Project acronym 1stProposal
Project An alternative development of analytic number theory and applications
Researcher (PI) ANDREW Granville
Host Institution (HI) UNIVERSITY COLLEGE LONDON
Country United Kingdom
Call Details Advanced Grant (AdG), PE1, ERC-2014-ADG
Summary The traditional (Riemann) approach to analytic number theory uses the zeros of zeta functions. This requires the associated multiplicative function, say f(n), to have special enough properties that the associated Dirichlet series may be analytically continued. In this proposal we continue to develop an approach which requires less of the multiplicative function, linking the original question with the mean value of f. Such techniques have been around for a long time but have generally been regarded as “ad hoc”. In this project we aim to show that one can develop a coherent approach to the whole subject, not only reproving all of the old results, but also many new ones that appear inaccessible to traditional methods.
Our first goal is to complete a monograph yielding a reworking of all the classical theory using these new methods and then to push forward in new directions. The most important is to extend these techniques to GL(n) L-functions, which we hope will now be feasible having found the correct framework in which to proceed. Since we rarely know how to analytically continue such L-functions this could be of great benefit to the subject.
We are developing the large sieve so that it can be used for individual moduli, and will determine a strong form of that. Also a new method to give asymptotics for mean values, when they are not too small.
We wish to incorporate techniques of analytic number theory into our theory, for example recent advances on mean values of Dirichlet polynomials. Also the recent breakthroughs on the sieve suggest strong links that need further exploration.
Additive combinatorics yields important results in many areas. There are strong analogies between its results, and those for multiplicative functions, especially in large value spectrum theory, and its applications. We hope to develop these further.
Much of this is joint work with K Soundararajan of Stanford University.
Summary
The traditional (Riemann) approach to analytic number theory uses the zeros of zeta functions. This requires the associated multiplicative function, say f(n), to have special enough properties that the associated Dirichlet series may be analytically continued. In this proposal we continue to develop an approach which requires less of the multiplicative function, linking the original question with the mean value of f. Such techniques have been around for a long time but have generally been regarded as “ad hoc”. In this project we aim to show that one can develop a coherent approach to the whole subject, not only reproving all of the old results, but also many new ones that appear inaccessible to traditional methods.
Our first goal is to complete a monograph yielding a reworking of all the classical theory using these new methods and then to push forward in new directions. The most important is to extend these techniques to GL(n) L-functions, which we hope will now be feasible having found the correct framework in which to proceed. Since we rarely know how to analytically continue such L-functions this could be of great benefit to the subject.
We are developing the large sieve so that it can be used for individual moduli, and will determine a strong form of that. Also a new method to give asymptotics for mean values, when they are not too small.
We wish to incorporate techniques of analytic number theory into our theory, for example recent advances on mean values of Dirichlet polynomials. Also the recent breakthroughs on the sieve suggest strong links that need further exploration.
Additive combinatorics yields important results in many areas. There are strong analogies between its results, and those for multiplicative functions, especially in large value spectrum theory, and its applications. We hope to develop these further.
Much of this is joint work with K Soundararajan of Stanford University.
Max ERC Funding
2 011 742 €
Duration
Start date: 2015-08-01, End date: 2020-07-31
Project acronym AAMOT
Project Arithmetic of automorphic motives
Researcher (PI) Michael Harris
Host Institution (HI) INSTITUT DES HAUTES ETUDES SCIENTIFIQUES
Country France
Call Details Advanced Grant (AdG), PE1, ERC-2011-ADG_20110209
Summary The primary purpose of this project is to build on recent spectacular progress in the Langlands program to study the arithmetic properties of automorphic motives constructed in the cohomology of Shimura varieties. Because automorphic methods are available to study the L-functions of these motives, which include elliptic curves and certain families of Calabi-Yau varieties over totally real fields (possibly after base change), they represent the most accessible class of varieties for which one can hope to verify fundamental conjectures on special values of L-functions, including Deligne's conjecture and the Main Conjecture of Iwasawa theory. Immediate goals include the proof of irreducibility of automorphic Galois representations; the establishment of period relations for automorphic and potentially automorphic realizations of motives in the cohomology of distinct Shimura varieties; the construction of p-adic L-functions for these and related motives, notably adjoint and tensor product L-functions in p-adic families; and the geometrization of the p-adic and mod p Langlands program. All four goals, as well as the others mentioned in the body of the proposal, are interconnected; the final goal provides a bridge to related work in geometric representation theory, algebraic geometry, and mathematical physics.
