Project acronym ATOMKI-PPROCESS
Project Nuclear reaction studies relevant to the astrophysical p-process nucleosynthesis
Researcher (PI) György Gyürky
Host Institution (HI) Magyar Tudomanyos Akademia Atommagkutato Intezete
Call Details Starting Grant (StG), PE2, ERC-2007-StG
Summary The astrophysical p-process, the stellar production mechanism of the heavy, proton rich isotopes (p-isotopes), is one of the least studied processes in nucleosynthesis. The astrophysical site(s) for the p-process could not yet be clearly identified. In order to reproduce the natural abundances of the p-isotopes, the p-process models must take into account a huge nuclear reaction network. A precise knowledge of the rate of the nuclear reactions in this network is essential for a reliable abundance calculation and for a clear assignment of the astrophysical site(s). For lack of experimental data the nuclear physics inputs for the reaction networks are based on statistical model calculations. These calculations are largely untested in the mass and energy range relevant to the p-process and the uncertainties in the reaction rate values result in a correspondingly uncertain prediction of the p-isotope abundances. Therefore, experiments aiming at the determination of reaction rates for the p-process are of great importance. In this project nuclear reaction cross section measurements will be carried out in the mass and energy range of p-process to check the reliability of the statistical model calculations and to put the p-process models on a more reliable base. The accelerators of the Institute of Nuclear Research in Debrecen, Hungary provide the necessary basis for such studies. The p-process model calculations are especially sensitive to the rates of reactions involving alpha particles and heavy nuclei. Because of technical difficulties, so far there are practically no experimental data available on such reactions and the uncertainty in these reaction rates is presently one of the biggest contributions to the uncertainty of p-isotope abundance calculations. With the help of the ERC grant the alpha-induced reaction cross sections can be measured on heavy isotopes for the first time, which could contribute to a better understanding of the astrophysical p-process.
Summary
The astrophysical p-process, the stellar production mechanism of the heavy, proton rich isotopes (p-isotopes), is one of the least studied processes in nucleosynthesis. The astrophysical site(s) for the p-process could not yet be clearly identified. In order to reproduce the natural abundances of the p-isotopes, the p-process models must take into account a huge nuclear reaction network. A precise knowledge of the rate of the nuclear reactions in this network is essential for a reliable abundance calculation and for a clear assignment of the astrophysical site(s). For lack of experimental data the nuclear physics inputs for the reaction networks are based on statistical model calculations. These calculations are largely untested in the mass and energy range relevant to the p-process and the uncertainties in the reaction rate values result in a correspondingly uncertain prediction of the p-isotope abundances. Therefore, experiments aiming at the determination of reaction rates for the p-process are of great importance. In this project nuclear reaction cross section measurements will be carried out in the mass and energy range of p-process to check the reliability of the statistical model calculations and to put the p-process models on a more reliable base. The accelerators of the Institute of Nuclear Research in Debrecen, Hungary provide the necessary basis for such studies. The p-process model calculations are especially sensitive to the rates of reactions involving alpha particles and heavy nuclei. Because of technical difficulties, so far there are practically no experimental data available on such reactions and the uncertainty in these reaction rates is presently one of the biggest contributions to the uncertainty of p-isotope abundance calculations. With the help of the ERC grant the alpha-induced reaction cross sections can be measured on heavy isotopes for the first time, which could contribute to a better understanding of the astrophysical p-process.
Max ERC Funding
750 000 €
Duration
Start date: 2008-07-01, End date: 2013-06-30
Project acronym CABUM
Project An investigation of the mechanisms at the interaction between cavitation bubbles and contaminants
Researcher (PI) Matevz DULAR
Host Institution (HI) UNIVERZA V LJUBLJANI
Call Details Consolidator Grant (CoG), PE8, ERC-2017-COG
Summary A sudden decrease in pressure triggers the formation of vapour and gas bubbles inside a liquid medium (also called cavitation). This leads to many (key) engineering problems: material loss, noise and vibration of hydraulic machinery. On the other hand, cavitation is a potentially a useful phenomenon: the extreme conditions are increasingly used for a wide variety of applications such as surface cleaning, enhanced chemistry, and waste water treatment (bacteria eradication and virus inactivation).
