Project acronym 15CBOOKTRADE
Project The 15th-century Book Trade: An Evidence-based Assessment and Visualization of the Distribution, Sale, and Reception of Books in the Renaissance
Researcher (PI) Cristina Dondi
Host Institution (HI) THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Country United Kingdom
Call Details Consolidator Grant (CoG), SH6, ERC-2013-CoG
Summary The idea that underpins this project is to use the material evidence from thousands of surviving 15th-c. books, as well as unique documentary evidence — the unpublished ledger of a Venetian bookseller in the 1480s which records the sale of 25,000 printed books with their prices — to address four fundamental questions relating to the introduction of printing in the West which have so far eluded scholarship, partly because of lack of evidence, partly because of the lack of effective tools to deal with existing evidence. The book trade differs from other trades operating in the medieval and early modern periods in that the goods traded survive in considerable numbers. Not only do they survive, but many of them bear stratified evidence of their history in the form of marks of ownership, prices, manuscript annotations, binding and decoration styles. A British Academy pilot project conceived by the PI produced a now internationally-used database which gathers together this kind of evidence for thousands of surviving 15th-c. printed books. For the first time, this makes it possible to track the circulation of books, their trade routes and later collecting, across Europe and the USA, and throughout the centuries. The objectives of this project are to examine (1) the distribution and trade-routes, national and international, of 15th-c. printed books, along with the identity of the buyers and users (private, institutional, religious, lay, female, male, and by profession) and their reading practices; (2) the books' contemporary market value; (3) the transmission and dissemination of the texts they contain, their survival and their loss (rebalancing potentially skewed scholarship); and (4) the circulation and re-use of the illustrations they contain. Finally, the project will experiment with the application of scientific visualization techniques to represent, geographically and chronologically, the movement of 15th-c. printed books and of the texts they contain.
Summary
The idea that underpins this project is to use the material evidence from thousands of surviving 15th-c. books, as well as unique documentary evidence — the unpublished ledger of a Venetian bookseller in the 1480s which records the sale of 25,000 printed books with their prices — to address four fundamental questions relating to the introduction of printing in the West which have so far eluded scholarship, partly because of lack of evidence, partly because of the lack of effective tools to deal with existing evidence. The book trade differs from other trades operating in the medieval and early modern periods in that the goods traded survive in considerable numbers. Not only do they survive, but many of them bear stratified evidence of their history in the form of marks of ownership, prices, manuscript annotations, binding and decoration styles. A British Academy pilot project conceived by the PI produced a now internationally-used database which gathers together this kind of evidence for thousands of surviving 15th-c. printed books. For the first time, this makes it possible to track the circulation of books, their trade routes and later collecting, across Europe and the USA, and throughout the centuries. The objectives of this project are to examine (1) the distribution and trade-routes, national and international, of 15th-c. printed books, along with the identity of the buyers and users (private, institutional, religious, lay, female, male, and by profession) and their reading practices; (2) the books' contemporary market value; (3) the transmission and dissemination of the texts they contain, their survival and their loss (rebalancing potentially skewed scholarship); and (4) the circulation and re-use of the illustrations they contain. Finally, the project will experiment with the application of scientific visualization techniques to represent, geographically and chronologically, the movement of 15th-c. printed books and of the texts they contain.
