Project acronym CONFRA
Project Conformal fractals in analysis, dynamics, physics
Researcher (PI) Stanislav Smirnov
Host Institution (HI) UNIVERSITE DE GENEVE
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary The goal of this project is to study conformally invariant fractal structures from the perspectives of analysis, dynamics, probability, geometry and physics, emphasizing interrelations of these fields. In the last two decades such structures emerged in several areas: continuum scaling limits of 2D critical models in statistical physics (percolation, Ising model); extremal configurations for various problems in complex analysis (multifractal harmonic measures, coefficient growth of univalent maps, Brennan's conjecture); chaotic sets for complex dynamical systems (Julia sets, Kleinian groups). Capitalizing on recent successes, I plan to continue my work in these areas, exploiting their interactions and connections to physics. I intend to achieve at least some of the following goals: * To establish that several critical lattice models have conformally invariant scaling limits, by building upon results on percolation and Ising models and finding discrete holomorphic observables. * To study geometric properties of arising fractal curves and random fields by connecting them to Schramm's SLE curves and Gaussian Free Fields. * To investigate massive scaling limits by describing them geometrically with generalizations of SLEs. * To lay mathematical framework behind relevant physical notions, such as Coulomb Gas (by relating height functions to GFFs) and Quantum Gravity (by identifying limits of random planar graphs with Liouville QGs). * To improve known bounds in several old questions in complex analysis by studying multifractal spectra of harmonic measures. * To estimate extremal behavior of such spectra by using holomorphic motions of (quasi) conformal maps and thermodynamic formalism. * To understand nature of extremal multifractals for harmonic measure by studying random and dynamical fractals. The topics involved range from century old to very young ones. Recently connections between them started to emerge, opening exciting possibilities for new developments in some long standing open problems.
Summary
The goal of this project is to study conformally invariant fractal structures from the perspectives of analysis, dynamics, probability, geometry and physics, emphasizing interrelations of these fields. In the last two decades such structures emerged in several areas: continuum scaling limits of 2D critical models in statistical physics (percolation, Ising model); extremal configurations for various problems in complex analysis (multifractal harmonic measures, coefficient growth of univalent maps, Brennan's conjecture); chaotic sets for complex dynamical systems (Julia sets, Kleinian groups). Capitalizing on recent successes, I plan to continue my work in these areas, exploiting their interactions and connections to physics. I intend to achieve at least some of the following goals: * To establish that several critical lattice models have conformally invariant scaling limits, by building upon results on percolation and Ising models and finding discrete holomorphic observables. * To study geometric properties of arising fractal curves and random fields by connecting them to Schramm's SLE curves and Gaussian Free Fields. * To investigate massive scaling limits by describing them geometrically with generalizations of SLEs. * To lay mathematical framework behind relevant physical notions, such as Coulomb Gas (by relating height functions to GFFs) and Quantum Gravity (by identifying limits of random planar graphs with Liouville QGs). * To improve known bounds in several old questions in complex analysis by studying multifractal spectra of harmonic measures. * To estimate extremal behavior of such spectra by using holomorphic motions of (quasi) conformal maps and thermodynamic formalism. * To understand nature of extremal multifractals for harmonic measure by studying random and dynamical fractals. The topics involved range from century old to very young ones. Recently connections between them started to emerge, opening exciting possibilities for new developments in some long standing open problems.
