Project acronym CORYPHEE
Project Cold Rydbergs: photoionization, electronic spectroscopy and electrostatic trapping
Researcher (PI) Frédéric Merkt
Host Institution (HI) EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Call Details Advanced Grant (AdG), PE4, ERC-2008-AdG
Summary Spectroscopic investigation of high (n >>20) molecular Rydberg states below and above the first adiabatic ionization threshold will be carried out with the aims of 1) obtaining fully resolved information on the vibrational, rotational, spin-orbit and hyperfine structures of these highly excited electronic states, 2) characterizing the role of nuclear spins in molecular photoionization, 3) determining the hyperfine structure of fundamental molecular cations at kHz resolution and accuracy by Rydberg series extrapolation, 4) measuring intervals between rovibrational levels of these molecular cations at sub MHz precision, 5) gaining a complete understanding, and providing an adequate description and classification, of angular momentum coupling (including nuclear spins) in high molecular Rydberg states, 6) testing theoretical predictions of the energy level structure of Rydberg molecules by ab initio multichannel quantum defect theory (MQDT) and of the rotational, vibrational and hyperfine levels of molecular cations by ab initio quantum chemistry and QED. The spectroscopic measurements using tunable narrow-band vacuum-ultraviolet and millimeter wave radiation sources will be performed on cold samples in supersonic beams as well as on trapped samples of translationally cold Rydberg atoms and molecules. To this end, our recent approach to trap H atoms in Rydberg states electrostatically (Hogan and Merkt, Phys. Rev. Lett. 100, 043001 (2008)) will be extended to molecules, and the possibility of transfering the trapped species from electrostatic traps to magnetic and optical traps will be explored.
Summary
Spectroscopic investigation of high (n >>20) molecular Rydberg states below and above the first adiabatic ionization threshold will be carried out with the aims of 1) obtaining fully resolved information on the vibrational, rotational, spin-orbit and hyperfine structures of these highly excited electronic states, 2) characterizing the role of nuclear spins in molecular photoionization, 3) determining the hyperfine structure of fundamental molecular cations at kHz resolution and accuracy by Rydberg series extrapolation, 4) measuring intervals between rovibrational levels of these molecular cations at sub MHz precision, 5) gaining a complete understanding, and providing an adequate description and classification, of angular momentum coupling (including nuclear spins) in high molecular Rydberg states, 6) testing theoretical predictions of the energy level structure of Rydberg molecules by ab initio multichannel quantum defect theory (MQDT) and of the rotational, vibrational and hyperfine levels of molecular cations by ab initio quantum chemistry and QED. The spectroscopic measurements using tunable narrow-band vacuum-ultraviolet and millimeter wave radiation sources will be performed on cold samples in supersonic beams as well as on trapped samples of translationally cold Rydberg atoms and molecules. To this end, our recent approach to trap H atoms in Rydberg states electrostatically (Hogan and Merkt, Phys. Rev. Lett. 100, 043001 (2008)) will be extended to molecules, and the possibility of transfering the trapped species from electrostatic traps to magnetic and optical traps will be explored.
Max ERC Funding
1 192 395 €
Duration
Start date: 2008-11-01, End date: 2013-10-31
Project acronym CRYTERION
Project Cryogenic Traps for Entanglement Research with Ions
Researcher (PI) Rainer Blatt
Host Institution (HI) UNIVERSITAET INNSBRUCK
Call Details Advanced Grant (AdG), PE2, ERC-2008-AdG
Summary Quantum computers offer a fundamentally new way of information processing. Within the scope of this proposal, quantum information processing with an ion trap quantum computer will be investigated. With the new combination of cryogenic technology and ion traps for quantum computing we intend to build a quantum information processor with strings of up to 50 ions and with two-dimensional ion arrays for an investigation of deterministic many-particle entanglement. The cryogenic traps will be applied for quantum simulations, for fundamental investigations concerning large-scale entanglement and for precision measurements enhanced by quantum metrology techniques employing entangled particles.