Max ERC Funding
1 999 172 €
Duration
Start date: 2014-04-01, End date: 2019-03-31
Project acronym ADaPt
Project Adaptation, Dispersals and Phenotype: understanding the roles of climate,
natural selection and energetics in shaping global hunter-gatherer adaptability
Researcher (PI) Jay Stock
Host Institution (HI) THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE
Country United Kingdom
Call Details Consolidator Grant (CoG), SH6, ERC-2013-CoG
Summary Relative to other species, humans are characterised by considerable biological diversity despite genetic homogeneity. This diversity is reflected in skeletal variation, but we lack sufficient understanding of the underlying mechanisms to adequately interpret the archaeological record. The proposed research will address problems in our current understanding of the origins of human variation in the past by: 1) documenting and interpreting the pattern of global hunter-gatherer variation relative to genetic phylogenies and climatic variation; 2) testing the relationship between environmental and skeletal variation among genetically related hunter-gatherers from different environments; 3) examining the adaptability of living humans to different environments, through the study of energetic expenditure and life history trade-offs associated with locomotion; and 4) investigating the relationship between muscle and skeletal variation associated with locomotion in diverse environments. This will be achieved by linking: a) detailed study of the global pattern of hunter-gatherer variation in the Late Pleistocene and Holocene with; b) ground-breaking experimental research which tests the relationship between energetic stress, muscle function, and bone variation in living humans. The first component tests the correspondence between skeletal variation and both genetic and climatic history, to infer mechanisms driving variation. The second component integrates this skeletal variation with experimental studies of living humans to, for the first time, directly test adaptive implications of skeletal variation observed in the past. ADaPt will provide the first links between prehistoric hunter-gatherer variation and the evolutionary parameters of life history and energetics that may have shaped our success as a species. It will lead to breakthroughs necessary to interpret variation in the archaeological record, relative to human dispersals and adaptation in the past.
Summary
Relative to other species, humans are characterised by considerable biological diversity despite genetic homogeneity. This diversity is reflected in skeletal variation, but we lack sufficient understanding of the underlying mechanisms to adequately interpret the archaeological record. The proposed research will address problems in our current understanding of the origins of human variation in the past by: 1) documenting and interpreting the pattern of global hunter-gatherer variation relative to genetic phylogenies and climatic variation; 2) testing the relationship between environmental and skeletal variation among genetically related hunter-gatherers from different environments; 3) examining the adaptability of living humans to different environments, through the study of energetic expenditure and life history trade-offs associated with locomotion; and 4) investigating the relationship between muscle and skeletal variation associated with locomotion in diverse environments. This will be achieved by linking: a) detailed study of the global pattern of hunter-gatherer variation in the Late Pleistocene and Holocene with; b) ground-breaking experimental research which tests the relationship between energetic stress, muscle function, and bone variation in living humans. The first component tests the correspondence between skeletal variation and both genetic and climatic history, to infer mechanisms driving variation. The second component integrates this skeletal variation with experimental studies of living humans to, for the first time, directly test adaptive implications of skeletal variation observed in the past. ADaPt will provide the first links between prehistoric hunter-gatherer variation and the evolutionary parameters of life history and energetics that may have shaped our success as a species. It will lead to breakthroughs necessary to interpret variation in the archaeological record, relative to human dispersals and adaptation in the past.
Max ERC Funding
1 911 485 €
Duration
Start date: 2014-07-01, End date: 2019-06-30
Project acronym COMOTION
Project Controlling the Motion of Complex Molecules and Particles
Researcher (PI) Jochen Kuepper
Host Institution (HI) STIFTUNG DEUTSCHES ELEKTRONEN-SYNCHROTRON DESY
Country Germany
Call Details Consolidator Grant (CoG), PE4, ERC-2013-CoG
Summary "The main objective of COMOTION is to enable novel experiments for the investigation of the intrinsic properties of large molecules, including biological samples like proteins, viruses, and small cells
-X-ray free-electron lasers have enabled the observation of near-atomic-resolution structures in diffraction- before-destruction experiments, for instance, of isolated mimiviruses and of proteins from microscopic crystals. The goal to record molecular movies with spatial and temporal atomic-resolution (femtoseconds and picometers) of individual molecules is near.
-The investigation of ultrafast, sub-femtosecond electron dynamics in small molecules is providing first results. Its extension to large molecules promises the unraveling of charge migration and energy transport in complex (bio)molecules.
-Matter-wave experiments of large molecules, with currently up to some hundred atoms, are testing the limits of quantum mechanics, particle-wave duality, and coherence. These metrology experiments also allow the precise measurement of molecular properties.
The principal obstacle for these and similar experiments in molecular sciences is the controlled production of samples of identical molecules in the gas phase. We will develop novel concepts and technologies for the manipulation of complex molecules, ranging from amino acids to proteins, viruses, nano-objects, and small cells: We will implement new methods to inject complex molecules into vacuum, to rapidly cool them, and to manipulate the motion of these cold gas-phase samples using combinations of external electric and electromagnetic fields. These external-field handles enable the spatial separation of molecules according to size, shape, and isomer.
