Project acronym AGALT
Project Asymptotic Geometric Analysis and Learning Theory
Researcher (PI) Shahar Mendelson
Host Institution (HI) TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Call Details Starting Grant (StG), PE1, ERC-2007-StG
Summary In a typical learning problem one tries to approximate an unknown function by a function from a given class using random data, sampled according to an unknown measure. In this project we will be interested in parameters that govern the complexity of a learning problem. It turns out that this complexity is determined by the geometry of certain sets in high dimension that are connected to the given class (random coordinate projections of the class). Thus, one has to understand the structure of these sets as a function of the dimension - which is given by the cardinality of the random sample. The resulting analysis leads to many theoretical questions in Asymptotic Geometric Analysis, Probability (most notably, Empirical Processes Theory) and Combinatorics, which are of independent interest beyond the application to Learning Theory. Our main goal is to describe the role of various complexity parameters involved in a learning problem, to analyze the connections between them and to investigate the way they determine the geometry of the relevant high dimensional sets. Some of the questions we intend to tackle are well known open problems and making progress towards their solution will have a significant theoretical impact. Moreover, this project should lead to a more complete theory of learning and is likely to have some practical impact, for example, in the design of more efficient learning algorithms.
Summary
In a typical learning problem one tries to approximate an unknown function by a function from a given class using random data, sampled according to an unknown measure. In this project we will be interested in parameters that govern the complexity of a learning problem. It turns out that this complexity is determined by the geometry of certain sets in high dimension that are connected to the given class (random coordinate projections of the class). Thus, one has to understand the structure of these sets as a function of the dimension - which is given by the cardinality of the random sample. The resulting analysis leads to many theoretical questions in Asymptotic Geometric Analysis, Probability (most notably, Empirical Processes Theory) and Combinatorics, which are of independent interest beyond the application to Learning Theory. Our main goal is to describe the role of various complexity parameters involved in a learning problem, to analyze the connections between them and to investigate the way they determine the geometry of the relevant high dimensional sets. Some of the questions we intend to tackle are well known open problems and making progress towards their solution will have a significant theoretical impact. Moreover, this project should lead to a more complete theory of learning and is likely to have some practical impact, for example, in the design of more efficient learning algorithms.
Max ERC Funding
750 000 €
Duration
Start date: 2009-03-01, End date: 2014-02-28
Project acronym ANISOTROPIC UNIVERSE
Project The anisotropic universe -- a reality or fluke?
Researcher (PI) Hans Kristian Kamfjord Eriksen
Host Institution (HI) UNIVERSITETET I OSLO
Call Details Starting Grant (StG), PE9, ERC-2010-StG_20091028
Summary "During the last decade, a strikingly successful cosmological concordance model has been established. With only six free parameters, nearly all observables, comprising millions of data points, may be fitted with outstanding precision. However, in this beautiful picture a few ""blemishes"" have turned up, apparently not consistent with the standard model: While the model predicts that the universe is isotropic (i.e., looks the same in all directions) and homogeneous (i.e., the statistical properties are the same everywhere), subtle hints of the contrary are now seen. For instance, peculiar preferred directions and correlations are observed in the cosmic microwave background; some studies considering nearby galaxies suggest the existence of anomalous large-scale cosmic flows; a study of distant quasars hints towards unexpected large-scale correlations. All of these reports are individually highly intriguing, and together they hint toward a more complicated and interesting universe than previously imagined -- but none of the reports can be considered decisive. One major obstacle in many cases has been the relatively poor data quality.
This is currently about to change, as the next generation of new and far more powerful experiments are coming online. Of special interest to me are Planck, an ESA-funded CMB satellite currently taking data; QUIET, a ground-based CMB polarization experiment located in Chile; and various large-scale structure (LSS) data sets, such as the SDSS and 2dF surveys, and in the future Euclid, a proposed galaxy survey satellite also funded by ESA. By combining the world s best data from both CMB and LSS measurements, I will in the proposed project attempt to settle this question: Is our universe really anisotropic? Or are these recent claims only the results of systematic errors or statistical flukes? If the claims turn out to hold against this tide of new and high-quality data, then cosmology as a whole may need to be re-written."