Summary
Quantum computers offer a fundamentally new way of information processing. Within the scope of this proposal, quantum information processing with an ion trap quantum computer will be investigated. With the new combination of cryogenic technology and ion traps for quantum computing we intend to build a quantum information processor with strings of up to 50 ions and with two-dimensional ion arrays for an investigation of deterministic many-particle entanglement. The cryogenic traps will be applied for quantum simulations, for fundamental investigations concerning large-scale entanglement and for precision measurements enhanced by quantum metrology techniques employing entangled particles.
Max ERC Funding
2 200 000 €
Duration
Start date: 2008-12-01, End date: 2013-11-30
Project acronym DAMAGE
Project DNA damage and the connection with cancer, premature aging and longevity
Researcher (PI) Jan Hendrik Jozef Hoeijmakers
Host Institution (HI) ERASMUS UNIVERSITAIR MEDISCH CENTRUM ROTTERDAM
Call Details Advanced Grant (AdG), LS1, ERC-2008-AdG
Summary We study DNA damage and genome stability and its impact on human health using nucleotide excision repair (NER) as paradigm. Patients with NER defects present a perplexing clinical heterogeneity ranging from extreme cancer predisposition to dramatic neurodevelopmental deficits. To elucidate the underlying mechanism we adopted an integral strategy from gene to patient and contributed to resolving the NER reaction in vitro and its dynamic organization in vivo, using molecular genetics, advanced life cell imaging and photobleaching. Mouse NER mutants revealed an unexpected link between DNA damage and (premature) aging, as strong as the DNA damage-cancer connection. We found a striking correlation between type/severity of the repair defect and degree of premature aging, with some mutants dying of aging in 3 weeks! Pathological and functional analysis and expression profiling confirmed that this is bona fide aging. Conditional mutants allowed targeting accelerated aging to specific organs/stages of development e.g. dramatic aging only in brain. Expression profiling revealed that short-lived repair mutants mount a survival response that attempts to extend lifespan by investing in defenses at the expense of growth. The ambitious objective of this multi-disciplinary proposal is to obtain an integral understanding of the biological/medical impact of DNA damage and the important survival response, with emphasis on rational-based prevention and intervention strategies for cancer and other aging-related diseases using the rapidly aging mouse mutants as tools. Triggering the survival response at adulthood is expected to postpone many aging-related diseases including cancer and to strongly improve quality of life at later age. We already identified compounds that influence rapid aging in mice and demonstrated the potency of the survival response to withstand ischemia reperfusion damage. Thus, this proposal addresses the major medical challenges faced by our society.
Summary
We study DNA damage and genome stability and its impact on human health using nucleotide excision repair (NER) as paradigm. Patients with NER defects present a perplexing clinical heterogeneity ranging from extreme cancer predisposition to dramatic neurodevelopmental deficits. To elucidate the underlying mechanism we adopted an integral strategy from gene to patient and contributed to resolving the NER reaction in vitro and its dynamic organization in vivo, using molecular genetics, advanced life cell imaging and photobleaching. Mouse NER mutants revealed an unexpected link between DNA damage and (premature) aging, as strong as the DNA damage-cancer connection. We found a striking correlation between type/severity of the repair defect and degree of premature aging, with some mutants dying of aging in 3 weeks! Pathological and functional analysis and expression profiling confirmed that this is bona fide aging. Conditional mutants allowed targeting accelerated aging to specific organs/stages of development e.g. dramatic aging only in brain. Expression profiling revealed that short-lived repair mutants mount a survival response that attempts to extend lifespan by investing in defenses at the expense of growth. The ambitious objective of this multi-disciplinary proposal is to obtain an integral understanding of the biological/medical impact of DNA damage and the important survival response, with emphasis on rational-based prevention and intervention strategies for cancer and other aging-related diseases using the rapidly aging mouse mutants as tools. Triggering the survival response at adulthood is expected to postpone many aging-related diseases including cancer and to strongly improve quality of life at later age. We already identified compounds that influence rapid aging in mice and demonstrated the potency of the survival response to withstand ischemia reperfusion damage. Thus, this proposal addresses the major medical challenges faced by our society.