Summary
The primary purpose of this project is to build on recent spectacular progress in the Langlands program to study the arithmetic properties of automorphic motives constructed in the cohomology of Shimura varieties. Because automorphic methods are available to study the L-functions of these motives, which include elliptic curves and certain families of Calabi-Yau varieties over totally real fields (possibly after base change), they represent the most accessible class of varieties for which one can hope to verify fundamental conjectures on special values of L-functions, including Deligne's conjecture and the Main Conjecture of Iwasawa theory. Immediate goals include the proof of irreducibility of automorphic Galois representations; the establishment of period relations for automorphic and potentially automorphic realizations of motives in the cohomology of distinct Shimura varieties; the construction of p-adic L-functions for these and related motives, notably adjoint and tensor product L-functions in p-adic families; and the geometrization of the p-adic and mod p Langlands program. All four goals, as well as the others mentioned in the body of the proposal, are interconnected; the final goal provides a bridge to related work in geometric representation theory, algebraic geometry, and mathematical physics.
Max ERC Funding
1 491 348 €
Duration
Start date: 2012-06-01, End date: 2018-05-31
Project acronym AAS
Project Approximate algebraic structure and applications
Researcher (PI) Ben Green
Host Institution (HI) THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Country United Kingdom
Call Details Starting Grant (StG), PE1, ERC-2011-StG_20101014
Summary This project studies several mathematical topics with a related theme, all of them part of the relatively new discipline known as additive combinatorics.
We look at approximate, or rough, variants of familiar mathematical notions such as group, polynomial or homomorphism. In each case we seek to describe the structure of these approximate objects, and then to give applications of the resulting theorems. This endeavour has already lead to groundbreaking results in the theory of prime numbers, group theory and combinatorial number theory.
Summary
This project studies several mathematical topics with a related theme, all of them part of the relatively new discipline known as additive combinatorics.
We look at approximate, or rough, variants of familiar mathematical notions such as group, polynomial or homomorphism. In each case we seek to describe the structure of these approximate objects, and then to give applications of the resulting theorems. This endeavour has already lead to groundbreaking results in the theory of prime numbers, group theory and combinatorial number theory.
Max ERC Funding
1 000 000 €
Duration
Start date: 2011-10-01, End date: 2016-09-30
Project acronym ABACUS
Project Advancing Behavioral and Cognitive Understanding of Speech
Researcher (PI) Bart De Boer
Host Institution (HI) VRIJE UNIVERSITEIT BRUSSEL
Country Belgium
Call Details Starting Grant (StG), SH4, ERC-2011-StG_20101124
Summary I intend to investigate what cognitive mechanisms give us combinatorial speech. Combinatorial speech is the ability to make new words using pre-existing speech sounds. Humans are the only apes that can do this, yet we do not know how our brains do it, nor how exactly we differ from other apes. Using new experimental techniques to study human behavior and new computational techniques to model human cognition, I will find out how we deal with combinatorial speech.
The experimental part will study individual and cultural learning. Experimental cultural learning is a new technique that simulates cultural evolution in the laboratory. Two types of cultural learning will be used: iterated learning, which simulates language transfer across generations, and social coordination, which simulates emergence of norms in a language community. Using the two types of cultural learning together with individual learning experiments will help to zero in, from three angles, on how humans deal with combinatorial speech. In addition it will make a methodological contribution by comparing the strengths and weaknesses of the three methods.