Despite this significant progress a large gap persists between the understanding of the mechanisms that contribute to the effects of cavitation and its application. Although engineers are already commercializing devices that employ cavitation, we are still not able to answer the fundamental question: What precisely are the mechanisms how bubbles can clean, disinfect, kill bacteria and enhance chemical activity? The overall objective of the project is to understand and determine the fundamental physics of the interaction of cavitation bubbles with different contaminants. To address this issue, the CABUM project will investigate the physical background of cavitation from physical, biological and engineering perspective on three complexity scales: i) on single bubble level, ii) on organised and iii) on random bubble clusters, producing a progressive multidisciplinary synergetic effect.
The proposed synergetic approach builds on the PI's preliminary research and employs novel experimental and numerical methodologies, some of which have been developed by the PI and his research group, to explore the physics of cavitation behaviour in interaction with bacteria and viruses.
Understanding the fundamental physical background of cavitation in interaction with contaminants will have a ground-breaking implications in various scientific fields (engineering, chemistry and biology) and will, in the future, enable the exploitation of cavitation in water and soil treatment processes.
Summary
A sudden decrease in pressure triggers the formation of vapour and gas bubbles inside a liquid medium (also called cavitation). This leads to many (key) engineering problems: material loss, noise and vibration of hydraulic machinery. On the other hand, cavitation is a potentially a useful phenomenon: the extreme conditions are increasingly used for a wide variety of applications such as surface cleaning, enhanced chemistry, and waste water treatment (bacteria eradication and virus inactivation).
Despite this significant progress a large gap persists between the understanding of the mechanisms that contribute to the effects of cavitation and its application. Although engineers are already commercializing devices that employ cavitation, we are still not able to answer the fundamental question: What precisely are the mechanisms how bubbles can clean, disinfect, kill bacteria and enhance chemical activity? The overall objective of the project is to understand and determine the fundamental physics of the interaction of cavitation bubbles with different contaminants. To address this issue, the CABUM project will investigate the physical background of cavitation from physical, biological and engineering perspective on three complexity scales: i) on single bubble level, ii) on organised and iii) on random bubble clusters, producing a progressive multidisciplinary synergetic effect.
The proposed synergetic approach builds on the PI's preliminary research and employs novel experimental and numerical methodologies, some of which have been developed by the PI and his research group, to explore the physics of cavitation behaviour in interaction with bacteria and viruses.
Understanding the fundamental physical background of cavitation in interaction with contaminants will have a ground-breaking implications in various scientific fields (engineering, chemistry and biology) and will, in the future, enable the exploitation of cavitation in water and soil treatment processes.
Max ERC Funding
1 904 565 €
Duration
Start date: 2018-07-01, End date: 2023-06-30
Project acronym COLLMOT
Project Complex structure and dynamics of collective motion
Researcher (PI) Tamás Vicsek
Host Institution (HI) EOTVOS LORAND TUDOMANYEGYETEM
Call Details Advanced Grant (AdG), PE3, ERC-2008-AdG
Summary Collective behaviour is a widespread phenomenon in nature and technology making it a very important subject to study in various contexts. The main goal we intend to achieve in our multidisciplinary research is the identification and documentation of new unifying principles describing the essential aspects of collective motion, being one of the most relevant and spectacular manifestations of collective behaviour. We shall carry out novel type of experiments, design models that are both simple and realistic enough to reproduce the observations and develop concepts for a better interpretation of the complexity of systems consisting of many organisms and such non-living objects as interacting robots. We plan to study systems ranging from cultures of migrating tissue cells through flocks of birds to collectively moving devices. The interrelation of these systems will be considered in order to deepen the understanding of the main patterns of group motion in both living and non-living systems by learning about the similar phenomena in the two domains of nature. Thus, we plan to understand the essential ingredients of flocking of birds by building collectively moving unmanned aerial vehicles while, in turn, high resolution spatiotemporal GPS data of pigeon flocks will be used to make helpful conclusions for the best designs for swarms of robots. In particular, we shall construct and build a set of vehicles that will be capable, for the first time, to exhibit flocking behaviour in the three-dimensional space. The methods we shall adopt will range from approaches used in statistical physics and network theory to various new techniques in cell biology and collective robotics. All this will be based on numerous prior results (both ours and others) published in leading interdisciplinary journals. The planned research will have the potential of leading to ground breaking results with significant implications in various fields of science and technology.