Max ERC Funding
2 000 000 €
Duration
Start date: 2010-01-01, End date: 2014-12-31
Project acronym DARE
Project Soil Foundation Structure Systems Beyond Conventional Seismic Failure Thresholds: Application to New or Existing Structures and Monuments
Researcher (PI) George Gazetas
Host Institution (HI) NATIONAL TECHNICAL UNIVERSITY OF ATHENS - NTUA
Call Details Advanced Grant (AdG), PE8, ERC-2008-AdG
Summary The main goal of the proposed research is to investigate the possibility of allowing below-ground support systems to respond to strong seismic shaking by going beyond a number of thresholds that would conventionally imply failure and are today forbidden by codes. Such thresholds include : (a) sliding at the soil-foundation interface ; (b) separation and uplifting of a shallow foundation from the soils ; (c) mobilization of bearing capacity failure mechanism for shallow foundations ; (d) structural yielding of pile foundations ; (e) combination of some of the above. Whereas under static loading conditions a slight exceedance of such thresholds leads to failure, the oscillatory nature of seismic shaking will allow such exceedances for a short period of time, with perhaps no detrimental or irreparable consequences. The latter take the form of permanent foundation displacements, rotations, or injuries , which the designer will aspire to confine within rational limits. The motivation and the need for this research has come from : (i) observations of actual behaviour in a variety of earthquakes ; conspicuous examples : the permanent tilting , overturning, and often survival of numerous buildings on extremely soft soil in Adapazari during the Kocaeli 1999 earthquake ; (ii) the foundation design of a number of critical structures (e.g., major bridge pier, air control tower, tall monuments, elevated water tanks,) against large seismic actions ; the disproportionately large overturning moment and/or base shear force of such slender structures can hardly be faced with today s conventional foundation methods, (iii) the need to seismically retrofit and rehabilitate older structures and historical monuments; (iv) structural yielding of pile foundations is now detectable (thanks to technological advances), thus eliminating one of the reasons for avoiding it.
Summary
The main goal of the proposed research is to investigate the possibility of allowing below-ground support systems to respond to strong seismic shaking by going beyond a number of thresholds that would conventionally imply failure and are today forbidden by codes. Such thresholds include : (a) sliding at the soil-foundation interface ; (b) separation and uplifting of a shallow foundation from the soils ; (c) mobilization of bearing capacity failure mechanism for shallow foundations ; (d) structural yielding of pile foundations ; (e) combination of some of the above. Whereas under static loading conditions a slight exceedance of such thresholds leads to failure, the oscillatory nature of seismic shaking will allow such exceedances for a short period of time, with perhaps no detrimental or irreparable consequences. The latter take the form of permanent foundation displacements, rotations, or injuries , which the designer will aspire to confine within rational limits. The motivation and the need for this research has come from : (i) observations of actual behaviour in a variety of earthquakes ; conspicuous examples : the permanent tilting , overturning, and often survival of numerous buildings on extremely soft soil in Adapazari during the Kocaeli 1999 earthquake ; (ii) the foundation design of a number of critical structures (e.g., major bridge pier, air control tower, tall monuments, elevated water tanks,) against large seismic actions ; the disproportionately large overturning moment and/or base shear force of such slender structures can hardly be faced with today s conventional foundation methods, (iii) the need to seismically retrofit and rehabilitate older structures and historical monuments; (iv) structural yielding of pile foundations is now detectable (thanks to technological advances), thus eliminating one of the reasons for avoiding it.