The computer modeling part will formalize hypotheses about how our brains deal with combinatorial speech. Two models will be built: a high-level model that will establish the basic algorithms with which combinatorial speech is learned and reproduced, and a neural model that will establish in more detail how the algorithms are implemented in the brain. In addition, the models, through increasing understanding of how humans deal with speech, will help bridge the performance gap between human and computer speech recognition.
The project will advance science in four ways: it will provide insight into how our unique ability for using combinatorial speech works, it will tell us how this is implemented in the brain, it will extend the novel methodology of experimental cultural learning and it will create new computer models for dealing with human speech.
Summary
I intend to investigate what cognitive mechanisms give us combinatorial speech. Combinatorial speech is the ability to make new words using pre-existing speech sounds. Humans are the only apes that can do this, yet we do not know how our brains do it, nor how exactly we differ from other apes. Using new experimental techniques to study human behavior and new computational techniques to model human cognition, I will find out how we deal with combinatorial speech.
The experimental part will study individual and cultural learning. Experimental cultural learning is a new technique that simulates cultural evolution in the laboratory. Two types of cultural learning will be used: iterated learning, which simulates language transfer across generations, and social coordination, which simulates emergence of norms in a language community. Using the two types of cultural learning together with individual learning experiments will help to zero in, from three angles, on how humans deal with combinatorial speech. In addition it will make a methodological contribution by comparing the strengths and weaknesses of the three methods.
The computer modeling part will formalize hypotheses about how our brains deal with combinatorial speech. Two models will be built: a high-level model that will establish the basic algorithms with which combinatorial speech is learned and reproduced, and a neural model that will establish in more detail how the algorithms are implemented in the brain. In addition, the models, through increasing understanding of how humans deal with speech, will help bridge the performance gap between human and computer speech recognition.
The project will advance science in four ways: it will provide insight into how our unique ability for using combinatorial speech works, it will tell us how this is implemented in the brain, it will extend the novel methodology of experimental cultural learning and it will create new computer models for dealing with human speech.
Max ERC Funding
1 276 620 €
Duration
Start date: 2012-02-01, End date: 2017-01-31
Project acronym aCROBAT
Project Circadian Regulation Of Brown Adipose Thermogenesis
Researcher (PI) Zachary Philip Gerhart-Hines
Host Institution (HI) KOBENHAVNS UNIVERSITET
Country Denmark
Call Details Starting Grant (StG), LS4, ERC-2014-STG
Summary Obesity and diabetes have reached pandemic proportions and new therapeutic strategies are critically needed. Brown adipose tissue (BAT), a major source of heat production, possesses significant energy-dissipating capacity and therefore represents a promising target to use in combating these diseases. Recently, I discovered a novel link between circadian rhythm and thermogenic stress in the control of the conserved, calorie-burning functions of BAT. Circadian and thermogenic signaling to BAT incorporates blood-borne hormonal and nutrient cues with direct neuronal input. Yet how these responses coordinately shape BAT energy-expending potential through the regulation of cell surface receptors, metabolic enzymes, and transcriptional effectors is still not understood. My primary goal is to investigate this previously unappreciated network of crosstalk that allows mammals to effectively orchestrate daily rhythms in BAT metabolism, while maintaining their ability to adapt to abrupt changes in energy demand. My group will address this question using gain and loss-of-function in vitro and in vivo studies, newly-generated mouse models, customized physiological phenotyping, and cutting-edge advances in next generation RNA sequencing and mass spectrometry. Preliminary, small-scale validations of our methodologies have already yielded a number of novel candidates that may drive key facets of BAT metabolism. Additionally, we will extend our circadian and thermogenic studies into humans to evaluate the translational potential. Our results will advance the fundamental understanding of how daily oscillations in bioenergetic networks establish a framework for the anticipation of and adaptation to environmental challenges. Importantly, we expect that these mechanistic insights will reveal pharmacological targets through which we can unlock evolutionary constraints and harness the energy-expending potential of BAT for the prevention and treatment of obesity and diabetes.