Max ERC Funding
1 278 000 €
Duration
Start date: 2009-01-01, End date: 2013-12-31
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
Project acronym EQUIARITH
Project Equidistribution in number theory
Researcher (PI) Philippe Michel
Host Institution (HI) ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary The purpose of this proposal is to investigate from various perspectives some equidistribution problems associated with homogeneous spaces of arithmetic type: a typical problem (basically solved) is the distribution of the set of representations of a large integer by an integral quadratic form. Another harder problem is the study of the distribution of special points on Shimura varieties. In a different direction (linked with quantum chaos), the study of the concentration of Laplacian (Maass) eigenforms or of sections of holomorphic bundles is related to similar problems. Given X such a space and G>L the underlying algebraic group and its corresponding lattice L, the above questions boil down to studying the distribution of H-orbits x.H (or more generally H-invariant measures)on the quotient L\G for some subgroups H. This question may be studied different methods: Harmonic Analysis (HA): given a function f on L\G one studies the period integral of f along x.H. This may be done by automorphic methods. In favorable circumstances, the above periods are related to L-functions which one may hope to treat by methods from analytic number theory (the subconvexity problem). Ergodic Theory (ET): one studies the properties of weak*-limits of the measures supported by x.H using rigidity techniques: depending on the nature of H, one might use either rigidity of unipotent actions or the more recent rigidity results for torus actions in rank >1. In fact, HA and ET are intertwined and complementary : the use of ET in this context require a substantial input from number theory and HA, while ET lead to a soft understanding of several features of HA. In addition, the Langlands correspondence principle make it possible to pass from one group G to another. Based on earlier experience, our goal is to develop these interactions systematically and to develop new approaches to outstanding arithmetic problems :eg. the subconvexity problem or the Andre/Oort conjecture.
Summary
The purpose of this proposal is to investigate from various perspectives some equidistribution problems associated with homogeneous spaces of arithmetic type: a typical problem (basically solved) is the distribution of the set of representations of a large integer by an integral quadratic form. Another harder problem is the study of the distribution of special points on Shimura varieties. In a different direction (linked with quantum chaos), the study of the concentration of Laplacian (Maass) eigenforms or of sections of holomorphic bundles is related to similar problems. Given X such a space and G>L the underlying algebraic group and its corresponding lattice L, the above questions boil down to studying the distribution of H-orbits x.H (or more generally H-invariant measures)on the quotient L\G for some subgroups H. This question may be studied different methods: Harmonic Analysis (HA): given a function f on L\G one studies the period integral of f along x.H. This may be done by automorphic methods. In favorable circumstances, the above periods are related to L-functions which one may hope to treat by methods from analytic number theory (the subconvexity problem). Ergodic Theory (ET): one studies the properties of weak*-limits of the measures supported by x.H using rigidity techniques: depending on the nature of H, one might use either rigidity of unipotent actions or the more recent rigidity results for torus actions in rank >1. In fact, HA and ET are intertwined and complementary : the use of ET in this context require a substantial input from number theory and HA, while ET lead to a soft understanding of several features of HA. In addition, the Langlands correspondence principle make it possible to pass from one group G to another. Based on earlier experience, our goal is to develop these interactions systematically and to develop new approaches to outstanding arithmetic problems :eg. the subconvexity problem or the Andre/Oort conjecture.
Max ERC Funding
866 000 €
Duration
Start date: 2008-12-01, End date: 2013-11-30
Project acronym EXPANDERS
Project Expander Graphs in Pure and Applied Mathematics
Researcher (PI) Alexander Lubotzky
Host Institution (HI) THE HEBREW UNIVERSITY OF JERUSALEM
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary Expander graphs are finite graphs which play a fundamental role in many areas of computer science such as: communication networks, algorithms and more. Several areas of deep mathematics have been used in order to give explicit constructions of such graphs e.g. Kazhdan property (T) from representation theory of semisimple Lie groups, Ramanujan conjecture from the theory of automorphic forms and more. In recent years, computer science has started to pay its debt to mathematics: expander graphs are playing an increasing role in several areas of pure mathematics. The goal of the current research plan is to deepen these connections in both directions with special emphasis of the more recent and surprising application of expanders to group theory, the geometry of 3-manifolds and number theory.