Max ERC Funding
2 399 992 €
Duration
Start date: 2008-12-01, End date: 2013-10-31
Project acronym DARWIN
Project Deep mm-Wave RF-CMOS Integrated Circuits
Researcher (PI) Michel Steyaert
Host Institution (HI) KATHOLIEKE UNIVERSITEIT LEUVEN
Call Details Advanced Grant (AdG), PE7, ERC-2008-AdG
Summary Wireless and mobile communication systems have become an important part of our daily environment. Since the introduction of the GSM-network in the early nineties, different wireless applications such as WiFi, Bluetooth, GPS, etc. have been brought into the market. This has become possible due to the high integration of integrated circuits in relatively cheap technologies. Besides the digital signal processing, those wireless applications require complex analog circuits operating at very high frequencies (RF circuits). In the early days these were implemented as discrete components or standalone ICs in expensive technologies such as GaAs, InP and SiGe. Due to the research towards nanometer CMOS technologies, and due to improved RF circuit techniques, RF-CMOS has been introduced since the mid nineties. The intention of this research project is to take the next big leap forward in wireless applications, i.e. the exploration and research, based on the vast RF-CMOS knowledge already existing, towards the Extremely High Frequencies which is above 70 GHz up to 300GHz, with wavelengths close to 1 mm. The research project is a logical evolution of the RF-CMOS research knowledges of the team. For that the "natural evolution" acronym DARWIN (Deep mm-Wave RF CMOS Integrated Circuits (with the M of CMOS inverted (W)) is choosen. Implementing circuit techniques in standard CMOS technologies at those frequencies is again an enormous challenge and will open a lot of new opportunities and applications towards the future due to possibilities in safety monitoring, e.g. collision radar detection for automobiles at 77 GHz, the need for high data-rate telecommunication systems, with capacity of 1-10 Gbps, and imaging for medical and security systems. The goal of the proposed project is to perform the necessary fundamental basic research to be able to implement these 70-300 GHz applications in CMOS technology (45 nm and below).
Summary
Wireless and mobile communication systems have become an important part of our daily environment. Since the introduction of the GSM-network in the early nineties, different wireless applications such as WiFi, Bluetooth, GPS, etc. have been brought into the market. This has become possible due to the high integration of integrated circuits in relatively cheap technologies. Besides the digital signal processing, those wireless applications require complex analog circuits operating at very high frequencies (RF circuits). In the early days these were implemented as discrete components or standalone ICs in expensive technologies such as GaAs, InP and SiGe. Due to the research towards nanometer CMOS technologies, and due to improved RF circuit techniques, RF-CMOS has been introduced since the mid nineties. The intention of this research project is to take the next big leap forward in wireless applications, i.e. the exploration and research, based on the vast RF-CMOS knowledge already existing, towards the Extremely High Frequencies which is above 70 GHz up to 300GHz, with wavelengths close to 1 mm. The research project is a logical evolution of the RF-CMOS research knowledges of the team. For that the "natural evolution" acronym DARWIN (Deep mm-Wave RF CMOS Integrated Circuits (with the M of CMOS inverted (W)) is choosen. Implementing circuit techniques in standard CMOS technologies at those frequencies is again an enormous challenge and will open a lot of new opportunities and applications towards the future due to possibilities in safety monitoring, e.g. collision radar detection for automobiles at 77 GHz, the need for high data-rate telecommunication systems, with capacity of 1-10 Gbps, and imaging for medical and security systems. The goal of the proposed project is to perform the necessary fundamental basic research to be able to implement these 70-300 GHz applications in CMOS technology (45 nm and below).