Summary
"During the last decade, a strikingly successful cosmological concordance model has been established. With only six free parameters, nearly all observables, comprising millions of data points, may be fitted with outstanding precision. However, in this beautiful picture a few ""blemishes"" have turned up, apparently not consistent with the standard model: While the model predicts that the universe is isotropic (i.e., looks the same in all directions) and homogeneous (i.e., the statistical properties are the same everywhere), subtle hints of the contrary are now seen. For instance, peculiar preferred directions and correlations are observed in the cosmic microwave background; some studies considering nearby galaxies suggest the existence of anomalous large-scale cosmic flows; a study of distant quasars hints towards unexpected large-scale correlations. All of these reports are individually highly intriguing, and together they hint toward a more complicated and interesting universe than previously imagined -- but none of the reports can be considered decisive. One major obstacle in many cases has been the relatively poor data quality.
This is currently about to change, as the next generation of new and far more powerful experiments are coming online. Of special interest to me are Planck, an ESA-funded CMB satellite currently taking data; QUIET, a ground-based CMB polarization experiment located in Chile; and various large-scale structure (LSS) data sets, such as the SDSS and 2dF surveys, and in the future Euclid, a proposed galaxy survey satellite also funded by ESA. By combining the world s best data from both CMB and LSS measurements, I will in the proposed project attempt to settle this question: Is our universe really anisotropic? Or are these recent claims only the results of systematic errors or statistical flukes? If the claims turn out to hold against this tide of new and high-quality data, then cosmology as a whole may need to be re-written."
Max ERC Funding
1 500 000 €
Duration
Start date: 2011-01-01, End date: 2015-12-31
Project acronym ANOPTSETCON
Project Analysis of optimal sets and optimal constants: old questions and new results
Researcher (PI) Aldo Pratelli
Host Institution (HI) FRIEDRICH-ALEXANDER-UNIVERSITAET ERLANGEN NUERNBERG
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary The analysis of geometric and functional inequalities naturally leads to consider the extremal cases, thus
looking for optimal sets, or optimal functions, or optimal constants. The most classical examples are the (different versions of the) isoperimetric inequality and the Sobolev-like inequalities. Much is known about equality cases and best constants, but there are still many questions which seem quite natural but yet have no answer. For instance, it is not known, even in the 2-dimensional space, the answer of a question by Brezis: which set,
among those with a given volume, has the biggest Sobolev-Poincaré constant for p=1? This is a very natural problem, and it appears reasonable that the optimal set should be the ball, but this has never been proved. The interest in problems like this relies not only in the extreme simplicity of the questions and in their classical flavour, but also in the new ideas and techniques which are needed to provide the answers.
The main techniques that we aim to use are fine arguments of symmetrization, geometric constructions and tools from mass transportation (which is well known to be deeply connected with functional inequalities). These are the basic tools that we already used to reach, in last years, many results in a specific direction, namely the search of sharp quantitative inequalities. Our first result, together with Fusco and Maggi, showed what follows. Everybody knows that the set which minimizes the perimeter with given volume is the ball.
But is it true that a set which almost minimizes the perimeter must be close to a ball? The question had been posed in the 1920's and many partial result appeared in the years. In our paper (Ann. of Math., 2007) we proved the sharp result. Many other results of this kind were obtained in last two years.
Summary
The analysis of geometric and functional inequalities naturally leads to consider the extremal cases, thus
looking for optimal sets, or optimal functions, or optimal constants. The most classical examples are the (different versions of the) isoperimetric inequality and the Sobolev-like inequalities. Much is known about equality cases and best constants, but there are still many questions which seem quite natural but yet have no answer. For instance, it is not known, even in the 2-dimensional space, the answer of a question by Brezis: which set,
among those with a given volume, has the biggest Sobolev-Poincaré constant for p=1? This is a very natural problem, and it appears reasonable that the optimal set should be the ball, but this has never been proved. The interest in problems like this relies not only in the extreme simplicity of the questions and in their classical flavour, but also in the new ideas and techniques which are needed to provide the answers.
The main techniques that we aim to use are fine arguments of symmetrization, geometric constructions and tools from mass transportation (which is well known to be deeply connected with functional inequalities). These are the basic tools that we already used to reach, in last years, many results in a specific direction, namely the search of sharp quantitative inequalities. Our first result, together with Fusco and Maggi, showed what follows. Everybody knows that the set which minimizes the perimeter with given volume is the ball.
But is it true that a set which almost minimizes the perimeter must be close to a ball? The question had been posed in the 1920's and many partial result appeared in the years. In our paper (Ann. of Math., 2007) we proved the sharp result. Many other results of this kind were obtained in last two years.