The generated controlled samples are ideally suited for the envisioned precision experiments. We will exploit them to record atomic-resolution molecular movies using the European XFEL, as well as to investigate the limits of quantum mechanics using matter-wave interferometry."
Summary
"The main objective of COMOTION is to enable novel experiments for the investigation of the intrinsic properties of large molecules, including biological samples like proteins, viruses, and small cells
-X-ray free-electron lasers have enabled the observation of near-atomic-resolution structures in diffraction- before-destruction experiments, for instance, of isolated mimiviruses and of proteins from microscopic crystals. The goal to record molecular movies with spatial and temporal atomic-resolution (femtoseconds and picometers) of individual molecules is near.
-The investigation of ultrafast, sub-femtosecond electron dynamics in small molecules is providing first results. Its extension to large molecules promises the unraveling of charge migration and energy transport in complex (bio)molecules.
-Matter-wave experiments of large molecules, with currently up to some hundred atoms, are testing the limits of quantum mechanics, particle-wave duality, and coherence. These metrology experiments also allow the precise measurement of molecular properties.
The principal obstacle for these and similar experiments in molecular sciences is the controlled production of samples of identical molecules in the gas phase. We will develop novel concepts and technologies for the manipulation of complex molecules, ranging from amino acids to proteins, viruses, nano-objects, and small cells: We will implement new methods to inject complex molecules into vacuum, to rapidly cool them, and to manipulate the motion of these cold gas-phase samples using combinations of external electric and electromagnetic fields. These external-field handles enable the spatial separation of molecules according to size, shape, and isomer.
The generated controlled samples are ideally suited for the envisioned precision experiments. We will exploit them to record atomic-resolution molecular movies using the European XFEL, as well as to investigate the limits of quantum mechanics using matter-wave interferometry."
Max ERC Funding
1 982 500 €
Duration
Start date: 2014-09-01, End date: 2019-08-31
Project acronym Critical
Project Behaviour near criticality
Researcher (PI) Martin Hairer
Host Institution (HI) THE UNIVERSITY OF WARWICK
Country United Kingdom
Call Details Consolidator Grant (CoG), PE1, ERC-2013-CoG
Summary "One of the main challenges of modern mathematical physics is to understand the behaviour of systems at or near criticality. In a number of cases, one can argue heuristically that this behaviour should be described by a nonlinear stochastic partial differential equation. Some examples of systems of interest are models of phase coexistence near the critical temperature, one-dimensional interface growth models, and models of absorption of a diffusing particle by random impurities. Unfortunately, the equations arising in all of these contexts are mathematically ill-posed. This is to the extent that they defeat not only ""standard"" stochastic PDE techniques (as developed by Da Prato / Zabczyk / Röckner / Walsh / Krylov / etc), but also more recent approaches based on Wick renormalisation of nonlinearities (Da Prato / Debussche / etc).
Over the past year or so, I have been developing a theory of regularity structures that allows to give a rigorous mathematical interpretation to such equations, which therefore allows to build the mathematical objects conjectured to describe the abovementioned systems near criticality. The aim of the proposal is to study the convergence of a variety of concrete microscopic models to these limiting objects. The main fundamental mathematical tools to be developed in this endeavour are a discrete analogue to the theory of regularity structures, as well as a number of nonlinear invariance principles.
If successful, the project will yield unique insight in the large-scale behaviour of a number of physically relevant systems in regimes where both nonlinear effects and random fluctuations compete with equal strength."
Summary
"One of the main challenges of modern mathematical physics is to understand the behaviour of systems at or near criticality. In a number of cases, one can argue heuristically that this behaviour should be described by a nonlinear stochastic partial differential equation. Some examples of systems of interest are models of phase coexistence near the critical temperature, one-dimensional interface growth models, and models of absorption of a diffusing particle by random impurities. Unfortunately, the equations arising in all of these contexts are mathematically ill-posed. This is to the extent that they defeat not only ""standard"" stochastic PDE techniques (as developed by Da Prato / Zabczyk / Röckner / Walsh / Krylov / etc), but also more recent approaches based on Wick renormalisation of nonlinearities (Da Prato / Debussche / etc).