Summary
Obesity and diabetes have reached pandemic proportions and new therapeutic strategies are critically needed. Brown adipose tissue (BAT), a major source of heat production, possesses significant energy-dissipating capacity and therefore represents a promising target to use in combating these diseases. Recently, I discovered a novel link between circadian rhythm and thermogenic stress in the control of the conserved, calorie-burning functions of BAT. Circadian and thermogenic signaling to BAT incorporates blood-borne hormonal and nutrient cues with direct neuronal input. Yet how these responses coordinately shape BAT energy-expending potential through the regulation of cell surface receptors, metabolic enzymes, and transcriptional effectors is still not understood. My primary goal is to investigate this previously unappreciated network of crosstalk that allows mammals to effectively orchestrate daily rhythms in BAT metabolism, while maintaining their ability to adapt to abrupt changes in energy demand. My group will address this question using gain and loss-of-function in vitro and in vivo studies, newly-generated mouse models, customized physiological phenotyping, and cutting-edge advances in next generation RNA sequencing and mass spectrometry. Preliminary, small-scale validations of our methodologies have already yielded a number of novel candidates that may drive key facets of BAT metabolism. Additionally, we will extend our circadian and thermogenic studies into humans to evaluate the translational potential. Our results will advance the fundamental understanding of how daily oscillations in bioenergetic networks establish a framework for the anticipation of and adaptation to environmental challenges. Importantly, we expect that these mechanistic insights will reveal pharmacological targets through which we can unlock evolutionary constraints and harness the energy-expending potential of BAT for the prevention and treatment of obesity and diabetes.
Max ERC Funding
1 497 008 €
Duration
Start date: 2015-05-01, End date: 2020-10-31
Project acronym ACROSSBORDERS
Project Across ancient borders and cultures: An Egyptian microcosm in Sudan during the 2nd millennium BC
Researcher (PI) Julia Budka
Host Institution (HI) LUDWIG-MAXIMILIANS-UNIVERSITAET MUENCHEN
Country Germany
Call Details Starting Grant (StG), SH6, ERC-2012-StG_20111124
Summary Pharaonic Egypt is commonly known for its pyramids and tomb treasures. The present knowledge of Egyptian everyday life and social structures derives mostly from mortuary records associated with the upper classes, whereas traces of ordinary life from domestic sites are generally disregarded. Settlement archaeology in Egypt and Nubia (Ancient North Sudan) is still in its infancy; it is timely to strenghten this field. Responsible for the pottery at three major settlement sites (Abydos and Elephantine in Egypt; Sai Island in Sudan), the PI is in a unique position to co-ordinate a research project on settlement patterns in Northeast Africa of the 2nd millennium BC based on the detailed analysis of material remains. The selected case studies situated across ancient and modern borders and of diverse environmental and cultural preconditions, show very similar archaeological remains. Up to now, no attempt has been made to explain this situation in detail.