Summary
Expander graphs are finite graphs which play a fundamental role in many areas of computer science such as: communication networks, algorithms and more. Several areas of deep mathematics have been used in order to give explicit constructions of such graphs e.g. Kazhdan property (T) from representation theory of semisimple Lie groups, Ramanujan conjecture from the theory of automorphic forms and more. In recent years, computer science has started to pay its debt to mathematics: expander graphs are playing an increasing role in several areas of pure mathematics. The goal of the current research plan is to deepen these connections in both directions with special emphasis of the more recent and surprising application of expanders to group theory, the geometry of 3-manifolds and number theory.
Max ERC Funding
1 082 504 €
Duration
Start date: 2008-10-01, End date: 2014-09-30
Project acronym FIRM
Project Mathematical Methods for Financial Risk Management
Researcher (PI) Halil Mete Soner
Host Institution (HI) EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary Since the pioneering works of Black & Scholes, Merton and Markowitch, sophisticated quantitative methods are being used to introduce more complex financial products each year. However, this exciting increase in the complexity forces the industry to engage in proper risk management practices. The recent financial crisis emanating from risky loan practices is a prime example of this acute need. This proposal focuses exactly on this general problem. We will develop mathematical techniques to measure and assess the financial risk of new instruments. In the theoretical direction, we will expand the scope of recent studies on risk measures of Artzner et-al., and the stochastic representation formulae proved by the principal investigator and his collaborators. The core research team consists of mathematicians and the finance faculty. The newly created state-of-the-art finance laboratory at the host institution will have direct access to financial data. Moreover, executive education that is performed in this unit enables the research group to have close contacts with high level executives of the financial industry. The theoretical side of the project focuses on nonlinear partial differential equations (PDE), backward stochastic differential equations (BSDE) and dynamic risk measures. Already a deep connection between BSDEs and dynamic risk measures is developed by Peng, Delbaen and collaborators. Also, the principal investigator and his collaborators developed connections to PDEs. In this project, we further investigate these connections. Chief goals of this project are theoretical results and computational techniques in the general areas of BSDEs, fully nonlinear PDEs, and the development of risk management practices that are acceptable by the industry. The composition of the research team and our expertise in quantitative methods, well position us to effectively formulate and study theoretical problems with financial impact.
Summary
Since the pioneering works of Black & Scholes, Merton and Markowitch, sophisticated quantitative methods are being used to introduce more complex financial products each year. However, this exciting increase in the complexity forces the industry to engage in proper risk management practices. The recent financial crisis emanating from risky loan practices is a prime example of this acute need. This proposal focuses exactly on this general problem. We will develop mathematical techniques to measure and assess the financial risk of new instruments. In the theoretical direction, we will expand the scope of recent studies on risk measures of Artzner et-al., and the stochastic representation formulae proved by the principal investigator and his collaborators. The core research team consists of mathematicians and the finance faculty. The newly created state-of-the-art finance laboratory at the host institution will have direct access to financial data. Moreover, executive education that is performed in this unit enables the research group to have close contacts with high level executives of the financial industry. The theoretical side of the project focuses on nonlinear partial differential equations (PDE), backward stochastic differential equations (BSDE) and dynamic risk measures. Already a deep connection between BSDEs and dynamic risk measures is developed by Peng, Delbaen and collaborators. Also, the principal investigator and his collaborators developed connections to PDEs. In this project, we further investigate these connections. Chief goals of this project are theoretical results and computational techniques in the general areas of BSDEs, fully nonlinear PDEs, and the development of risk management practices that are acceptable by the industry. The composition of the research team and our expertise in quantitative methods, well position us to effectively formulate and study theoretical problems with financial impact.
