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 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 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 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 BeyondtheElite
Project Beyond the Elite: Jewish Daily Life in Medieval Europe
Researcher (PI) Elisheva Baumgarten
Host Institution (HI) THE HEBREW UNIVERSITY OF JERUSALEM
Call Details Consolidator Grant (CoG), SH6, ERC-2015-CoG
Summary The two fundamental challenges of this project are the integration of medieval Jewries and their histories within the framework of European history without undermining their distinct communal status and the creation of a history of everyday medieval Jewish life that includes those who were not part of the learned elite. The study will focus on the Jewish communities of northern Europe (roughly modern Germany, northern France and England) from 1100-1350. From the mid-thirteenth century these medieval Jewish communities were subject to growing persecution. The approaches proposed to access daily praxis seek to highlight tangible dimensions of religious life rather than the more common study of ideologies to date. This task is complex because the extant sources in Hebrew as well as those in Latin and vernacular were written by the learned elite and will require a broad survey of multiple textual and material sources.
Four main strands will be examined and combined:
1. An outline of the strata of Jewish society, better defining the elites and other groups.
2. A study of select communal and familial spaces such as the house, the synagogue, the market place have yet to be examined as social spaces.
3. Ritual and urban rhythms especially the annual cycle, connecting between Jewish and Christian environments.
4. Material culture, as objects were used by Jews and Christians alike.
Aspects of material culture, the physical environment and urban rhythms are often described as “neutral” yet will be mined to demonstrate how they exemplified difference while being simultaneously ubiquitous in local cultures. The deterioration of relations between Jews and Christians will provide a gauge for examining change during this period. The final stage of the project will include comparative case studies of other Jewish communities. I expect my findings will inform scholars of medieval culture at large and promote comparative methodologies for studying other minority ethnic groups
Summary
The two fundamental challenges of this project are the integration of medieval Jewries and their histories within the framework of European history without undermining their distinct communal status and the creation of a history of everyday medieval Jewish life that includes those who were not part of the learned elite. The study will focus on the Jewish communities of northern Europe (roughly modern Germany, northern France and England) from 1100-1350. From the mid-thirteenth century these medieval Jewish communities were subject to growing persecution. The approaches proposed to access daily praxis seek to highlight tangible dimensions of religious life rather than the more common study of ideologies to date. This task is complex because the extant sources in Hebrew as well as those in Latin and vernacular were written by the learned elite and will require a broad survey of multiple textual and material sources.
Four main strands will be examined and combined:
1. An outline of the strata of Jewish society, better defining the elites and other groups.
2. A study of select communal and familial spaces such as the house, the synagogue, the market place have yet to be examined as social spaces.