The focus of the project is the well-preserved, only partially explored site of Sai Island, seemingly an Egyptian microcosm in New Kingdom Upper Nubia. Little time is left to conduct the requisite large-scale archaeology as Sai is endangered by the planned high dam of Dal. With the application of microarchaeology we will introduce an approach that is new in Egyptian settlement archaeology. Our interdisciplinary research will result in novel insights into (a) multifaceted lives on Sai at a micro-spatial level and (b) domestic life in 2nd millennium BC Egypt and Nubia from a macroscopic view. The present understanding of the political situation in Upper Nubia during the New Kingdom as based on written records will be significantly enlarged by the envisaged approach. Furthermore, in reconstructing Sai Island as “home away from home”, the project presents a showcase study of what we can learn about acculturation and adaptation from ancient cultures, in this case from the coexistence of Egyptians and Nubians
Summary
Pharaonic Egypt is commonly known for its pyramids and tomb treasures. The present knowledge of Egyptian everyday life and social structures derives mostly from mortuary records associated with the upper classes, whereas traces of ordinary life from domestic sites are generally disregarded. Settlement archaeology in Egypt and Nubia (Ancient North Sudan) is still in its infancy; it is timely to strenghten this field. Responsible for the pottery at three major settlement sites (Abydos and Elephantine in Egypt; Sai Island in Sudan), the PI is in a unique position to co-ordinate a research project on settlement patterns in Northeast Africa of the 2nd millennium BC based on the detailed analysis of material remains. The selected case studies situated across ancient and modern borders and of diverse environmental and cultural preconditions, show very similar archaeological remains. Up to now, no attempt has been made to explain this situation in detail.
The focus of the project is the well-preserved, only partially explored site of Sai Island, seemingly an Egyptian microcosm in New Kingdom Upper Nubia. Little time is left to conduct the requisite large-scale archaeology as Sai is endangered by the planned high dam of Dal. With the application of microarchaeology we will introduce an approach that is new in Egyptian settlement archaeology. Our interdisciplinary research will result in novel insights into (a) multifaceted lives on Sai at a micro-spatial level and (b) domestic life in 2nd millennium BC Egypt and Nubia from a macroscopic view. The present understanding of the political situation in Upper Nubia during the New Kingdom as based on written records will be significantly enlarged by the envisaged approach. Furthermore, in reconstructing Sai Island as “home away from home”, the project presents a showcase study of what we can learn about acculturation and adaptation from ancient cultures, in this case from the coexistence of Egyptians and Nubians
Max ERC Funding
1 497 460 €
Duration
Start date: 2012-12-01, End date: 2018-04-30
Project acronym ADAM
Project The Adaptive Auditory Mind
Researcher (PI) Shihab Shamma
Host Institution (HI) ECOLE NORMALE SUPERIEURE
Country France
Call Details Advanced Grant (AdG), SH4, ERC-2011-ADG_20110406
Summary Listening in realistic situations is an active process that engages perceptual and cognitive faculties, endowing speech with meaning, music with joy, and environmental sounds with emotion. Through hearing, humans and other animals navigate complex acoustic scenes, separate sound mixtures, and assess their behavioral relevance. These remarkable feats are currently beyond our understanding and exceed the capabilities of the most sophisticated audio engineering systems. The goal of the proposed research is to investigate experimentally a novel view of hearing, where active hearing emerges from a deep interplay between adaptive sensory processes and goal-directed cognition. Specifically, we shall explore the postulate that versatile perception is mediated by rapid-plasticity at the neuronal level. At the conjunction of sensory and cognitive processing, rapid-plasticity pervades all levels of auditory system, from the cochlea up to the auditory and prefrontal cortices. Exploiting fundamental statistical regularities of acoustics, it is what allows humans and other animal to deal so successfully with natural acoustic scenes where artificial systems fail. The project builds on the internationally recognized leadership of the PI in the fields of physiology and computational modeling, combined with the expertise of the Co-Investigator in psychophysics. Building on these highly complementary fields and several technical innovations, we hope to promote a novel view of auditory perception and cognition. We aim also to contribute significantly to translational research in the domain of signal processing for clinical hearing aids, given that many current limitations are not technological but rather conceptual. The project will finally result in the creation of laboratory facilities and an intellectual network unique in France and rare in all of Europe, combining cognitive, neural, and computational approaches to auditory neuroscience.