Max ERC Funding
880 560 €
Duration
Start date: 2008-12-01, End date: 2013-11-30
Project acronym FQHE
Project Statistics of Fractionally Charged Quasi-Particles
Researcher (PI) Mordehai (Moty) Heiblum
Host Institution (HI) WEIZMANN INSTITUTE OF SCIENCE
Call Details Advanced Grant (AdG), PE3, ERC-2008-AdG
Summary The discovery of the fractional quantum Hall effect created a revolution in solid state research by introducing a new state of matter resulting from strong electron interactions. The new state is characterized by excitations (quasi-particles) that carry fractional charge, which are expected to obey fractional statistics. While odd denominator fractional states are expected to have an abelian statistics, the newly discovered 5/2 even denominator fractional state is expected to have a non-abelian statistics. Moreover, a large number of emerging proposals predict that the latter state can be employed for topological quantum computing ( Station Q was founded by Microsoft Corp. in order to pursue this goal). This proposal aims at studying the abelian and non-abelian fractional charges, and in particular to observe their peculiar statistics. While charges are preferably determined by measuring quantum shot noise, their statistics must be determined via interference experiments, where one particle goes around another. The experiments are very demanding since the even denominator fractions turn to be very fragile and thus can be observed only in the purest possible two dimensional electron gas and at the lowest temperatures. While until very recently such high quality samples were available only by a single grower (in the USA), we have the capability now to grow extremely pure samples with profound even denominator states. As will be detailed in the proposal, we have all the necessary tools to study charge and statistics of these fascinating excitations, due to our experience in crystal growth, shot noise and interferometry measurements.
Summary
The discovery of the fractional quantum Hall effect created a revolution in solid state research by introducing a new state of matter resulting from strong electron interactions. The new state is characterized by excitations (quasi-particles) that carry fractional charge, which are expected to obey fractional statistics. While odd denominator fractional states are expected to have an abelian statistics, the newly discovered 5/2 even denominator fractional state is expected to have a non-abelian statistics. Moreover, a large number of emerging proposals predict that the latter state can be employed for topological quantum computing ( Station Q was founded by Microsoft Corp. in order to pursue this goal). This proposal aims at studying the abelian and non-abelian fractional charges, and in particular to observe their peculiar statistics. While charges are preferably determined by measuring quantum shot noise, their statistics must be determined via interference experiments, where one particle goes around another. The experiments are very demanding since the even denominator fractions turn to be very fragile and thus can be observed only in the purest possible two dimensional electron gas and at the lowest temperatures. While until very recently such high quality samples were available only by a single grower (in the USA), we have the capability now to grow extremely pure samples with profound even denominator states. As will be detailed in the proposal, we have all the necessary tools to study charge and statistics of these fascinating excitations, due to our experience in crystal growth, shot noise and interferometry measurements.
Max ERC Funding
2 000 000 €
Duration
Start date: 2009-01-01, End date: 2013-12-31
Project acronym MATHCARD
Project Mathematical Modelling and Simulation of the Cardiovascular System
Researcher (PI) Alfio Quarteroni
Host Institution (HI) ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary This research project aims at the development, analysis and computer implementation of mathematical models of the cardiovascular system. Our goal is to describe and simulate the anatomic structure and the physiological response of the human cardiovascular system in healthy or diseased states. This demands to address many fundamental issues. Blood flow interacts both mechanically and chemically with the vessel walls and tissue, giving rise to complex fluid-structure interaction problems. The mathematical analysis of these problems is complicated and the related numerical analysis difficult. We propose to extend the recently achieved results on blood flow simulations by directing our analysis in several new directions. Our goal is to encompass aspects of metabolic regulation, micro-circulation, the electrical and mechanical activity of the heart, and their interactions. Modelling and optimisation of drugs delivery in clinical diseases will be addressed as well. This requires the understanding of transport, diffusion and reaction processes within the blood and organs of the body. The emphasis of this project will be put on mathematical modelling, numerical analysis, algorithm implementation, computational efficiency, validation and verification. Our purpose is to set up a mathematical simulation platform eventually leading to the improvement of vascular diseases diagnosis, setting up of surgical planning, and cure of inflammatory processes in the circulatory system. This platform might also help physicians to construct and evaluate combined anatomic/physiological models to predict the outcome of alternative treatment plans for individual patients.