Summary
Collective behaviour is a widespread phenomenon in nature and technology making it a very important subject to study in various contexts. The main goal we intend to achieve in our multidisciplinary research is the identification and documentation of new unifying principles describing the essential aspects of collective motion, being one of the most relevant and spectacular manifestations of collective behaviour. We shall carry out novel type of experiments, design models that are both simple and realistic enough to reproduce the observations and develop concepts for a better interpretation of the complexity of systems consisting of many organisms and such non-living objects as interacting robots. We plan to study systems ranging from cultures of migrating tissue cells through flocks of birds to collectively moving devices. The interrelation of these systems will be considered in order to deepen the understanding of the main patterns of group motion in both living and non-living systems by learning about the similar phenomena in the two domains of nature. Thus, we plan to understand the essential ingredients of flocking of birds by building collectively moving unmanned aerial vehicles while, in turn, high resolution spatiotemporal GPS data of pigeon flocks will be used to make helpful conclusions for the best designs for swarms of robots. In particular, we shall construct and build a set of vehicles that will be capable, for the first time, to exhibit flocking behaviour in the three-dimensional space. The methods we shall adopt will range from approaches used in statistical physics and network theory to various new techniques in cell biology and collective robotics. All this will be based on numerous prior results (both ours and others) published in leading interdisciplinary journals. The planned research will have the potential of leading to ground breaking results with significant implications in various fields of science and technology.
Max ERC Funding
1 248 000 €
Duration
Start date: 2009-03-01, End date: 2015-02-28
Project acronym COOPAIRENT
Project Cooper pairs as a source of entanglement
Researcher (PI) Szabolcs Csonka
Host Institution (HI) BUDAPESTI MUSZAKI ES GAZDASAGTUDOMANYI EGYETEM
Call Details Starting Grant (StG), PE3, ERC-2010-StG_20091028
Summary Entanglement and non-locality are spectacular fundamentals of quantum mechanics and basic resources of future quantum computation algorithms. Electronic entanglement has attracted increasing attention during the last years. The electron spin as a purely quantum mechanical two level system has been put forward as a promising candidate for storing quantum information in solid state. Recently, great progress has been achieved in manipulation and read-out of quantum dot based spin Qubits. However, electron spin is also suitable to transfer quantum information, since mobile electrons can be coherently transmitted in a solid state device preserving the spin information. Thus, electron spin could provide a general platform for on-chip quantum computation and information processing.
Although several theoretical concepts have been worked out to address spin entangled mobile electrons, the absence of an entangler device has not allowed their realization so far. The aim of the present proposal is to overcome this experimental challenge and explore the entanglement of spatially separated electron pairs. Superconductors provide a natural source of entanglement, because their ground-state is composed of Cooper pairs in a spin-singlet state. However, the splitting of the Cooper pairs into separate electrons has to be enforced, which has been very recently realized by the applicant in two quantum dot Y-junction. This Y-junction will be used as a central building block to split Cooper pairs in a controlled fashion and the non-local nature of spin and charge correlations will be addressed in various device configurations.
Our research project will lead to a fundamental understanding of the production, manipulation and detection of spin entangled mobile electron pairs, thus it will significantly extend the frontiers of quantum coherence and opens a new horizon in the field of on-chip quantum information technologies.