Over the past year or so, I have been developing a theory of regularity structures that allows to give a rigorous mathematical interpretation to such equations, which therefore allows to build the mathematical objects conjectured to describe the abovementioned systems near criticality. The aim of the proposal is to study the convergence of a variety of concrete microscopic models to these limiting objects. The main fundamental mathematical tools to be developed in this endeavour are a discrete analogue to the theory of regularity structures, as well as a number of nonlinear invariance principles.
If successful, the project will yield unique insight in the large-scale behaviour of a number of physically relevant systems in regimes where both nonlinear effects and random fluctuations compete with equal strength."
Max ERC Funding
1 526 234 €
Duration
Start date: 2014-09-01, End date: 2019-08-31
Project acronym DNAFOLDIMS
Project Advanced mass spectrometry approaches to reveal nucleic acid folding energy landscapes
Researcher (PI) Valerie Gabelica
Host Institution (HI) INSTITUT NATIONAL DE LA SANTE ET DE LA RECHERCHE MEDICALE
Country France
Call Details Consolidator Grant (CoG), PE4, ERC-2013-CoG
Summary "50 years after the discovery of the DNA double helix, the variety of structures that nucleic acids can adopt continues to surprise the scientific community. Specific structures and conformational changes are linked to important functions in cell regulation. Understanding the principles that govern how small molecules such as natural metabolites or synthetic drugs modulate the nucleic acid structures is of prime importance for molecular biology and pharmacology. The field however suffers from the lack of suitable experimental tools to monitor all assemblies and structures formed when a small molecule encounters its targets.
The goal of my project is to develop unique mass spectrometry-based approaches to detect, quantify and characterize all these assemblies and structures. Our team’s strength will be to integrate a multidisciplinary approach, from physical and analytical chemistry to molecular biology. We will address the fundamentals of nucleic acid ionization and transfer in the gas phase, develop a unique instrumental setup combining mass spectrometry, ion mobility and circular dichroism ion spectroscopy, and apply these new approaches to biologically important nucleic acids, in order to reveal the mechanisms of ligand-induced conformational changes in important regulatory structures such as G-quadruplex or riboswitches.
This research will also have broader impact, as the approaches and concepts developed here for nucleic acids will contribute fundamental advances in mass spectrometry, and will be transferrable to other supramolecular or biological complexes."
Summary
"50 years after the discovery of the DNA double helix, the variety of structures that nucleic acids can adopt continues to surprise the scientific community. Specific structures and conformational changes are linked to important functions in cell regulation. Understanding the principles that govern how small molecules such as natural metabolites or synthetic drugs modulate the nucleic acid structures is of prime importance for molecular biology and pharmacology. The field however suffers from the lack of suitable experimental tools to monitor all assemblies and structures formed when a small molecule encounters its targets.
The goal of my project is to develop unique mass spectrometry-based approaches to detect, quantify and characterize all these assemblies and structures. Our team’s strength will be to integrate a multidisciplinary approach, from physical and analytical chemistry to molecular biology. We will address the fundamentals of nucleic acid ionization and transfer in the gas phase, develop a unique instrumental setup combining mass spectrometry, ion mobility and circular dichroism ion spectroscopy, and apply these new approaches to biologically important nucleic acids, in order to reveal the mechanisms of ligand-induced conformational changes in important regulatory structures such as G-quadruplex or riboswitches.
This research will also have broader impact, as the approaches and concepts developed here for nucleic acids will contribute fundamental advances in mass spectrometry, and will be transferrable to other supramolecular or biological complexes."