Max ERC Funding
2 042 640 €
Duration
Start date: 2009-01-01, End date: 2013-12-31
Project acronym DEEP
Project Deep Earth Elastic Properties and a Universal Pressure Scale
Researcher (PI) Daniel Frost
Host Institution (HI) UNIVERSITAT BAYREUTH
Call Details Advanced Grant (AdG), PE10, ERC-2008-AdG
Summary Knowledge of the physical and chemical state of the Earth s inner silicate mantle is central to our understanding of plate tectonics, mantle convection, magma generation and the composition of the Earth as a whole. The key to this knowledge is the ability to interpret studies of seismic wave velocities through the deep Earth using laboratory measurements of mineral sound velocities at high pressures and temperatures. Scientists have for many years measured these properties as a function of pressure but due to the experimental difficulties the majority of studies have been performed only at room temperature. Large extrapolations of these data to mantle temperatures are required to link seismic velocity observations with physical and chemical properties of mantle rocks, resulting in large uncertainties that obscure firm conclusions. An additional uncertainty arises because there is currently no primary scale for accurately measuring pressure at high temperatures. In this study mineral sound velocities and densities will be measured in the diamond anvil cell at simultaneous high pressures and high temperatures to at least 50 GPa and 1300K. This will be possible by a pioneering combination of Brillouin scattering spectroscopy, to measure sound velocities, and single crystal X-ray diffraction determinations of density. By making both types of measurements on the same sample while it is maintained at a constant pressure and temperature, the pressure can be independently measured. These absolute pressure determinations will be used to derive a new universal pressure scale for use at high temperatures. Sound velocities of the major mantle minerals will be determined at high temperatures and absolute pressures thereby drastically decreasing the uncertainties in velocity calculations for rock assemblages at deep mantle conditions. The resulting data will be employed to finally interpret a host of seismic observations made at both global and local scales.
Summary
Knowledge of the physical and chemical state of the Earth s inner silicate mantle is central to our understanding of plate tectonics, mantle convection, magma generation and the composition of the Earth as a whole. The key to this knowledge is the ability to interpret studies of seismic wave velocities through the deep Earth using laboratory measurements of mineral sound velocities at high pressures and temperatures. Scientists have for many years measured these properties as a function of pressure but due to the experimental difficulties the majority of studies have been performed only at room temperature. Large extrapolations of these data to mantle temperatures are required to link seismic velocity observations with physical and chemical properties of mantle rocks, resulting in large uncertainties that obscure firm conclusions. An additional uncertainty arises because there is currently no primary scale for accurately measuring pressure at high temperatures. In this study mineral sound velocities and densities will be measured in the diamond anvil cell at simultaneous high pressures and high temperatures to at least 50 GPa and 1300K. This will be possible by a pioneering combination of Brillouin scattering spectroscopy, to measure sound velocities, and single crystal X-ray diffraction determinations of density. By making both types of measurements on the same sample while it is maintained at a constant pressure and temperature, the pressure can be independently measured. These absolute pressure determinations will be used to derive a new universal pressure scale for use at high temperatures. Sound velocities of the major mantle minerals will be determined at high temperatures and absolute pressures thereby drastically decreasing the uncertainties in velocity calculations for rock assemblages at deep mantle conditions. The resulting data will be employed to finally interpret a host of seismic observations made at both global and local scales.
Max ERC Funding
2 079 888 €
Duration
Start date: 2009-02-01, End date: 2014-07-31
Project acronym DEFCON1
Project A NEW DEFINITION OF CONSCIOUSNESS
Researcher (PI) Victor Albert Farid Lamme
Host Institution (HI) UNIVERSITEIT VAN AMSTERDAM
Call Details Advanced Grant (AdG), SH4, ERC-2008-AdG
Summary The study of consciousness is considered one of the final frontiers in science. After centuries of introspection, philosophy, and psychology it is thought that neuroscience will now answer the age-old questions like who is conscious, when, and what of. This will take more, however, than the current approach of finding the neural correlate of consciousness (NCC). We need a new science of consciousness. What is the problem? Behaviour is considered the gold standard of consciousness: when someone says he is conscious, he is, and when he says not, he isn t. But it is impossible to reliably gauge the presence or absence of conscious sensations from behaviour. We will always conflate consciousness with cognitive functions enabling the report, such as attention, working memory or language. Finding the NCC is doomed to fail. Instead, arguments from neuroscience should be allowed to reshape the definition of consciousness. Behavioural or introspective ideas may be a starting point, but ultimately, neural arguments should be allowed to overrule behavioural evidence. I will show how a new neuro-behavioural definition of consciousness can dissociate consciousness from cognition, explains key features of conscious experience, and allows us to understand consciousness at a much more fundamental level. Experiments in man and monkey will test essential predictions of the new definition of consciousness, using techniques such as intracortical recording, EEG, fMRI and pharmacological intervention, combined with psychophysics, learning paradigms or manipulations of consciousness. If these confirm the idea, the new definition of consciousness should be adopted. This means we are in for a change. The new definition of consciousness will move our notion of mind towards that of brain. The sacred first person perspective on consciousness has to be given up. What we may gain, however, is a much better science of consciousness.