Max ERC Funding
540 000 €
Duration
Start date: 2010-08-01, End date: 2015-07-31
Project acronym ANTHOS
Project Analytic Number Theory: Higher Order Structures
Researcher (PI) Valentin Blomer
Host Institution (HI) GEORG-AUGUST-UNIVERSITAT GOTTINGENSTIFTUNG OFFENTLICHEN RECHTS
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary This is a proposal for research at the interface of analytic number theory, automorphic forms and algebraic geometry. Motivated by fundamental conjectures in number theory, classical problems will be investigated in higher order situations: general number fields, automorphic forms on higher rank groups, the arithmetic of algebraic varieties of higher degree. In particular, I want to focus on
- computation of moments of L-function of degree 3 and higher with applications to subconvexity and/or non-vanishing, as well as subconvexity for multiple L-functions;
- bounds for sup-norms of cusp forms on various spaces and equidistribution of Hecke correspondences;
- automorphic forms on higher rank groups and general number fields, in particular new bounds towards the Ramanujan conjecture;
- a proof of Manin's conjecture for a certain class of singular algebraic varieties.
The underlying methods are closely related; for example, rational points on algebraic varieties
will be counted by a multiple L-series technique.
Summary
This is a proposal for research at the interface of analytic number theory, automorphic forms and algebraic geometry. Motivated by fundamental conjectures in number theory, classical problems will be investigated in higher order situations: general number fields, automorphic forms on higher rank groups, the arithmetic of algebraic varieties of higher degree. In particular, I want to focus on
- computation of moments of L-function of degree 3 and higher with applications to subconvexity and/or non-vanishing, as well as subconvexity for multiple L-functions;
- bounds for sup-norms of cusp forms on various spaces and equidistribution of Hecke correspondences;
- automorphic forms on higher rank groups and general number fields, in particular new bounds towards the Ramanujan conjecture;
- a proof of Manin's conjecture for a certain class of singular algebraic varieties.
The underlying methods are closely related; for example, rational points on algebraic varieties
will be counted by a multiple L-series technique.
Max ERC Funding
1 004 000 €
Duration
Start date: 2010-10-01, End date: 2015-09-30
Project acronym AQSER
Project Automorphic q-series and their application
Researcher (PI) Kathrin Bringmann
Host Institution (HI) UNIVERSITAET ZU KOELN
Call Details Starting Grant (StG), PE1, ERC-2013-StG
Summary This proposal aims to unravel mysteries at the frontier of number theory and other areas of mathematics and physics. The main focus will be to understand and exploit “modularity” of q-hypergeometric series. “Modular forms are functions on the complex plane that are inordinately symmetric.” (Mazur) The motivation comes from the wide-reaching applications of modularity in combinatorics, percolation, Lie theory, and physics (black holes).
The interplay between automorphic forms, q-series, and other areas of mathematics and physics is often two-sided. On the one hand, the other areas provide interesting examples of automorphic objects and predict their behavior. Sometimes these even motivate new classes of automorphic objects which have not been previously studied. On the other hand, knowing that certain generating functions are modular gives one access to deep theoretical tools to prove results in other areas. “Mathematics is a language, and we need that language to understand the physics of our universe.”(Ooguri) Understanding this interplay has attracted attention of researchers from a variety of areas. However, proofs of modularity of q-hypergeometric series currently fall far short of a comprehensive theory to describe the interplay between them and automorphic forms. A recent conjecture of W. Nahm relates the modularity of such series to K-theory. In this proposal I aim to fill this gap and provide a better understanding of this interplay by building a general structural framework enveloping these q-series. For this I will employ new kinds of automorphic objects and embed the functions of interest into bigger families
A successful outcome of the proposed research will open further horizons and also answer open questions, even those in other areas which were not addressed in this proposal; for example the new theory could be applied to better understand Donaldson invariants.
Summary
This proposal aims to unravel mysteries at the frontier of number theory and other areas of mathematics and physics. The main focus will be to understand and exploit “modularity” of q-hypergeometric series. “Modular forms are functions on the complex plane that are inordinately symmetric.” (Mazur) The motivation comes from the wide-reaching applications of modularity in combinatorics, percolation, Lie theory, and physics (black holes).