Summary
Entanglement and non-locality are spectacular fundamentals of quantum mechanics and basic resources of future quantum computation algorithms. Electronic entanglement has attracted increasing attention during the last years. The electron spin as a purely quantum mechanical two level system has been put forward as a promising candidate for storing quantum information in solid state. Recently, great progress has been achieved in manipulation and read-out of quantum dot based spin Qubits. However, electron spin is also suitable to transfer quantum information, since mobile electrons can be coherently transmitted in a solid state device preserving the spin information. Thus, electron spin could provide a general platform for on-chip quantum computation and information processing.
Although several theoretical concepts have been worked out to address spin entangled mobile electrons, the absence of an entangler device has not allowed their realization so far. The aim of the present proposal is to overcome this experimental challenge and explore the entanglement of spatially separated electron pairs. Superconductors provide a natural source of entanglement, because their ground-state is composed of Cooper pairs in a spin-singlet state. However, the splitting of the Cooper pairs into separate electrons has to be enforced, which has been very recently realized by the applicant in two quantum dot Y-junction. This Y-junction will be used as a central building block to split Cooper pairs in a controlled fashion and the non-local nature of spin and charge correlations will be addressed in various device configurations.
Our research project will lead to a fundamental understanding of the production, manipulation and detection of spin entangled mobile electron pairs, thus it will significantly extend the frontiers of quantum coherence and opens a new horizon in the field of on-chip quantum information technologies.
Max ERC Funding
1 496 112 €
Duration
Start date: 2011-02-01, End date: 2016-10-31
Project acronym DISCONV
Project DISCRETE AND CONVEX GEOMETRY: CHALLENGES, METHODS, APPLICATIONS
Researcher (PI) Imre Barany
Host Institution (HI) MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Call Details Advanced Grant (AdG), PE1, ERC-2010-AdG_20100224
Summary Title: Discrete and convex geometry: challenges, methods, applications
Abstract: Research in discrete and convex geometry, using tools from combinatorics, algebraic
topology, probability theory, number theory, and algebra, with applications in theoretical
computer science, integer programming, and operations research. Algorithmic aspects are
emphasized and often serve as motivation or simply dictate the questions. The proposed
problems can be grouped into three main areas: (1) Geometric transversal, selection, and
incidence problems, including algorithmic complexity of Tverberg's theorem, weak
epsilon-nets, the k-set problem, and algebraic approaches to the Erdos unit distance problem.
(2) Topological methods and questions, in particular topological Tverberg-type theorems,
algorithmic complexity of the existence of equivariant maps, mass partition problems, and the
generalized HeX lemma for the k-coloured d-dimensional grid. (3) Lattice polytopes and random
polytopes, including Arnold's question on the number of convex lattice polytopes, limit
shapes of lattice polytopes in dimension 3 and higher, comparison of random polytopes and
lattice polytopes, the integer convex hull and its randomized version.
Summary
Title: Discrete and convex geometry: challenges, methods, applications
Abstract: Research in discrete and convex geometry, using tools from combinatorics, algebraic
topology, probability theory, number theory, and algebra, with applications in theoretical
computer science, integer programming, and operations research. Algorithmic aspects are
emphasized and often serve as motivation or simply dictate the questions. The proposed
problems can be grouped into three main areas: (1) Geometric transversal, selection, and
incidence problems, including algorithmic complexity of Tverberg's theorem, weak
epsilon-nets, the k-set problem, and algebraic approaches to the Erdos unit distance problem.
(2) Topological methods and questions, in particular topological Tverberg-type theorems,
algorithmic complexity of the existence of equivariant maps, mass partition problems, and the
generalized HeX lemma for the k-coloured d-dimensional grid. (3) Lattice polytopes and random
polytopes, including Arnold's question on the number of convex lattice polytopes, limit
shapes of lattice polytopes in dimension 3 and higher, comparison of random polytopes and
lattice polytopes, the integer convex hull and its randomized version.
Max ERC Funding
1 298 012 €
Duration
Start date: 2011-04-01, End date: 2017-03-31
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 EPIDELAY
Project Delay differential models and transmission dynamics of infectious diseases
Researcher (PI) Gergely Röst
Host Institution (HI) SZEGEDI TUDOMANYEGYETEM
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary The aim of this project is to develop and analyse infinite dimensional dynamical models for the transmission dynamics and propagation of infectious diseases. We use an integrated approach which spans from the abstract theory of functional differential equations to the practical problems of epidemiology, with serious implications to public health policy, prevention, control and mitigation strategies in cases such as the ongoing battle against the nascent H1N1 pandemic.