Summary
The study of consciousness is considered one of the final frontiers in science. After centuries of introspection, philosophy, and psychology it is thought that neuroscience will now answer the age-old questions like who is conscious, when, and what of. This will take more, however, than the current approach of finding the neural correlate of consciousness (NCC). We need a new science of consciousness. What is the problem? Behaviour is considered the gold standard of consciousness: when someone says he is conscious, he is, and when he says not, he isn t. But it is impossible to reliably gauge the presence or absence of conscious sensations from behaviour. We will always conflate consciousness with cognitive functions enabling the report, such as attention, working memory or language. Finding the NCC is doomed to fail. Instead, arguments from neuroscience should be allowed to reshape the definition of consciousness. Behavioural or introspective ideas may be a starting point, but ultimately, neural arguments should be allowed to overrule behavioural evidence. I will show how a new neuro-behavioural definition of consciousness can dissociate consciousness from cognition, explains key features of conscious experience, and allows us to understand consciousness at a much more fundamental level. Experiments in man and monkey will test essential predictions of the new definition of consciousness, using techniques such as intracortical recording, EEG, fMRI and pharmacological intervention, combined with psychophysics, learning paradigms or manipulations of consciousness. If these confirm the idea, the new definition of consciousness should be adopted. This means we are in for a change. The new definition of consciousness will move our notion of mind towards that of brain. The sacred first person perspective on consciousness has to be given up. What we may gain, however, is a much better science of consciousness.
Max ERC Funding
2 344 800 €
Duration
Start date: 2009-03-01, End date: 2014-02-28
Project acronym DIPOLAR ROTOR ARRAY
Project Regular Arrays of Artificial Surface-Mounted Dipolar Molecular Rotors
Researcher (PI) Josef Michl
Host Institution (HI) USTAV ORGANICKE CHEMIE A BIOCHEMIE, AV CR, V.V.I.
Call Details Advanced Grant (AdG), PE5, ERC-2008-AdG
Summary We propose a feasibility demonstration of an unprecedented concept: preparation of regular two-dimensional arrays of artificial surface-mounted dipolar molecular rotors and control of their coherent motion by the application of an outside electric field. The proposal involves a highly interdisciplinary endeavor, which requires experience in synthesis (preparation of molecular rotors), surface chemistry (assembly of rotors into arrays on surfaces), surface spectroscopy and scanning microscopy (characterization of rotor arrays on surfaces), and theory (modeling of rotor dynamics). The principal investigator is presently actively working and publishing in all of these subdisciplines.
Summary
We propose a feasibility demonstration of an unprecedented concept: preparation of regular two-dimensional arrays of artificial surface-mounted dipolar molecular rotors and control of their coherent motion by the application of an outside electric field. The proposal involves a highly interdisciplinary endeavor, which requires experience in synthesis (preparation of molecular rotors), surface chemistry (assembly of rotors into arrays on surfaces), surface spectroscopy and scanning microscopy (characterization of rotor arrays on surfaces), and theory (modeling of rotor dynamics). The principal investigator is presently actively working and publishing in all of these subdisciplines.