Max ERC Funding
2 021 755 €
Duration
Start date: 2014-06-01, End date: 2019-05-31
Project acronym ESTYMA
Project Excited state quantum dynamics in molecular aggregates: a unified description from biology to devices
Researcher (PI) Alessandro Troisi
Host Institution (HI) THE UNIVERSITY OF LIVERPOOL
Country United Kingdom
Call Details Consolidator Grant (CoG), PE4, ERC-2013-CoG
Summary The coherent dynamics of excitons in systems of biological interest and in organic materials can now be studied with advanced experimental techniques, including two dimensional electronic spectroscopy, with time resolution of few femtoseconds. The theory of open quantum systems, that should support the interpretation of these new experiments, has been developed in different contexts over the past 60 years but seems now very inadequate for the problems of current interest. First of all, the systems under investigation are extremely complex and the most common approach, based on the development of phenomenological models, is often not very informative. Many different models yield results in agreement with the experiments and there is no systematic way to derive these models or to select the best model among many. Secondly, the quantum dynamics of excitons is so fast that one cannot assume that the dynamics of environment is much faster than the dynamics of the system, an assumption crucial for most theories. A remedy to the current limitation is proposed here through the following research objectives.
(1) A general and automatic protocol will be developed to generate simple treatable models of the system from an accurate atomistic description of the same system based on computational chemistry methods.
(2) A professionally-written software will be developed to study the quantum dynamics of model Hamiltonians for excitons in molecular aggregates. This software will incorporate different methodologies and will be designed to be usable also by non-specialists in the theory of quantum open systems (e.g. spectroscopists, computational chemists).
(3) A broad number of problems will be studied with this methodology including (i) exciton dynamics in light harvesting complexes and artificial proteins and (ii) exciton dynamics in molecular aggregates of relevance for organic electronics devices.
Summary
The coherent dynamics of excitons in systems of biological interest and in organic materials can now be studied with advanced experimental techniques, including two dimensional electronic spectroscopy, with time resolution of few femtoseconds. The theory of open quantum systems, that should support the interpretation of these new experiments, has been developed in different contexts over the past 60 years but seems now very inadequate for the problems of current interest. First of all, the systems under investigation are extremely complex and the most common approach, based on the development of phenomenological models, is often not very informative. Many different models yield results in agreement with the experiments and there is no systematic way to derive these models or to select the best model among many. Secondly, the quantum dynamics of excitons is so fast that one cannot assume that the dynamics of environment is much faster than the dynamics of the system, an assumption crucial for most theories. A remedy to the current limitation is proposed here through the following research objectives.
(1) A general and automatic protocol will be developed to generate simple treatable models of the system from an accurate atomistic description of the same system based on computational chemistry methods.
(2) A professionally-written software will be developed to study the quantum dynamics of model Hamiltonians for excitons in molecular aggregates. This software will incorporate different methodologies and will be designed to be usable also by non-specialists in the theory of quantum open systems (e.g. spectroscopists, computational chemists).
(3) A broad number of problems will be studied with this methodology including (i) exciton dynamics in light harvesting complexes and artificial proteins and (ii) exciton dynamics in molecular aggregates of relevance for organic electronics devices.
Max ERC Funding
1 512 873 €
Duration
Start date: 2014-04-01, End date: 2019-03-31
Project acronym EXONMR
Project "Exploiting 17O NMR Spectroscopy: Atomic-Scale Structure, Disorder and Dynamics in Solids"
Researcher (PI) Sharon Elizabeth Marie Ashbrook
Host Institution (HI) THE UNIVERSITY COURT OF THE UNIVERSITY OF ST ANDREWS
Country United Kingdom
Call Details Consolidator Grant (CoG), PE4, ERC-2013-CoG
Summary "The fundamental importance of oxide-based systems in technology, energy materials, geochemistry and catalysis, and the presence of oxygen in many biomaterials, should have resulted in oxygen nuclear magnetic resonance (NMR) spectroscopy emerging as a vital tool for materials characterization. NMR offers an element-specific, atomic-scale probe of the local environment, providing a potentially powerful probe of local structure, disorder and dynamics in solids. However, despite the almost ubiquitous presence of oxygen in inorganic solids, oxygen NMR studies have been relatively scarce in comparison to other nuclei, owing primarily to the low natural abundance of the NMR-active isotope, 17O (0.037%). Hence, isotopic enrichment is necessary, often at considerable cost and effort. Furthermore, the presence of anisotropic quadrupolar broadening (and the need for complex high-resolution experiments) has also limited the development and application of 17O NMR to date. Here, we propose to develop an internationally-leading research programme to exploit the largely untapped potential of 17O spectroscopy. This wide-ranging programme will involve (i) the exploration of novel synthetic approaches for cost-efficient isotopic enrichment, (ii) the development of new solid-state NMR methodology, specific for 17O, (iii) the application of state-of-the-art first-principles calculations of 17O NMR parameters and (iv) the application of these methods to three different areas of investigation: high-pressure silicate minerals, microporous materials and ceramics for waste encapsulation. The ultimate long-term aim is to change the way in which solid-state chemists characterise materials; so that solid-state NMR (and 17O NMR in particular) is viewed as a necessary and important step in the refinement of a detailed structural model."