Delay differential equations are one of the most powerful mathematical modeling tools and they arise naturally in various applications from life sciences to engineering and physics, whenever temporal delays are important. In abstract terms, functional differential equations describe dynamical systems, when their evolution depends on the solution at prior times.
The central theme of this project is to forge strong links between the abstract theory of delay differential equations and practical aspects of epidemiology. Our research will combine competencies in different fields of mathematics and embrace theoretical issues as well as real life applications.
In particular, the theory of equations with state dependent delays is extremely challenging, and this field is at present on the verge of a breakthrough. Developing new theories in this area and connecting them to relevant applications would go far beyond the current research frontier of mathematical epidemiology and could open a new chapter in disease modeling.
Summary
The aim of this project is to develop and analyse infinite dimensional dynamical models for the transmission dynamics and propagation of infectious diseases. We use an integrated approach which spans from the abstract theory of functional differential equations to the practical problems of epidemiology, with serious implications to public health policy, prevention, control and mitigation strategies in cases such as the ongoing battle against the nascent H1N1 pandemic.
Delay differential equations are one of the most powerful mathematical modeling tools and they arise naturally in various applications from life sciences to engineering and physics, whenever temporal delays are important. In abstract terms, functional differential equations describe dynamical systems, when their evolution depends on the solution at prior times.
The central theme of this project is to forge strong links between the abstract theory of delay differential equations and practical aspects of epidemiology. Our research will combine competencies in different fields of mathematics and embrace theoretical issues as well as real life applications.
In particular, the theory of equations with state dependent delays is extremely challenging, and this field is at present on the verge of a breakthrough. Developing new theories in this area and connecting them to relevant applications would go far beyond the current research frontier of mathematical epidemiology and could open a new chapter in disease modeling.
Max ERC Funding
796 800 €
Duration
Start date: 2011-05-01, End date: 2016-12-31
Project acronym FORCEMAP
Project Intramolecular force mapping of enzymes in action: the role of strain in motor mechanisms
Researcher (PI) András Málnási-Csizmadia
Host Institution (HI) EOTVOS LORAND TUDOMANYEGYETEM
Call Details Starting Grant (StG), LS1, ERC-2007-StG
Summary A fundamental but unexplored problem in biology is whether and how enzymes use mechanical strain during their functioning. It is now evident that the knowledge of atomic structures and chemical interactions is not sufficient to understand the intricate mechanisms underlying enzyme specificity and efficiency. Several lines of evidence suggest that mechanical effects play crucial roles in enzyme activity. Therefore we aim to create detailed force maps that reveal how the intramolecular distribution of mechanical strains changes during the enzyme cycle and how these rearrangements drive the enzyme processes. The applicability of current nanotechniques for the investigation of this problem is limited because they do not allow simultaneous measurement of mechanical and enzymatic parameters. Thus we seek to open new avenues of research by developing site-specific sensors and passive or photoinducible molecular springs to measure force-dependent chemical/structural changes with high spatiotemporal resolution in myosin. Since force perturbations occur very rapidly, we are able to combine experimental studies with quasi-realistic in silico simulations to describe the physical background of enzyme function. We expect that our research will yield fundamental insights into the role of intramolecular strains in enzymes and thus greatly aid the design and control of enzyme processes (specificity, activity, regulation). Our studies may also lead to new paradigms in the understanding of motor systems.