Max ERC Funding
2 457 600 €
Duration
Start date: 2009-02-01, End date: 2014-07-31
Project acronym DISCRETECONT
Project From discrete to contimuous: understanding discrete structures through continuous approximation
Researcher (PI) László Lovász
Host Institution (HI) EOTVOS LORAND TUDOMANYEGYETEM
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary Important methods and results in discrete mathematics arise from the interaction between discrete mathematics and ``continuous'' areas like analysis or geometry. Classical examples of this include topological methods, linear and semidefinite optimization generating functions and more. More recent areas stressing this connection are the theory of limit objects of growing sequences of finite structures (graphs, hypergraphs, sequences), differential equations on networks, geometric representations of graphs. Perhaps most promising is the study of limits of growing graph and hypergraph sequences. In resent work by the Proposer and his collaborators, this area has found highly nontrivial connections with extremal graph theory, the theory of property testing in computer science, to additive number theory, the theory of random graphs, and measure theory as well as geometric representations of graphs. This proposal's goal is to explore these interactions, with the participation of a number of researchers from different areas of mathematics.
Summary
Important methods and results in discrete mathematics arise from the interaction between discrete mathematics and ``continuous'' areas like analysis or geometry. Classical examples of this include topological methods, linear and semidefinite optimization generating functions and more. More recent areas stressing this connection are the theory of limit objects of growing sequences of finite structures (graphs, hypergraphs, sequences), differential equations on networks, geometric representations of graphs. Perhaps most promising is the study of limits of growing graph and hypergraph sequences. In resent work by the Proposer and his collaborators, this area has found highly nontrivial connections with extremal graph theory, the theory of property testing in computer science, to additive number theory, the theory of random graphs, and measure theory as well as geometric representations of graphs. This proposal's goal is to explore these interactions, with the participation of a number of researchers from different areas of mathematics.
Max ERC Funding
739 671 €
Duration
Start date: 2009-01-01, End date: 2014-06-30
Project acronym DMMCA
Project Discrete Mathematics: methods, challenges and applications
Researcher (PI) Noga Alon
Host Institution (HI) TEL AVIV UNIVERSITY
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary Discrete Mathematics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. Some of the main reasons for this growth are the broad applications of tools and techniques from extremal and probabilistic combinatorics in the rapid development of theoretical Computer Science, in the spectacular recent results in Additive Number Theory and in the study of basic questions in Information Theory. While in the past many of the basic combinatorial results were obtained mainly by ingenuity and detailed reasoning, the modern theory has grown out of this early stage, and often relies on deep, well developed tools, like the probabilistic method, algebraic, topological and geometric techniques. The work of the principal investigator, partly jointly with several collaborators and students, and partly in individual efforts, has played a significant role in the introduction of powerful algebraic, probabilistic, spectral and geometric techniques that influenced the development of modern combinatorics. In the present project he aims to try and further develop such tools, trying to tackle some basic open problems in Combinatorics, as well as significant questions in Additive Combinatorics, Information Theory, and theoretical Computer Science. Progress on the problems mentioned in this proposal, and the study of related ones, is expected to provide new insights on these problems and to lead to the development of novel fruitful techniques that are likely to be useful in Discrete Mathematics as well as in related areas.
Summary
Discrete Mathematics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. Some of the main reasons for this growth are the broad applications of tools and techniques from extremal and probabilistic combinatorics in the rapid development of theoretical Computer Science, in the spectacular recent results in Additive Number Theory and in the study of basic questions in Information Theory. While in the past many of the basic combinatorial results were obtained mainly by ingenuity and detailed reasoning, the modern theory has grown out of this early stage, and often relies on deep, well developed tools, like the probabilistic method, algebraic, topological and geometric techniques. The work of the principal investigator, partly jointly with several collaborators and students, and partly in individual efforts, has played a significant role in the introduction of powerful algebraic, probabilistic, spectral and geometric techniques that influenced the development of modern combinatorics. In the present project he aims to try and further develop such tools, trying to tackle some basic open problems in Combinatorics, as well as significant questions in Additive Combinatorics, Information Theory, and theoretical Computer Science. Progress on the problems mentioned in this proposal, and the study of related ones, is expected to provide new insights on these problems and to lead to the development of novel fruitful techniques that are likely to be useful in Discrete Mathematics as well as in related areas.
Max ERC Funding
1 061 300 €
Duration
Start date: 2008-12-01, End date: 2013-11-30