Summary
This research project aims at the development, analysis and computer implementation of mathematical models of the cardiovascular system. Our goal is to describe and simulate the anatomic structure and the physiological response of the human cardiovascular system in healthy or diseased states. This demands to address many fundamental issues. Blood flow interacts both mechanically and chemically with the vessel walls and tissue, giving rise to complex fluid-structure interaction problems. The mathematical analysis of these problems is complicated and the related numerical analysis difficult. We propose to extend the recently achieved results on blood flow simulations by directing our analysis in several new directions. Our goal is to encompass aspects of metabolic regulation, micro-circulation, the electrical and mechanical activity of the heart, and their interactions. Modelling and optimisation of drugs delivery in clinical diseases will be addressed as well. This requires the understanding of transport, diffusion and reaction processes within the blood and organs of the body. The emphasis of this project will be put on mathematical modelling, numerical analysis, algorithm implementation, computational efficiency, validation and verification. Our purpose is to set up a mathematical simulation platform eventually leading to the improvement of vascular diseases diagnosis, setting up of surgical planning, and cure of inflammatory processes in the circulatory system. This platform might also help physicians to construct and evaluate combined anatomic/physiological models to predict the outcome of alternative treatment plans for individual patients.
Max ERC Funding
1 810 992 €
Duration
Start date: 2009-01-01, End date: 2014-06-30
Project acronym NANOSQUID
Project Scanning Nano-SQUID on a Tip
Researcher (PI) Eli Zeldov
Host Institution (HI) WEIZMANN INSTITUTE OF SCIENCE
Call Details Advanced Grant (AdG), PE3, ERC-2008-AdG
Summary At the boundaries of physics research it is constantly necessary to introduce new tools and methods to expand the horizons and address fundamental issues. In this proposal, we will develop and then apply radically new tools that will enable groundbreaking progress in the field of vortex matter in superconductors and will be of great importance to condensed matter physics and nanoscience. We propose a new scanning magnetic imaging method based on self-aligned fabrication of Josephson junctions with characteristic sizes of 10 nm and superconducting quantum interference devices (SQUID) with typical diameter of 100 nm on the end of a pulled quartz tip. Such nano-SQUID on a tip will provide high-sensitivity high-bandwidth mapping of static and dynamic magnetic fields on nanometer scale that is significantly beyond the state of the art. We will develop a new washboard frequency dynamic microscopy for imaging of site-dependent vortex velocities over a remarkable range of over six orders of magnitude in velocity that is expected to reveal the most interesting dynamic phenomena in vortex mater that could not be investigated so far. Our study will provide a novel bottom-up comprehension of microscopic vortex dynamics from single vortex up to numerous predicted dynamic phase transitions, including disorder-dependent depinning processes, plastic deformations, channel flow, metastabilities and memory effects, moving smectic, moving Bragg glass, and dynamic melting. We will also develop a hybrid technology that combines a single electron transistor with nano-SQUID which will provide an unprecedented simultaneous nanoscale imaging of magnetic and electric fields. Using these tools we will carry out innovative studies of additional nano-systems and exciting quantum phenomena, including quantum tunneling in molecular magnets, spin injection and magnetic domain wall dynamics, vortex charge, unconventional superconductivity, and coexistence of superconductivity and ferromagnetism.