The interplay between automorphic forms, q-series, and other areas of mathematics and physics is often two-sided. On the one hand, the other areas provide interesting examples of automorphic objects and predict their behavior. Sometimes these even motivate new classes of automorphic objects which have not been previously studied. On the other hand, knowing that certain generating functions are modular gives one access to deep theoretical tools to prove results in other areas. “Mathematics is a language, and we need that language to understand the physics of our universe.”(Ooguri) Understanding this interplay has attracted attention of researchers from a variety of areas. However, proofs of modularity of q-hypergeometric series currently fall far short of a comprehensive theory to describe the interplay between them and automorphic forms. A recent conjecture of W. Nahm relates the modularity of such series to K-theory. In this proposal I aim to fill this gap and provide a better understanding of this interplay by building a general structural framework enveloping these q-series. For this I will employ new kinds of automorphic objects and embed the functions of interest into bigger families
A successful outcome of the proposed research will open further horizons and also answer open questions, even those in other areas which were not addressed in this proposal; for example the new theory could be applied to better understand Donaldson invariants.
Max ERC Funding
1 240 500 €
Duration
Start date: 2014-01-01, End date: 2019-04-30
Project acronym ASTROLAB
Project Cold Collisions and the Pathways Toward Life in Interstellar Space
Researcher (PI) Holger Kreckel
Host Institution (HI) MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Call Details Starting Grant (StG), PE9, ERC-2012-StG_20111012
Summary Modern telescopes like Herschel and ALMA open up a new window into molecular astrophysics to investigate a surprisingly rich chemistry that operates even at low densities and low temperatures. Observations with these instruments have the potential of unraveling key questions of astrobiology, like the accumulation of water and pre-biotic organic molecules on (exo)planets from asteroids and comets. Hand-in-hand with the heightened observational activities comes a strong demand for a thorough understanding of the molecular formation mechanisms. The vast majority of interstellar molecules are formed in ion-neutral reactions that remain efficient even at low temperatures. Unfortunately, the unusual nature of these processes under terrestrial conditions makes their laboratory study extremely difficult.
To address these issues, I propose to build a versatile merged beams setup for laboratory studies of ion-neutral collisions at the Cryogenic Storage Ring (CSR), the most ambitious of the next-generation storage devices under development worldwide. With this experimental setup, I will make use of a low-temperature and low-density environment that is ideal to simulate the conditions prevailing in interstellar space. The cryogenic surrounding, in combination with laser-generated ground state atom beams, will allow me to perform precise energy-resolved rate coefficient measurements for reactions between cold molecular ions (like, e.g., H2+, H3+, HCO+, CH2+, CH3+, etc.) and neutral atoms (H, D, C or O) in order to shed light on long-standing problems of astrochemistry and the formation of organic molecules in space.
With the large variability of the collision energy (corresponding to 40-40000 K), I will be able to provide data that are crucial for the interpretation of molecular observations in a variety of objects, ranging from cold molecular clouds to warm layers in protoplanetary disks.
Summary
Modern telescopes like Herschel and ALMA open up a new window into molecular astrophysics to investigate a surprisingly rich chemistry that operates even at low densities and low temperatures. Observations with these instruments have the potential of unraveling key questions of astrobiology, like the accumulation of water and pre-biotic organic molecules on (exo)planets from asteroids and comets. Hand-in-hand with the heightened observational activities comes a strong demand for a thorough understanding of the molecular formation mechanisms. The vast majority of interstellar molecules are formed in ion-neutral reactions that remain efficient even at low temperatures. Unfortunately, the unusual nature of these processes under terrestrial conditions makes their laboratory study extremely difficult.
To address these issues, I propose to build a versatile merged beams setup for laboratory studies of ion-neutral collisions at the Cryogenic Storage Ring (CSR), the most ambitious of the next-generation storage devices under development worldwide. With this experimental setup, I will make use of a low-temperature and low-density environment that is ideal to simulate the conditions prevailing in interstellar space. The cryogenic surrounding, in combination with laser-generated ground state atom beams, will allow me to perform precise energy-resolved rate coefficient measurements for reactions between cold molecular ions (like, e.g., H2+, H3+, HCO+, CH2+, CH3+, etc.) and neutral atoms (H, D, C or O) in order to shed light on long-standing problems of astrochemistry and the formation of organic molecules in space.
With the large variability of the collision energy (corresponding to 40-40000 K), I will be able to provide data that are crucial for the interpretation of molecular observations in a variety of objects, ranging from cold molecular clouds to warm layers in protoplanetary disks.