3. Ritual and urban rhythms especially the annual cycle, connecting between Jewish and Christian environments.
4. Material culture, as objects were used by Jews and Christians alike.
Aspects of material culture, the physical environment and urban rhythms are often described as “neutral” yet will be mined to demonstrate how they exemplified difference while being simultaneously ubiquitous in local cultures. The deterioration of relations between Jews and Christians will provide a gauge for examining change during this period. The final stage of the project will include comparative case studies of other Jewish communities. I expect my findings will inform scholars of medieval culture at large and promote comparative methodologies for studying other minority ethnic groups
Max ERC Funding
1 941 688 €
Duration
Start date: 2016-11-01, End date: 2021-10-31
Project acronym BioMet
Project Selective Functionalization of Saturated Hydrocarbons
Researcher (PI) Ilan MAREK
Host Institution (HI) TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Call Details Advanced Grant (AdG), PE5, ERC-2017-ADG
Summary Despite that C–H functionalization represents a paradigm shift from the standard logic of organic synthesis, the selective activation of non-functionalized alkanes has puzzled chemists for centuries and is always referred to one of the remaining major challenges in chemical sciences. Alkanes are inert compounds representing the major constituents of natural gas and petroleum. Converting these cheap and widely available hydrocarbon feedstocks into added-value intermediates would tremendously affect the field of chemistry. For long saturated hydrocarbons, one must distinguish between non-equivalent but chemically very similar alkane substrate C−H bonds, and for functionalization at the terminus position, one must favor activation of the stronger, primary C−H bonds at the expense of weaker and numerous secondary C-H bonds. The goal of this work is to develop a general principle in organic synthesis for the preparation of a wide variety of more complex molecular architectures from saturated hydrocarbons. In our approach, the alkane will first be transformed into an alkene that will subsequently be engaged in a metal-catalyzed hydrometalation/migration sequence. The first step of the sequence, ideally represented by the removal of two hydrogen atoms, will be performed by the use of a mutated strain of Rhodococcus. The position and geometry of the formed double bond has no effect on the second step of the reaction as the metal-catalyzed hydrometalation/migration will isomerize the double bond along the carbon skeleton to selectively produce the primary organometallic species. Trapping the resulting organometallic derivatives with a large variety of electrophiles will provide the desired functionalized alkane. This work will lead to the invention of new, selective and efficient processes for the utilization of simple hydrocarbons and valorize the synthetic potential of raw hydrocarbon feedstock for the environmentally benign production of new compounds and new materials.
Summary
Despite that C–H functionalization represents a paradigm shift from the standard logic of organic synthesis, the selective activation of non-functionalized alkanes has puzzled chemists for centuries and is always referred to one of the remaining major challenges in chemical sciences. Alkanes are inert compounds representing the major constituents of natural gas and petroleum. Converting these cheap and widely available hydrocarbon feedstocks into added-value intermediates would tremendously affect the field of chemistry. For long saturated hydrocarbons, one must distinguish between non-equivalent but chemically very similar alkane substrate C−H bonds, and for functionalization at the terminus position, one must favor activation of the stronger, primary C−H bonds at the expense of weaker and numerous secondary C-H bonds. The goal of this work is to develop a general principle in organic synthesis for the preparation of a wide variety of more complex molecular architectures from saturated hydrocarbons. In our approach, the alkane will first be transformed into an alkene that will subsequently be engaged in a metal-catalyzed hydrometalation/migration sequence. The first step of the sequence, ideally represented by the removal of two hydrogen atoms, will be performed by the use of a mutated strain of Rhodococcus. The position and geometry of the formed double bond has no effect on the second step of the reaction as the metal-catalyzed hydrometalation/migration will isomerize the double bond along the carbon skeleton to selectively produce the primary organometallic species. Trapping the resulting organometallic derivatives with a large variety of electrophiles will provide the desired functionalized alkane. This work will lead to the invention of new, selective and efficient processes for the utilization of simple hydrocarbons and valorize the synthetic potential of raw hydrocarbon feedstock for the environmentally benign production of new compounds and new materials.
Max ERC Funding
2 499 375 €
Duration
Start date: 2018-11-01, End date: 2023-10-31
Project acronym BIONICS
Project Bio-Inspired Routes for Controlling the Structure and Properties of Materials: Reusing proven tricks on new materials
Researcher (PI) Boaz Pokroy
Host Institution (HI) TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Call Details Starting Grant (StG), PE5, ERC-2013-StG
Summary "In the course of biomineralization, organisms produce a large variety of functional biogenic crystals that exhibit fascinating mechanical, optical, magnetic and other characteristics. More specifically, when living organisms grow crystals they can effectively control polymorph selection as well as the crystal morphology, shape, and even atomic structure. Materials existing in nature have extraordinary and specific functions, yet the materials employed in nature are quite different from those engineers would select.
I propose to emulate specific strategies used by organisms in forming structural biogenic crystals, and to apply these strategies biomimetically so as to form new structural materials with new properties and characteristics. This bio-inspired approach will involve the adoption of three specific biological strategies. We believe that this procedure will open up new ways to control the structure and properties of smart materials.