Summary
At the boundaries of physics research it is constantly necessary to introduce new tools and methods to expand the horizons and address fundamental issues. In this proposal, we will develop and then apply radically new tools that will enable groundbreaking progress in the field of vortex matter in superconductors and will be of great importance to condensed matter physics and nanoscience. We propose a new scanning magnetic imaging method based on self-aligned fabrication of Josephson junctions with characteristic sizes of 10 nm and superconducting quantum interference devices (SQUID) with typical diameter of 100 nm on the end of a pulled quartz tip. Such nano-SQUID on a tip will provide high-sensitivity high-bandwidth mapping of static and dynamic magnetic fields on nanometer scale that is significantly beyond the state of the art. We will develop a new washboard frequency dynamic microscopy for imaging of site-dependent vortex velocities over a remarkable range of over six orders of magnitude in velocity that is expected to reveal the most interesting dynamic phenomena in vortex mater that could not be investigated so far. Our study will provide a novel bottom-up comprehension of microscopic vortex dynamics from single vortex up to numerous predicted dynamic phase transitions, including disorder-dependent depinning processes, plastic deformations, channel flow, metastabilities and memory effects, moving smectic, moving Bragg glass, and dynamic melting. We will also develop a hybrid technology that combines a single electron transistor with nano-SQUID which will provide an unprecedented simultaneous nanoscale imaging of magnetic and electric fields. Using these tools we will carry out innovative studies of additional nano-systems and exciting quantum phenomena, including quantum tunneling in molecular magnets, spin injection and magnetic domain wall dynamics, vortex charge, unconventional superconductivity, and coexistence of superconductivity and ferromagnetism.
Max ERC Funding
2 000 000 €
Duration
Start date: 2008-12-01, End date: 2013-11-30
Project acronym PROPEREMO
Project Production and perception of emotion: An affective sciences approach
Researcher (PI) Klaus Scherer
Host Institution (HI) UNIVERSITE DE GENEVE
Call Details Advanced Grant (AdG), SH4, ERC-2008-AdG
Summary Emotion is a prime example of the complexity of human mind and behaviour, a psychobiological mechanism shaped by language and culture, which has puzzled scholars in the humanities and social sciences over the centuries. In an effort to reconcile conflicting theoretical traditions, we advocate a componential approach which treats event appraisal, motivational shifts, physiological responses, motor expression, and subjective feeling as dynamically interrelated and integrated components during emotion episodes. Using a prediction-generating theoretical model, we will address both production (elicitation and reaction patterns) and perception (observer inference of emotion from expressive cues). Key issues are the cognitive architecture and mental chronometry of appraisal, neurophysiological structures of relevance and valence detection, the emergence of conscious feelings due to the synchronization of brain/body systems, the generating mechanism for motor expression, the dimensionality of affective space, and the role of embodiment and empathy in perceiving and interpreting emotional expressions. Using multiple paradigms in laboratory, game, simulation, virtual reality, and field settings, we will critically test theory-driven hypotheses by examining brain structures and circuits (via neuroimagery), behaviour (via monitoring decisions and actions), psychophysiological responses (via electrographic recording), facial, vocal, and bodily expressions (via micro-coding and image processing), and conscious feeling (via advanced self-report procedures). In this endeavour, we benefit from extensive research experience, access to outstanding infrastructure, advanced analysis and synthesis methods, validated experimental paradigms as well as, most importantly, from the joint competence of an interdisciplinary affective science group involving philosophers, linguists, psychologists, neuroscientists, behavioural economists, anthropologists, and computer scientists.
Summary
Emotion is a prime example of the complexity of human mind and behaviour, a psychobiological mechanism shaped by language and culture, which has puzzled scholars in the humanities and social sciences over the centuries. In an effort to reconcile conflicting theoretical traditions, we advocate a componential approach which treats event appraisal, motivational shifts, physiological responses, motor expression, and subjective feeling as dynamically interrelated and integrated components during emotion episodes. Using a prediction-generating theoretical model, we will address both production (elicitation and reaction patterns) and perception (observer inference of emotion from expressive cues). Key issues are the cognitive architecture and mental chronometry of appraisal, neurophysiological structures of relevance and valence detection, the emergence of conscious feelings due to the synchronization of brain/body systems, the generating mechanism for motor expression, the dimensionality of affective space, and the role of embodiment and empathy in perceiving and interpreting emotional expressions. Using multiple paradigms in laboratory, game, simulation, virtual reality, and field settings, we will critically test theory-driven hypotheses by examining brain structures and circuits (via neuroimagery), behaviour (via monitoring decisions and actions), psychophysiological responses (via electrographic recording), facial, vocal, and bodily expressions (via micro-coding and image processing), and conscious feeling (via advanced self-report procedures). In this endeavour, we benefit from extensive research experience, access to outstanding infrastructure, advanced analysis and synthesis methods, validated experimental paradigms as well as, most importantly, from the joint competence of an interdisciplinary affective science group involving philosophers, linguists, psychologists, neuroscientists, behavioural economists, anthropologists, and computer scientists.