Summary
"The fundamental importance of oxide-based systems in technology, energy materials, geochemistry and catalysis, and the presence of oxygen in many biomaterials, should have resulted in oxygen nuclear magnetic resonance (NMR) spectroscopy emerging as a vital tool for materials characterization. NMR offers an element-specific, atomic-scale probe of the local environment, providing a potentially powerful probe of local structure, disorder and dynamics in solids. However, despite the almost ubiquitous presence of oxygen in inorganic solids, oxygen NMR studies have been relatively scarce in comparison to other nuclei, owing primarily to the low natural abundance of the NMR-active isotope, 17O (0.037%). Hence, isotopic enrichment is necessary, often at considerable cost and effort. Furthermore, the presence of anisotropic quadrupolar broadening (and the need for complex high-resolution experiments) has also limited the development and application of 17O NMR to date. Here, we propose to develop an internationally-leading research programme to exploit the largely untapped potential of 17O spectroscopy. This wide-ranging programme will involve (i) the exploration of novel synthetic approaches for cost-efficient isotopic enrichment, (ii) the development of new solid-state NMR methodology, specific for 17O, (iii) the application of state-of-the-art first-principles calculations of 17O NMR parameters and (iv) the application of these methods to three different areas of investigation: high-pressure silicate minerals, microporous materials and ceramics for waste encapsulation. The ultimate long-term aim is to change the way in which solid-state chemists characterise materials; so that solid-state NMR (and 17O NMR in particular) is viewed as a necessary and important step in the refinement of a detailed structural model."
Max ERC Funding
1 902 188 €
Duration
Start date: 2014-04-01, End date: 2019-03-31
Project acronym GEOMETRICSTRUCTURES
Project Deformation Spaces of Geometric Structures
Researcher (PI) Anna Wienhard
Host Institution (HI) RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG
Country Germany
Call Details Consolidator Grant (CoG), PE1, ERC-2013-CoG
Summary "Moduli spaces of flat bundles and representation varieties play a prominent role in various areas of mathematics. Historically such spaces first arose in the study of systems of analytic differential equations. Closely related, and in fact locally homeomorphic, are deformation spaces of locally homogeneous geometric structures. Such deformation spaces often arise as solutions to basic geometric problems, and their global properties provide powerful topological invariants, in particular for three- and four-dimensional manifolds.
Due to the ubiquity of these spaces, methods and viewpoints from various areas of mathematics such as dynamical systems, algebraic geometry, gauge theory, representation theory, partial differential equations, number theory and complex analysis can be combined, and their interplay gives rise to the richness of this subject. In recent year there has also been an increasing interaction with theoretical physics, which has been fruitful for both sides.
In recent years the deformation theory of geometric structures has received revived attention due to new developments, which involve in a deeper way the connections to Lie theory and gauge theory. Unexpectedly, many new examples of deformation spaces of geometric structures appeared. Two such developments are Higher Teichmueller theory and Anosov representations of hyperbolic groups, which generalize classical Teichmueller theory and the theory of quasi-Fuchsian representations to the context of Lie groups of higher rank.
The goal of the proposal is to understand the fine structure and internal geometry of deformation spaces of geometric structures, and to further develop the structure theory of discrete subgroups in higher rank Lie groups. Of particular interest are deformation spaces with appear in the connection with higher Teichmueller theory, because they are expected to be of similar mathematical significance as classical Teichmueller space."
Summary
"Moduli spaces of flat bundles and representation varieties play a prominent role in various areas of mathematics. Historically such spaces first arose in the study of systems of analytic differential equations. Closely related, and in fact locally homeomorphic, are deformation spaces of locally homogeneous geometric structures. Such deformation spaces often arise as solutions to basic geometric problems, and their global properties provide powerful topological invariants, in particular for three- and four-dimensional manifolds.