Max ERC Funding
1 486 800 €
Duration
Start date: 2012-09-01, End date: 2017-11-30
Project acronym Beacon
Project Beacons in the Dark
Researcher (PI) Paulo César Carvalho Freire
Host Institution (HI) MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Call Details Starting Grant (StG), PE9, ERC-2011-StG_20101014
Summary BEACON aims at performing an ambitious multi-disciplinary (optical, radio astronomy and theoretical physics) study to enable a fundamentally improved understanding of gravitation and space-time. For almost a century Einstein's general relativity has been the last word on gravity. However, superstring theory predicts new gravitational phenomena beyond relativity. In this proposal I will attempt to detect these new phenomena, with a sensitivity 20 times better than state-of-the-art attempts. A successful detection would take physics beyond its current understanding of the Universe.
These new gravitational phenomena are emission of dipolar gravitational waves and the violation of the strong equivalence principle (SEP). I plan to look for them by timing newly discovered binary pulsars. I will improve upon the best current limits on dipolar gravitational wave emission by a factor of 20 within the time of this proposal. I also plan to develop a test of the Strong Equivalence Principle using a new pulsar/main-sequence star binary. The precision of this test is likely to surpass the current best limits within the time frame of this proposal and then keep improving indefinitely with time. This happens because this is the cleanest gravitational experiment ever carried out.
In order to further these goals, I plan to build the ultimate pulsar observing system. By taking advantage of recent technological advances in microwave engineering (particularly sensitive ultra-wide band receivers) digital electronics (fast analogue-to-digital converters and digital spectrometers) and computing, my team and me will be able to greatly improve the sensitivity and precision for pulsar timing experiments and exploit the capabilities of modern radio telescopes to their limits.
Pulsars are the beacons that will guide me in these new, uncharted seas.
Summary
BEACON aims at performing an ambitious multi-disciplinary (optical, radio astronomy and theoretical physics) study to enable a fundamentally improved understanding of gravitation and space-time. For almost a century Einstein's general relativity has been the last word on gravity. However, superstring theory predicts new gravitational phenomena beyond relativity. In this proposal I will attempt to detect these new phenomena, with a sensitivity 20 times better than state-of-the-art attempts. A successful detection would take physics beyond its current understanding of the Universe.
These new gravitational phenomena are emission of dipolar gravitational waves and the violation of the strong equivalence principle (SEP). I plan to look for them by timing newly discovered binary pulsars. I will improve upon the best current limits on dipolar gravitational wave emission by a factor of 20 within the time of this proposal. I also plan to develop a test of the Strong Equivalence Principle using a new pulsar/main-sequence star binary. The precision of this test is likely to surpass the current best limits within the time frame of this proposal and then keep improving indefinitely with time. This happens because this is the cleanest gravitational experiment ever carried out.
In order to further these goals, I plan to build the ultimate pulsar observing system. By taking advantage of recent technological advances in microwave engineering (particularly sensitive ultra-wide band receivers) digital electronics (fast analogue-to-digital converters and digital spectrometers) and computing, my team and me will be able to greatly improve the sensitivity and precision for pulsar timing experiments and exploit the capabilities of modern radio telescopes to their limits.
Pulsars are the beacons that will guide me in these new, uncharted seas.
Max ERC Funding
1 892 376 €
Duration
Start date: 2011-09-01, End date: 2016-08-31
Project acronym BeyondA1
Project Set theory beyond the first uncountable cardinal
Researcher (PI) Assaf Shmuel Rinot
Host Institution (HI) BAR ILAN UNIVERSITY
Call Details Starting Grant (StG), PE1, ERC-2018-STG
Summary We propose to establish a research group that will unveil the combinatorial nature of the second uncountable cardinal. This includes its Ramsey-theoretic, order-theoretic, graph-theoretic and topological features. Among others, we will be directly addressing fundamental problems due to Erdos, Rado, Galvin, and Shelah.
While some of these problems are old and well-known, an unexpected series of breakthroughs from the last three years suggest that now is a promising point in time to carry out such a project. Indeed, through a short period, four previously unattainable problems concerning the second uncountable cardinal were successfully tackled: Aspero on a club-guessing problem of Shelah, Krueger on the club-isomorphism problem for Aronszajn trees, Neeman on the isomorphism problem for dense sets of reals, and the PI on the Souslin problem. Each of these results was obtained through the development of a completely new technical framework, and these frameworks could now pave the way for the solution of some major open questions.