The three bio-inspired strategies that we will utilize are:
(i) to control the short-range order of amorphous materials, making it possible to predetermine the polymorph obtained when they transform from the amorphous to the succeeding crystalline phase;
(ii) to control the morphology of single crystals of various functional materials so that they can have intricate and curved surfaces and yet maintain their single-crystal nature;
(iii) to entrap organic molecules into single crystals of functional materials so as to tailor and manipulate their electronic structure.
The proposed research has significant potential for opening up new routes for the formation of novel functional materials. Specifically, it will make it possible for us
(1) to produce single, intricately shaped crystals without the need to etch, drill or polish;
(2) to control the short-range order of amorphous materials and hence the polymorph of the successive crystalline phase;
(3) to tune the band gap of semiconductors via incorporation of tailored bio-molecules."
Summary
"In the course of biomineralization, organisms produce a large variety of functional biogenic crystals that exhibit fascinating mechanical, optical, magnetic and other characteristics. More specifically, when living organisms grow crystals they can effectively control polymorph selection as well as the crystal morphology, shape, and even atomic structure. Materials existing in nature have extraordinary and specific functions, yet the materials employed in nature are quite different from those engineers would select.
I propose to emulate specific strategies used by organisms in forming structural biogenic crystals, and to apply these strategies biomimetically so as to form new structural materials with new properties and characteristics. This bio-inspired approach will involve the adoption of three specific biological strategies. We believe that this procedure will open up new ways to control the structure and properties of smart materials.
The three bio-inspired strategies that we will utilize are:
(i) to control the short-range order of amorphous materials, making it possible to predetermine the polymorph obtained when they transform from the amorphous to the succeeding crystalline phase;
(ii) to control the morphology of single crystals of various functional materials so that they can have intricate and curved surfaces and yet maintain their single-crystal nature;
(iii) to entrap organic molecules into single crystals of functional materials so as to tailor and manipulate their electronic structure.
The proposed research has significant potential for opening up new routes for the formation of novel functional materials. Specifically, it will make it possible for us
(1) to produce single, intricately shaped crystals without the need to etch, drill or polish;
(2) to control the short-range order of amorphous materials and hence the polymorph of the successive crystalline phase;
(3) to tune the band gap of semiconductors via incorporation of tailored bio-molecules."
Max ERC Funding
1 500 000 €
Duration
Start date: 2013-09-01, End date: 2018-08-31
Project acronym BirNonArchGeom
Project Birational and non-archimedean geometries
Researcher (PI) Michael TEMKIN
Host Institution (HI) THE HEBREW UNIVERSITY OF JERUSALEM
Call Details Consolidator Grant (CoG), PE1, ERC-2017-COG
Summary Resolution of singularities is one of classical, central and difficult areas of algebraic geometry, with a centennial history of intensive research and contributions of such great names as Zariski, Hironaka and Abhyankar. Nowadays, desingularization of schemes of characteristic zero is very well understood, while semistable reduction of morphisms and desingularization in positive characteristic are still waiting for major breakthroughs. In addition to the classical techniques with their triumph in characteristic zero, modern resolution of singularities includes de Jong's method of alterations, toroidal methods, formal analytic and non-archimedean methods, etc.
The aim of the proposed research is to study nearly all directions in resolution of singularities and semistable reduction, as well as the wild ramification phenomena, which are probably the main obstacle to transfer methods from characteristic zero to positive characteristic.
The methods of algebraic and non-archimedean geometries are intertwined in the proposal, though algebraic geometry is somewhat dominating, especially due to the new stack-theoretic techniques. It seems very probable that increasing the symbiosis between birational and non-archimedean geometries will be one of by-products of this research.
Summary
Resolution of singularities is one of classical, central and difficult areas of algebraic geometry, with a centennial history of intensive research and contributions of such great names as Zariski, Hironaka and Abhyankar. Nowadays, desingularization of schemes of characteristic zero is very well understood, while semistable reduction of morphisms and desingularization in positive characteristic are still waiting for major breakthroughs. In addition to the classical techniques with their triumph in characteristic zero, modern resolution of singularities includes de Jong's method of alterations, toroidal methods, formal analytic and non-archimedean methods, etc.