Due to the ubiquity of these spaces, methods and viewpoints from various areas of mathematics such as dynamical systems, algebraic geometry, gauge theory, representation theory, partial differential equations, number theory and complex analysis can be combined, and their interplay gives rise to the richness of this subject. In recent year there has also been an increasing interaction with theoretical physics, which has been fruitful for both sides.
In recent years the deformation theory of geometric structures has received revived attention due to new developments, which involve in a deeper way the connections to Lie theory and gauge theory. Unexpectedly, many new examples of deformation spaces of geometric structures appeared. Two such developments are Higher Teichmueller theory and Anosov representations of hyperbolic groups, which generalize classical Teichmueller theory and the theory of quasi-Fuchsian representations to the context of Lie groups of higher rank.
The goal of the proposal is to understand the fine structure and internal geometry of deformation spaces of geometric structures, and to further develop the structure theory of discrete subgroups in higher rank Lie groups. Of particular interest are deformation spaces with appear in the connection with higher Teichmueller theory, because they are expected to be of similar mathematical significance as classical Teichmueller space."
Max ERC Funding
1 570 327 €
Duration
Start date: 2014-01-01, End date: 2018-12-31
Project acronym GETEMO
Project Geometry, Groups and Model Theory
Researcher (PI) Emmanuel, Francois, Jean Breuillard
Host Institution (HI) Westfälische Wilhelms-Universität Münster
Country Germany
Call Details Consolidator Grant (CoG), PE1, ERC-2013-CoG
Summary Our proposed research lies at the interface of Geometry, Group Theory, Number Theory and Combinatorics. In recent years, striking results were obtained in those disciplines with the help of a surprise newcomer at the border between mathematics and logic: Model Theory. Bringing its unique point of view and its powerful formalism, Model Theory made a resounding entry into several different fields of mathematics. Here shedding new light on a classical phenomenon, there solving a long-standing open problem via a completely new method.
Recent examples of concrete mathematical problems where Model Theory interacted in a fruitful manner abound: the local version of Hilbert's 5th problem by Goldbring and van den Dries, Szemeredi's theorems in combinatorics and graph theory, the André-Oort conjecture in diophantine geometry (Pila, Wilkie, Zannier), etc. In this vein, and building on Hrushovski's model-theoretic work, Green, Tao and myself recently settled a conjecture of Lindenstrauss pertaining to the structure of approximate groups.
Our plan in this project is to put these methods into further use, to collaborate with model theorists, and to start looking through this prism at a small collection of familiar problems coming from combinatorics, group theory, analysis and spectral geometry of metric spaces, or from arithmetic geometry. Among them: extend our study of approximate groups to the general setting of locally compact groups, obtain uniform estimates on the spectrum of Cayley graphs of large finite groups, prove an analogue for character varieties of the Pink-Zilber conjectures in relation with rigidity theory for discrete subgroups of Lie groups, and clarify the links between uniform spectral gaps and height lower bounds in diophantine geometry with a view towards Lehmer's conjecture.
Summary
Our proposed research lies at the interface of Geometry, Group Theory, Number Theory and Combinatorics. In recent years, striking results were obtained in those disciplines with the help of a surprise newcomer at the border between mathematics and logic: Model Theory. Bringing its unique point of view and its powerful formalism, Model Theory made a resounding entry into several different fields of mathematics. Here shedding new light on a classical phenomenon, there solving a long-standing open problem via a completely new method.
Recent examples of concrete mathematical problems where Model Theory interacted in a fruitful manner abound: the local version of Hilbert's 5th problem by Goldbring and van den Dries, Szemeredi's theorems in combinatorics and graph theory, the André-Oort conjecture in diophantine geometry (Pila, Wilkie, Zannier), etc. In this vein, and building on Hrushovski's model-theoretic work, Green, Tao and myself recently settled a conjecture of Lindenstrauss pertaining to the structure of approximate groups.