Summary
Listening in realistic situations is an active process that engages perceptual and cognitive faculties, endowing speech with meaning, music with joy, and environmental sounds with emotion. Through hearing, humans and other animals navigate complex acoustic scenes, separate sound mixtures, and assess their behavioral relevance. These remarkable feats are currently beyond our understanding and exceed the capabilities of the most sophisticated audio engineering systems. The goal of the proposed research is to investigate experimentally a novel view of hearing, where active hearing emerges from a deep interplay between adaptive sensory processes and goal-directed cognition. Specifically, we shall explore the postulate that versatile perception is mediated by rapid-plasticity at the neuronal level. At the conjunction of sensory and cognitive processing, rapid-plasticity pervades all levels of auditory system, from the cochlea up to the auditory and prefrontal cortices. Exploiting fundamental statistical regularities of acoustics, it is what allows humans and other animal to deal so successfully with natural acoustic scenes where artificial systems fail. The project builds on the internationally recognized leadership of the PI in the fields of physiology and computational modeling, combined with the expertise of the Co-Investigator in psychophysics. Building on these highly complementary fields and several technical innovations, we hope to promote a novel view of auditory perception and cognition. We aim also to contribute significantly to translational research in the domain of signal processing for clinical hearing aids, given that many current limitations are not technological but rather conceptual. The project will finally result in the creation of laboratory facilities and an intellectual network unique in France and rare in all of Europe, combining cognitive, neural, and computational approaches to auditory neuroscience.
Max ERC Funding
3 199 078 €
Duration
Start date: 2012-10-01, End date: 2018-09-30
Project acronym ADDICTION
Project Beyond the Genetics of Addiction
Researcher (PI) Jacqueline Mignon Vink
Host Institution (HI) STICHTING KATHOLIEKE UNIVERSITEIT
Country Netherlands
Call Details Starting Grant (StG), SH4, ERC-2011-StG_20101124
Summary My proposal seeks to explain the complex interplay between genetic and environmental causes of individual variation in substance use and the risk for abuse. Substance use is common. Substances like nicotine and cannabis have well-known negative health consequences, while alcohol and caffeine use may be both beneficial and detrimental, depending on quantity and frequency of use. Twin studies (including my own) demonstrated that both heritable and environmental factors play a role.
My proposal on substance use (nicotine, alcohol, cannabis and caffeine) is organized around several key objectives: 1. To unravel the complex contribution of genetic and environmental factors to substance use by using extended twin family designs; 2. To identify and confirm genes and gene networks involved in substance use by using DNA-variant data; 3. To explore gene expression patterns with RNA data in substance users versus non-users; 4. To investigate biomarkers in substance users versus non-users using blood or urine; 5. To unravel relation between substance use and health by linking twin-family data to national medical databases.
To realize these aims I will use the extensive resources of the Netherlands Twin Register (NTR); including both the longitudinal phenotype database and the biological samples. I have been involved in data collection, coordination of data collection and analyzing NTR data since 1999. With my comprehensive experience in data collection, data analyses and my knowledge in the field of behavior genetics and addiction research I will be able to successfully lead this cutting-edge project. Additional data crucial for the project will be collected by my team. Large samples will be available for this study and state-of-the art methods will be used to analyze the data. All together, my project will offer powerful approaches to unravel the complex interaction between genetic and environmental causes of individual differences in substance use and the risk for abuse.
Summary
My proposal seeks to explain the complex interplay between genetic and environmental causes of individual variation in substance use and the risk for abuse. Substance use is common. Substances like nicotine and cannabis have well-known negative health consequences, while alcohol and caffeine use may be both beneficial and detrimental, depending on quantity and frequency of use. Twin studies (including my own) demonstrated that both heritable and environmental factors play a role.
My proposal on substance use (nicotine, alcohol, cannabis and caffeine) is organized around several key objectives: 1. To unravel the complex contribution of genetic and environmental factors to substance use by using extended twin family designs; 2. To identify and confirm genes and gene networks involved in substance use by using DNA-variant data; 3. To explore gene expression patterns with RNA data in substance users versus non-users; 4. To investigate biomarkers in substance users versus non-users using blood or urine; 5. To unravel relation between substance use and health by linking twin-family data to national medical databases.