Summary
A fundamental but unexplored problem in biology is whether and how enzymes use mechanical strain during their functioning. It is now evident that the knowledge of atomic structures and chemical interactions is not sufficient to understand the intricate mechanisms underlying enzyme specificity and efficiency. Several lines of evidence suggest that mechanical effects play crucial roles in enzyme activity. Therefore we aim to create detailed force maps that reveal how the intramolecular distribution of mechanical strains changes during the enzyme cycle and how these rearrangements drive the enzyme processes. The applicability of current nanotechniques for the investigation of this problem is limited because they do not allow simultaneous measurement of mechanical and enzymatic parameters. Thus we seek to open new avenues of research by developing site-specific sensors and passive or photoinducible molecular springs to measure force-dependent chemical/structural changes with high spatiotemporal resolution in myosin. Since force perturbations occur very rapidly, we are able to combine experimental studies with quasi-realistic in silico simulations to describe the physical background of enzyme function. We expect that our research will yield fundamental insights into the role of intramolecular strains in enzymes and thus greatly aid the design and control of enzyme processes (specificity, activity, regulation). Our studies may also lead to new paradigms in the understanding of motor systems.
Max ERC Funding
750 000 €
Duration
Start date: 2008-09-01, End date: 2014-08-31
Project acronym GalNUC
Project Astrophysical Dynamics and Statistical Physics of Galactic Nuclei
Researcher (PI) Bence Kocsis
Host Institution (HI) EOTVOS LORAND TUDOMANYEGYETEM
Call Details Starting Grant (StG), PE9, ERC-2014-STG
Summary We address some of the major unsolved questions of galactic nuclei using methods of condensed matter physics. Galactic nuclei host a central supermassive black hole, a dense population of stars and compact objects, and in many cases a bright gaseous disk feeding the supermassive black hole. The observed stellar distribution exhibits both spherical and counterrotating disk-like structures. Existing theoretical models cannot convincingly explain the origin of the stellar disks. Is there also a “dark cusp” or “dark disk” of stellar mass black holes? Are there intermediate mass black holes in the Galactic center? We examine the statistical physics of galactic nuclei and their long term dynamical evolution. A star orbiting a supermassive black hole on an eccentric precessing orbit covers an axisymmetric annulus. The long-term gravitational interaction between such annuli is similar to the Coulomb interaction between axisymmetric molecules constituting a liquid crystal. We apply standard methods of condensed matter physics to examine these astrophysical systems. The observed disk and spherical structures represent isotropic-nematic phase transitions. We derive the phase space distribution and time-evolution of different stellar components including a population of black holes. Further, we investigate the interaction of a stellar cluster with a gaseous disk, if present. This leads to the formation of gaps, warps, and spiral waves in the disk, the redistribution of stellar objects, and possibly the formation of intermediate mass black holes. We explore the implications for electromagnetic and gravitational wave observatories. Dark disks of black holes could provide the most frequent source of gravitational waves for LIGO and VIRGO. These detectors will open a new window on the Universe; the proposed project will open a new field in gravitational wave astrophysics to interpret the sources. We also explore implications for electromagnetic observations.
Summary
We address some of the major unsolved questions of galactic nuclei using methods of condensed matter physics. Galactic nuclei host a central supermassive black hole, a dense population of stars and compact objects, and in many cases a bright gaseous disk feeding the supermassive black hole. The observed stellar distribution exhibits both spherical and counterrotating disk-like structures. Existing theoretical models cannot convincingly explain the origin of the stellar disks. Is there also a “dark cusp” or “dark disk” of stellar mass black holes? Are there intermediate mass black holes in the Galactic center? We examine the statistical physics of galactic nuclei and their long term dynamical evolution. A star orbiting a supermassive black hole on an eccentric precessing orbit covers an axisymmetric annulus. The long-term gravitational interaction between such annuli is similar to the Coulomb interaction between axisymmetric molecules constituting a liquid crystal. We apply standard methods of condensed matter physics to examine these astrophysical systems. The observed disk and spherical structures represent isotropic-nematic phase transitions. We derive the phase space distribution and time-evolution of different stellar components including a population of black holes. Further, we investigate the interaction of a stellar cluster with a gaseous disk, if present. This leads to the formation of gaps, warps, and spiral waves in the disk, the redistribution of stellar objects, and possibly the formation of intermediate mass black holes. We explore the implications for electromagnetic and gravitational wave observatories. Dark disks of black holes could provide the most frequent source of gravitational waves for LIGO and VIRGO. These detectors will open a new window on the Universe; the proposed project will open a new field in gravitational wave astrophysics to interpret the sources. We also explore implications for electromagnetic observations.