Our plan in this project is to put these methods into further use, to collaborate with model theorists, and to start looking through this prism at a small collection of familiar problems coming from combinatorics, group theory, analysis and spectral geometry of metric spaces, or from arithmetic geometry. Among them: extend our study of approximate groups to the general setting of locally compact groups, obtain uniform estimates on the spectrum of Cayley graphs of large finite groups, prove an analogue for character varieties of the Pink-Zilber conjectures in relation with rigidity theory for discrete subgroups of Lie groups, and clarify the links between uniform spectral gaps and height lower bounds in diophantine geometry with a view towards Lehmer's conjecture.
Max ERC Funding
1 284 000 €
Duration
Start date: 2014-06-01, End date: 2019-05-31
Project acronym HAPDEGMT
Project Harmonic Analysis, Partial Differential Equations and Geometric Measure Theory
Researcher (PI) Jose Maria Martell Berrocal
Host Institution (HI) AGENCIA ESTATAL CONSEJO SUPERIOR DEINVESTIGACIONES CIENTIFICAS
Country Spain
Call Details Consolidator Grant (CoG), PE1, ERC-2013-CoG
Summary The origin of Harmonic Analysis goes back to the study of the heat diffusion, modeled by a differential equation, and the claim made by Fourier that every periodic function can be represented as a series of sines and cosines. In this statement we can find the motivation to many of the advances that have been made in this field. Partial Differential Equations model many phenomena from the natural, economic and social sciences. Existence, uniqueness, convergence to the boundary data, regularity of solutions, a priori estimates, etc., can be studied for a given PDE. Often, Harmonic Analysis plays an important role in such problems and, when the scenarios are not very friendly, Harmonic Analysis turns out to be fundamental. Not very friendly scenarios are those where one lacks of smoothness either in the coefficients of the PDE and/or in the domains where the PDE is solved. Some of these problems lead to obtain the boundedness of certain singular integral operators and this drives one to the classical and modern Calderón-Zygmund theory, the paradigm of Harmonic Analysis. When studying the behavior of the solutions of the given PDE near the boundary, one needs to understand the geometrical features of the domains and then Geometric Measure Theory jumps into the picture.
This ambitious project lies between the interface of three areas: Harmonic Analysis, PDE and Geometric Measure theory. It seeks deep results motivated by elliptic PDE using techniques from Harmonic Analysis and Geometric Measure Theory.This project is built upon results obtained by the applicant in these three areas. Some of them are very recent and have gone significantly beyond the state of the art. The methods to be used have been shown to be very robust and therefore they might be useful towards its applicability in other regimes. Crucial to this project is the use of Harmonic Analysis where the applicant has already obtained important contributions.
Summary
The origin of Harmonic Analysis goes back to the study of the heat diffusion, modeled by a differential equation, and the claim made by Fourier that every periodic function can be represented as a series of sines and cosines. In this statement we can find the motivation to many of the advances that have been made in this field. Partial Differential Equations model many phenomena from the natural, economic and social sciences. Existence, uniqueness, convergence to the boundary data, regularity of solutions, a priori estimates, etc., can be studied for a given PDE. Often, Harmonic Analysis plays an important role in such problems and, when the scenarios are not very friendly, Harmonic Analysis turns out to be fundamental. Not very friendly scenarios are those where one lacks of smoothness either in the coefficients of the PDE and/or in the domains where the PDE is solved. Some of these problems lead to obtain the boundedness of certain singular integral operators and this drives one to the classical and modern Calderón-Zygmund theory, the paradigm of Harmonic Analysis. When studying the behavior of the solutions of the given PDE near the boundary, one needs to understand the geometrical features of the domains and then Geometric Measure Theory jumps into the picture.
This ambitious project lies between the interface of three areas: Harmonic Analysis, PDE and Geometric Measure theory. It seeks deep results motivated by elliptic PDE using techniques from Harmonic Analysis and Geometric Measure Theory.This project is built upon results obtained by the applicant in these three areas. Some of them are very recent and have gone significantly beyond the state of the art. The methods to be used have been shown to be very robust and therefore they might be useful towards its applicability in other regimes. Crucial to this project is the use of Harmonic Analysis where the applicant has already obtained important contributions.
Max ERC Funding
1 429 790 €
Duration
Start date: 2014-01-01, End date: 2018-12-31