To realize these aims I will use the extensive resources of the Netherlands Twin Register (NTR); including both the longitudinal phenotype database and the biological samples. I have been involved in data collection, coordination of data collection and analyzing NTR data since 1999. With my comprehensive experience in data collection, data analyses and my knowledge in the field of behavior genetics and addiction research I will be able to successfully lead this cutting-edge project. Additional data crucial for the project will be collected by my team. Large samples will be available for this study and state-of-the art methods will be used to analyze the data. All together, my project will offer powerful approaches to unravel the complex interaction between genetic and environmental causes of individual differences in substance use and the risk for abuse.
Max ERC Funding
1 491 964 €
Duration
Start date: 2011-12-01, End date: 2017-05-31
Project acronym AF and MSOGR
Project Automorphic Forms and Moduli Spaces of Galois Representations
Researcher (PI) Toby Gee
Host Institution (HI) IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE
Country United Kingdom
Call Details Starting Grant (StG), PE1, ERC-2012-StG_20111012
Summary I propose to establish a research group to develop completely new tools in order to solve three important problems on the relationships between automorphic forms and Galois representations, which lie at the heart of the Langlands program. The first is to prove Serre’s conjecture for real quadratic fields. I will use automorphic induction to transfer the problem to U(4) over the rational numbers, where I will use automorphy lifting theorems and results on the weight part of Serre's conjecture that I established in my earlier work to reduce the problem to proving results in small weight and level. I will prove these base cases via integral p-adic Hodge theory and discriminant bounds.
The second is to develop a geometric theory of moduli spaces of mod p and p-adic Galois representations, and to use it to establish the Breuil–Mézard conjecture in arbitrary dimension, by reinterpreting the conjecture in geometric terms. This will transform the subject by building the first connections between the p-adic Langlands program and the geometric Langlands program, providing an entirely new world of techniques for number theorists. As a consequence of the Breuil-Mézard conjecture, I will be able to deduce far stronger automorphy lifting theorems (in arbitrary dimension) than those currently available.
The third is to completely determine the reduction mod p of certain two-dimensional crystalline representations, and as an application prove a strengthened version of the Gouvêa–Mazur conjecture. I will do this by means of explicit computations with the p-adic local Langlands correspondence for GL_2(Q_p), as well as by improving existing arguments which prove multiplicity one theorems via automorphy lifting theorems. This work will show that the existence of counterexamples to the Gouvêa-Mazur conjecture is due to a purely local phenomenon, and that when this local obstruction vanishes, far stronger conjectures of Buzzard on the slopes of the U_p operator hold.
Summary
I propose to establish a research group to develop completely new tools in order to solve three important problems on the relationships between automorphic forms and Galois representations, which lie at the heart of the Langlands program. The first is to prove Serre’s conjecture for real quadratic fields. I will use automorphic induction to transfer the problem to U(4) over the rational numbers, where I will use automorphy lifting theorems and results on the weight part of Serre's conjecture that I established in my earlier work to reduce the problem to proving results in small weight and level. I will prove these base cases via integral p-adic Hodge theory and discriminant bounds.
The second is to develop a geometric theory of moduli spaces of mod p and p-adic Galois representations, and to use it to establish the Breuil–Mézard conjecture in arbitrary dimension, by reinterpreting the conjecture in geometric terms. This will transform the subject by building the first connections between the p-adic Langlands program and the geometric Langlands program, providing an entirely new world of techniques for number theorists. As a consequence of the Breuil-Mézard conjecture, I will be able to deduce far stronger automorphy lifting theorems (in arbitrary dimension) than those currently available.