A goal of the highest risk in this project is the discovery of a consistent (possibly, parameterized) forcing axiom that will (preferably, simultaneously) provide structure theorems for stationary sets, linearly ordered sets, trees, graphs, and partition relations, as well as the refutation of various forms of club-guessing principles, all at the level of the second uncountable cardinal. In comparison, at the level of the first uncountable cardinal, a forcing axiom due to Foreman, Magidor and Shelah achieves exactly that.
To approach our goals, the proposed project is divided into four core areas: Uncountable trees, Ramsey theory on ordinals, Club-guessing principles, and Forcing Axioms. There is a rich bilateral interaction between any pair of the four different cores, but the proposed division will allow an efficient allocation of manpower, and will increase the chances of parallel success.
Summary
We propose to establish a research group that will unveil the combinatorial nature of the second uncountable cardinal. This includes its Ramsey-theoretic, order-theoretic, graph-theoretic and topological features. Among others, we will be directly addressing fundamental problems due to Erdos, Rado, Galvin, and Shelah.
While some of these problems are old and well-known, an unexpected series of breakthroughs from the last three years suggest that now is a promising point in time to carry out such a project. Indeed, through a short period, four previously unattainable problems concerning the second uncountable cardinal were successfully tackled: Aspero on a club-guessing problem of Shelah, Krueger on the club-isomorphism problem for Aronszajn trees, Neeman on the isomorphism problem for dense sets of reals, and the PI on the Souslin problem. Each of these results was obtained through the development of a completely new technical framework, and these frameworks could now pave the way for the solution of some major open questions.
A goal of the highest risk in this project is the discovery of a consistent (possibly, parameterized) forcing axiom that will (preferably, simultaneously) provide structure theorems for stationary sets, linearly ordered sets, trees, graphs, and partition relations, as well as the refutation of various forms of club-guessing principles, all at the level of the second uncountable cardinal. In comparison, at the level of the first uncountable cardinal, a forcing axiom due to Foreman, Magidor and Shelah achieves exactly that.
To approach our goals, the proposed project is divided into four core areas: Uncountable trees, Ramsey theory on ordinals, Club-guessing principles, and Forcing Axioms. There is a rich bilateral interaction between any pair of the four different cores, but the proposed division will allow an efficient allocation of manpower, and will increase the chances of parallel success.
Max ERC Funding
1 362 500 €
Duration
Start date: 2018-10-01, End date: 2023-09-30
Project acronym BIOSTRUCT
Project Multiscale mathematical modelling of dynamics of structure formation in cell systems
Researcher (PI) Anna Marciniak-Czochra
Host Institution (HI) RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG
Call Details Starting Grant (StG), PE1, ERC-2007-StG
Summary The aim of this transdisciplinary project is to develop and analyse multiscale mathematical models of pattern formation in multicellular systems controlled by the dynamics of intracellular signalling pathways and cell-to-cell communication and to develop new mathematical methods for the modelling of such complex processes. This aim will be achieved through a close collaboration with experimental groups and comprehensive analytical investigations of the mathematical problems arising in the modelling of these biological processes. The mathematical methods and techniques to be employed will be the analysis of systems of partial differential equations, asymptotic analysis, as well as methods of dynamical systems. These techniques will be used to formulate the models and to study the spatio-temporal behaviour of solutions, especially stability and dependence on characteristic scales, geometry, initial data and key parameters. Advanced numerical methods will be applied to simulate the models. This comprehensive methodology goes beyond the state-of-the-art, since usually the analyses are limited to a single aspect of model behaviour. Groundbreaking impacts envisioned are threefold: (i) The project will contribute to the understanding of mechanisms of structure formation in the developmental process, in the context of recently discovered signalling pathways. In addition, some of the factors and mechanisms playing a role in developmental processes, such as Wnt signalling, are implicated in carcinogenesis, for instance colon and lung cancer. (ii) Accurate quantitative and predictive mathematical models of cell proliferation and differentiation are important for the control of tumour growth and tissue egeneration; (iii) Qualitative analysis of multiscale mathematical models of biological phenomena generates challenging mathematical problems and, therefore, the project will lead to the development of new mathematical theories and tools.
