability. We propose to apply new ideas that combine variational arguments with other techniques which have connections with mass transportation. Further, we think that it is worth to explore in more detail the connection among mass transportation, singular integrals, and uniform rectifiability.
We are also interested in the field of quasiconformal mappings. We plan to study a problem regarding the quasiconformal distortion of quasicircles. This problem consists in proving that the bounds obtained recently by S. Smirnov on the dimension of K-quasicircles are optimal. We want to apply techniques from quantitative geometric measure theory to deal with this question.
Another question that we intend to explore lies in the interplay of harmonic analysis, geometric measure theory and partial differential equations. This concerns an old problem on the unique continuation of harmonic functions at the boundary open C^1 or Lipschitz domain. All the results known by now deal with smoother Dini domains."
Summary
"We propose to study different questions in the area of the so called geometric analysis. Most of the topics we are interested in deal with the connection between the behavior of singular integrals and the geometry of sets and measures. The study of this connection has been shown to be extremely helpful in the solution of certain long standing problems in the last years, such as the solution of the Painlev\'e problem or the obtaining of the optimal distortion bounds for quasiconformal mappings by Astala.
More specifically, we would like to study the relationship between the L^2 boundedness of singular integrals associated with Riesz and other related kernels, and rectifiability and other geometric notions. The so called David-Semmes problem is probably the main open problem in this area. Up to now, the techniques used to deal with this problem come from multiscale analysis and involve ideas from Littlewood-Paley theory and quantitative techniques of rectifiability. We propose to apply new ideas that combine variational arguments with other techniques which have connections with mass transportation. Further, we think that it is worth to explore in more detail the connection among mass transportation, singular integrals, and uniform rectifiability.
We are also interested in the field of quasiconformal mappings. We plan to study a problem regarding the quasiconformal distortion of quasicircles. This problem consists in proving that the bounds obtained recently by S. Smirnov on the dimension of K-quasicircles are optimal. We want to apply techniques from quantitative geometric measure theory to deal with this question.
Another question that we intend to explore lies in the interplay of harmonic analysis, geometric measure theory and partial differential equations. This concerns an old problem on the unique continuation of harmonic functions at the boundary open C^1 or Lipschitz domain. All the results known by now deal with smoother Dini domains."
Max ERC Funding
1 105 930 €
Duration
Start date: 2013-05-01, End date: 2018-04-30
Project acronym ARITHQUANTUMCHAOS
Project Arithmetic and Quantum Chaos
Researcher (PI) Zeev Rudnick
Host Institution (HI) TEL AVIV UNIVERSITY
Call Details Advanced Grant (AdG), PE1, ERC-2012-ADG_20120216
Summary Quantum Chaos is an emerging discipline which is crossing over from Physics into Pure Mathematics. The recent crossover is driven in part by a connection with Number Theory. This project explores several aspects of this interrelationship and is composed of a number of sub-projects. The sub-projects deal with: statistics of energy levels and wave functions of pseudo-integrable systems, a hitherto unexplored subject in the mathematical community which is not well understood in the physics community; with statistics of zeros of zeta functions over function fields, a purely number theoretic topic which is linked to the subproject on Quantum Chaos through the mysterious connections to Random Matrix Theory and an analogy between energy levels and zeta zeros; and with spatial statistics in arithmetic.
Summary
Quantum Chaos is an emerging discipline which is crossing over from Physics into Pure Mathematics. The recent crossover is driven in part by a connection with Number Theory. This project explores several aspects of this interrelationship and is composed of a number of sub-projects. The sub-projects deal with: statistics of energy levels and wave functions of pseudo-integrable systems, a hitherto unexplored subject in the mathematical community which is not well understood in the physics community; with statistics of zeros of zeta functions over function fields, a purely number theoretic topic which is linked to the subproject on Quantum Chaos through the mysterious connections to Random Matrix Theory and an analogy between energy levels and zeta zeros; and with spatial statistics in arithmetic.
Max ERC Funding
1 714 000 €
Duration
Start date: 2013-02-01, End date: 2019-01-31
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 BIDECASEOX
Project Bio-inspired Design of Catalysts for Selective Oxidations of C-H and C=C Bonds
Researcher (PI) Miguel Costas Salgueiro
Host Institution (HI) UNIVERSITAT DE GIRONA
Call Details Starting Grant (StG), PE5, ERC-2009-StG
Summary The selective functionalization of C-H and C=C bonds remains a formidable unsolved problem, owing to their inert nature. Novel alkane and alkene oxidation reactions exhibiting good and/or unprecedented selectivities will have a big impact on bulk and fine chemistry by opening novel methodologies that will allow removal of protection-deprotection sequences, thus streamlining synthetic strategies. These goals are targeted in this project via design of iron and manganese catalysts inspired by structural elements of the active site of non-heme enzymes of the Rieske Dioxygenase family. Selectivity is pursued via rational design of catalysts that will exploit substrate recognition-exclusion phenomena, and control over proton and electron affinity of the active species. Moreover, these catalysts will employ H2O2 as oxidant, and will operate under mild conditions (pressure and temperature). The fundamental mechanistic aspects of the catalytic reactions, and the species implicated in C-H and C=C oxidation events will also be studied with the aim of building on the necessary knowledge to design future generations of catalysts, and provide models to understand the chemistry taking place in non-heme iron and manganese-dependent oxygenases.
Summary
The selective functionalization of C-H and C=C bonds remains a formidable unsolved problem, owing to their inert nature. Novel alkane and alkene oxidation reactions exhibiting good and/or unprecedented selectivities will have a big impact on bulk and fine chemistry by opening novel methodologies that will allow removal of protection-deprotection sequences, thus streamlining synthetic strategies. These goals are targeted in this project via design of iron and manganese catalysts inspired by structural elements of the active site of non-heme enzymes of the Rieske Dioxygenase family. Selectivity is pursued via rational design of catalysts that will exploit substrate recognition-exclusion phenomena, and control over proton and electron affinity of the active species. Moreover, these catalysts will employ H2O2 as oxidant, and will operate under mild conditions (pressure and temperature). The fundamental mechanistic aspects of the catalytic reactions, and the species implicated in C-H and C=C oxidation events will also be studied with the aim of building on the necessary knowledge to design future generations of catalysts, and provide models to understand the chemistry taking place in non-heme iron and manganese-dependent oxygenases.
Max ERC Funding
1 299 998 €
Duration
Start date: 2009-11-01, End date: 2015-10-31