The aim of the proposed research is to study nearly all directions in resolution of singularities and semistable reduction, as well as the wild ramification phenomena, which are probably the main obstacle to transfer methods from characteristic zero to positive characteristic.
The methods of algebraic and non-archimedean geometries are intertwined in the proposal, though algebraic geometry is somewhat dominating, especially due to the new stack-theoretic techniques. It seems very probable that increasing the symbiosis between birational and non-archimedean geometries will be one of by-products of this research.
Max ERC Funding
1 365 600 €
Duration
Start date: 2018-05-01, End date: 2023-04-30
Project acronym BOTTOM-UP_SYSCHEM
Project Systems Chemistry from Bottom Up: Switching, Gating and Oscillations in Non Enzymatic Peptide Networks
Researcher (PI) Gonen Ashkenasy
Host Institution (HI) BEN-GURION UNIVERSITY OF THE NEGEV
Call Details Starting Grant (StG), PE5, ERC-2010-StG_20091028
Summary The study of synthetic molecular networks is of fundamental importance for understanding the organizational principles of biological systems and may well be the key to unraveling the origins of life. In addition, such systems may be useful for parallel synthesis of molecules, implementation of catalysis via multi-step pathways, and as media for various applications in nano-medicine and nano-electronics. We have been involved recently in developing peptide-based replicating networks and revealed their dynamic characteristics. We argue here that the structural information embedded in the polypeptide chains is sufficiently rich to allow the construction of peptide 'Systems Chemistry', namely, to facilitate the use of replicating networks as cell-mimetics, featuring complex dynamic behavior. To bring this novel idea to reality, we plan to take a unique holistic approach by studying such networks both experimentally and via simulations, for elucidating basic-principles and towards applications in adjacent fields, such as molecular electronics. Towards realizing these aims, we will study three separate but inter-related objectives: (i) design and characterization of networks that react and rewire in response to external triggers, such as light, (ii) design of networks that operate via new dynamic rules of product formation that lead to oscillations, and (iii) exploitation of the molecular information gathered from the networks as means to control switching and gating in molecular electronic devices. We believe that achieving the project's objectives will be highly significant for the development of the arising field of Systems Chemistry, and in addition will provide valuable tools for studying related scientific fields, such as systems biology and molecular electronics.
Summary
The study of synthetic molecular networks is of fundamental importance for understanding the organizational principles of biological systems and may well be the key to unraveling the origins of life. In addition, such systems may be useful for parallel synthesis of molecules, implementation of catalysis via multi-step pathways, and as media for various applications in nano-medicine and nano-electronics. We have been involved recently in developing peptide-based replicating networks and revealed their dynamic characteristics. We argue here that the structural information embedded in the polypeptide chains is sufficiently rich to allow the construction of peptide 'Systems Chemistry', namely, to facilitate the use of replicating networks as cell-mimetics, featuring complex dynamic behavior. To bring this novel idea to reality, we plan to take a unique holistic approach by studying such networks both experimentally and via simulations, for elucidating basic-principles and towards applications in adjacent fields, such as molecular electronics. Towards realizing these aims, we will study three separate but inter-related objectives: (i) design and characterization of networks that react and rewire in response to external triggers, such as light, (ii) design of networks that operate via new dynamic rules of product formation that lead to oscillations, and (iii) exploitation of the molecular information gathered from the networks as means to control switching and gating in molecular electronic devices. We believe that achieving the project's objectives will be highly significant for the development of the arising field of Systems Chemistry, and in addition will provide valuable tools for studying related scientific fields, such as systems biology and molecular electronics.
Max ERC Funding
1 500 000 €
Duration
Start date: 2010-10-01, End date: 2015-09-30