Summary
The aim of this transdisciplinary project is to develop and analyse multiscale mathematical models of pattern formation in multicellular systems controlled by the dynamics of intracellular signalling pathways and cell-to-cell communication and to develop new mathematical methods for the modelling of such complex processes. This aim will be achieved through a close collaboration with experimental groups and comprehensive analytical investigations of the mathematical problems arising in the modelling of these biological processes. The mathematical methods and techniques to be employed will be the analysis of systems of partial differential equations, asymptotic analysis, as well as methods of dynamical systems. These techniques will be used to formulate the models and to study the spatio-temporal behaviour of solutions, especially stability and dependence on characteristic scales, geometry, initial data and key parameters. Advanced numerical methods will be applied to simulate the models. This comprehensive methodology goes beyond the state-of-the-art, since usually the analyses are limited to a single aspect of model behaviour. Groundbreaking impacts envisioned are threefold: (i) The project will contribute to the understanding of mechanisms of structure formation in the developmental process, in the context of recently discovered signalling pathways. In addition, some of the factors and mechanisms playing a role in developmental processes, such as Wnt signalling, are implicated in carcinogenesis, for instance colon and lung cancer. (ii) Accurate quantitative and predictive mathematical models of cell proliferation and differentiation are important for the control of tumour growth and tissue egeneration; (iii) Qualitative analysis of multiscale mathematical models of biological phenomena generates challenging mathematical problems and, therefore, the project will lead to the development of new mathematical theories and tools.
Max ERC Funding
750 000 €
Duration
Start date: 2008-09-01, End date: 2013-08-31
Project acronym BLAST
Project Eclipsing binary stars as cutting edge laboratories for astrophysics of stellar
structure, stellar evolution and planet formation
Researcher (PI) Maciej Konacki
Host Institution (HI) CENTRUM ASTRONOMICZNE IM. MIKOLAJAKOPERNIKA POLSKIEJ AKADEMII NAUK
Call Details Starting Grant (StG), PE9, ERC-2010-StG_20091028
Summary Spectroscopic binary stars (SB2s) and in particular spectroscopic eclipsing binaries are one of the most useful objects in astrophysics. Their photometric and spectroscopic observations allow one to determine basic parameters of stars and carry out a wide range of tests of stellar structure, evolution and dynamics. Perhaps somewhat surprisingly, they can also contribute to our understanding of the formation and evolution of (extrasolar) planets. We will study eclipsing binary stars by combining the classic - stellar astronomy - and the modern - extrasolar planets - subjects into a cutting edge project.
We propose to search for and subsequently characterize circumbinary planets around ~350 eclipsing SB2s using our own novel cutting edge radial velocity technique for binary stars and a modern version of the photometry based eclipse timing of eclipsing binary stars employing 0.5-m robotic telescopes. We will also derive basic parameters of up to ~700 stars (~350 binaries) with an unprecedented precision. In particular for about 50% of our sample we expect to deliver masses of the components with an accuracy ~10-100 times better than the current state of the art.
Our project will provide unique constraints for the theories of planet formation and evolution and an unprecedented in quality set of the basic parameters of stars to test the theories of the stellar structure and evolution.
Summary
Spectroscopic binary stars (SB2s) and in particular spectroscopic eclipsing binaries are one of the most useful objects in astrophysics. Their photometric and spectroscopic observations allow one to determine basic parameters of stars and carry out a wide range of tests of stellar structure, evolution and dynamics. Perhaps somewhat surprisingly, they can also contribute to our understanding of the formation and evolution of (extrasolar) planets. We will study eclipsing binary stars by combining the classic - stellar astronomy - and the modern - extrasolar planets - subjects into a cutting edge project.
We propose to search for and subsequently characterize circumbinary planets around ~350 eclipsing SB2s using our own novel cutting edge radial velocity technique for binary stars and a modern version of the photometry based eclipse timing of eclipsing binary stars employing 0.5-m robotic telescopes. We will also derive basic parameters of up to ~700 stars (~350 binaries) with an unprecedented precision. In particular for about 50% of our sample we expect to deliver masses of the components with an accuracy ~10-100 times better than the current state of the art.
Our project will provide unique constraints for the theories of planet formation and evolution and an unprecedented in quality set of the basic parameters of stars to test the theories of the stellar structure and evolution.
Max ERC Funding
1 500 000 €
Duration
Start date: 2010-12-01, End date: 2016-11-30