Max ERC Funding
1 511 436 €
Duration
Start date: 2015-08-01, End date: 2020-07-31
Project acronym GROGandGIN
Project Growth in Groups and Graph Isomorphism Now
Researcher (PI) Laszlo Pyber
Host Institution (HI) MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Call Details Advanced Grant (AdG), PE1, ERC-2016-ADG
Summary "In recent years there has been spectacular progress in studying growth in groups. A central result in this new area, obtained by Pyber-Szabo' (with a similar result proved by Breuillard-Green-Tao), shows that powers of generating subsets of finite simple groups of ""bounded dimension"" grow fast. Extending this Product Theorem Szabo' and the PI also proved a weaker version of a conjecture of Helfgott-Lindenstrauss. The Product Theorem has deep consequences in the study of groups, number theory and random walks. A central open question of the area is to remove the dependence on dimension in our Product Theorem. The PI formulated a new Conjecture, as a step forward. The way to further progress is via combining techniques from asymptotic group theory and probability theory. It is from this perspective that the current GROGandGIN proposal addresses issues concerning random walks. We examine how recent probabilistic arguments for random walks in the symmetric group may be transferred to matrix groups. While the first results in the subject of growth concern matrix groups we see an evolving theory of growth in permutation groups. This relies on earlier work of Babai and the PI which aims at finding proofs which do not use the Classification of Finite Simple Groups (CFSG). Similarly, Babai's famous Quasipolynomial Graph Isomorphism Algorithm builds on ideas from CFSG-free proofs due to him. The PI has recently removed CFSG from the analysis of Babai's algorithm. Our method goes ""halfway"" towards removing CFSG from proofs of growth results for permutation groups, currently a major open problem. The GROGandGIN initiative plans to improve various other parts of Babai's paper, working with several people who look at it from different angles, with an eye towards obtaining a Polynomial Graph Isomorphism algorithm. The GROGandGIN team will also study growth in Lie groups since the theory of random walks in Lie groups has been revitalised using analogues of our Product Theorem."
Summary
"In recent years there has been spectacular progress in studying growth in groups. A central result in this new area, obtained by Pyber-Szabo' (with a similar result proved by Breuillard-Green-Tao), shows that powers of generating subsets of finite simple groups of ""bounded dimension"" grow fast. Extending this Product Theorem Szabo' and the PI also proved a weaker version of a conjecture of Helfgott-Lindenstrauss. The Product Theorem has deep consequences in the study of groups, number theory and random walks. A central open question of the area is to remove the dependence on dimension in our Product Theorem. The PI formulated a new Conjecture, as a step forward. The way to further progress is via combining techniques from asymptotic group theory and probability theory. It is from this perspective that the current GROGandGIN proposal addresses issues concerning random walks. We examine how recent probabilistic arguments for random walks in the symmetric group may be transferred to matrix groups. While the first results in the subject of growth concern matrix groups we see an evolving theory of growth in permutation groups. This relies on earlier work of Babai and the PI which aims at finding proofs which do not use the Classification of Finite Simple Groups (CFSG). Similarly, Babai's famous Quasipolynomial Graph Isomorphism Algorithm builds on ideas from CFSG-free proofs due to him. The PI has recently removed CFSG from the analysis of Babai's algorithm. Our method goes ""halfway"" towards removing CFSG from proofs of growth results for permutation groups, currently a major open problem. The GROGandGIN initiative plans to improve various other parts of Babai's paper, working with several people who look at it from different angles, with an eye towards obtaining a Polynomial Graph Isomorphism algorithm. The GROGandGIN team will also study growth in Lie groups since the theory of random walks in Lie groups has been revitalised using analogues of our Product Theorem."
Max ERC Funding
1 965 340 €
Duration
Start date: 2017-08-01, End date: 2022-07-31