Max ERC Funding
2 371 331 €
Duration
Start date: 2009-03-01, End date: 2015-02-28
Project acronym QON
Project Quantum optics using nanostructures: from many-body physics to quantum information processing
Researcher (PI) Atac Imamoglu
Host Institution (HI) EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Call Details Advanced Grant (AdG), PE3, ERC-2008-AdG
Summary Spins in nanostructures have emerged as a new paradigm for studying quantum optical phenomena in the solid-state. Motivated by potential applications in quantum information processing, the research in this field has focused on isolating a single confined spin from its environment and implementing coherent manipulation. On the other hand, it has been realized that the principal decoherence mechanisms for confined spins, stemming from interactions with nuclear or electron spin reservoirs, are intimately linked to fascinating many-body condensed-matter physics. We propose to use quantum optical techniques to investigate physics of nanostructures in two opposite but equally interesting regimes, where reservoir couplings are either suppressed to facilitate coherent control or enhanced to promote many body effects. The principal focus of our investigation of many-body phenomena will be on the first observation of optical signatures of the Kondo effect arising from exchange coupling between a confined spin and an electron spin reservoir. In addition, we propose to study nonequilibrium dynamics of quantum dot nuclear spins as well as strongly correlated system of interacting polaritons in coupled nano-cavities. To minimize spin decoherence and to implement quantum control, we propose to use nano-cavity assisted optical manipulation of two-electron spin states in double quantum dots; thanks to its resilience against spin decoherence, this system should allow us to realize elementary quantum information tasks such as spin-polarization conversion and spin entanglement. In addition to indium/gallium arsenide based structures, we propose to study semiconducting carbon nanotubes where hyperfine interactions that lead to spin decoherence can be avoided. Our nanotube experiments will focus on understanding the elementary quantum optical properties, with the ultimate goal of demonstrating coherent optical spin manipulation.
Summary
Spins in nanostructures have emerged as a new paradigm for studying quantum optical phenomena in the solid-state. Motivated by potential applications in quantum information processing, the research in this field has focused on isolating a single confined spin from its environment and implementing coherent manipulation. On the other hand, it has been realized that the principal decoherence mechanisms for confined spins, stemming from interactions with nuclear or electron spin reservoirs, are intimately linked to fascinating many-body condensed-matter physics. We propose to use quantum optical techniques to investigate physics of nanostructures in two opposite but equally interesting regimes, where reservoir couplings are either suppressed to facilitate coherent control or enhanced to promote many body effects. The principal focus of our investigation of many-body phenomena will be on the first observation of optical signatures of the Kondo effect arising from exchange coupling between a confined spin and an electron spin reservoir. In addition, we propose to study nonequilibrium dynamics of quantum dot nuclear spins as well as strongly correlated system of interacting polaritons in coupled nano-cavities. To minimize spin decoherence and to implement quantum control, we propose to use nano-cavity assisted optical manipulation of two-electron spin states in double quantum dots; thanks to its resilience against spin decoherence, this system should allow us to realize elementary quantum information tasks such as spin-polarization conversion and spin entanglement. In addition to indium/gallium arsenide based structures, we propose to study semiconducting carbon nanotubes where hyperfine interactions that lead to spin decoherence can be avoided. Our nanotube experiments will focus on understanding the elementary quantum optical properties, with the ultimate goal of demonstrating coherent optical spin manipulation.
Max ERC Funding
2 300 000 €
Duration
Start date: 2008-11-01, End date: 2013-10-31