The third is to completely determine the reduction mod p of certain two-dimensional crystalline representations, and as an application prove a strengthened version of the Gouvêa–Mazur conjecture. I will do this by means of explicit computations with the p-adic local Langlands correspondence for GL_2(Q_p), as well as by improving existing arguments which prove multiplicity one theorems via automorphy lifting theorems. This work will show that the existence of counterexamples to the Gouvêa-Mazur conjecture is due to a purely local phenomenon, and that when this local obstruction vanishes, far stronger conjectures of Buzzard on the slopes of the U_p operator hold.
Max ERC Funding
1 131 339 €
Duration
Start date: 2012-10-01, End date: 2017-09-30
Project acronym AFRIGOS
Project African Governance and Space: Transport Corridors, Border Towns and Port Cities in Transition
Researcher (PI) Paul Christopher Nugent
Host Institution (HI) THE UNIVERSITY OF EDINBURGH
Country United Kingdom
Call Details Advanced Grant (AdG), SH2, ERC-2014-ADG
Summary AFRIGOS investigates the process of 'respacing' Africa, a political drive towards regional and continental integration, on the one hand, and the re-casting of Africa's engagement with the global economy, on the other. This is reflected in unprecedented levels of investment in physical and communications infrastructure, and the outsourcing of key functions of Customs, Immigration and security agencies. AFRIGOS poses the question of how far respacing is genuinely forging institutions that are facilitating or obstructing the movement of people and goods; that are enabling or preventing urban and border spaces from being more effectively and responsively governed; and that take into account the needs of African populations whose livelihoods are rooted in mobility and informality. The principal research questions are approached through a comparative study of port cities, border towns and other strategic nodes situated along the busiest transport corridors in East, Central, West and Southern Africa. These represent sites of remarkable dynamism and cosmopolitanism, which reflects their role in connecting African urban centres to each other and to other global cities.
AFRIGOS considers how governance 'assemblages' are forged at different scales and is explicitly comparative. It works through 5 connected Streams that address specific questions: 1. AGENDA-SETTING is concerned with policy (re-)formulation. 2. PERIPHERAL URBANISM examines governance in border towns and port cities. 3. BORDER WORKERS addresses everyday governance emerging through the interaction of officials and others who make their livelihoods from the border. 4. CONNECTIVE INFRASTRUCTURE looks as the transformative effects of new technologies. 5. PEOPLE & GOODS IN MOTION traces the passage of people and goods and the regimes of regulation to which they are subjected. AFRIGOS contributes to interdisciplinary research on borderland studies, multi-level governance and the everyday state.
Summary
AFRIGOS investigates the process of 'respacing' Africa, a political drive towards regional and continental integration, on the one hand, and the re-casting of Africa's engagement with the global economy, on the other. This is reflected in unprecedented levels of investment in physical and communications infrastructure, and the outsourcing of key functions of Customs, Immigration and security agencies. AFRIGOS poses the question of how far respacing is genuinely forging institutions that are facilitating or obstructing the movement of people and goods; that are enabling or preventing urban and border spaces from being more effectively and responsively governed; and that take into account the needs of African populations whose livelihoods are rooted in mobility and informality. The principal research questions are approached through a comparative study of port cities, border towns and other strategic nodes situated along the busiest transport corridors in East, Central, West and Southern Africa. These represent sites of remarkable dynamism and cosmopolitanism, which reflects their role in connecting African urban centres to each other and to other global cities.
AFRIGOS considers how governance 'assemblages' are forged at different scales and is explicitly comparative. It works through 5 connected Streams that address specific questions: 1. AGENDA-SETTING is concerned with policy (re-)formulation. 2. PERIPHERAL URBANISM examines governance in border towns and port cities. 3. BORDER WORKERS addresses everyday governance emerging through the interaction of officials and others who make their livelihoods from the border. 4. CONNECTIVE INFRASTRUCTURE looks as the transformative effects of new technologies. 5. PEOPLE & GOODS IN MOTION traces the passage of people and goods and the regimes of regulation to which they are subjected. AFRIGOS contributes to interdisciplinary research on borderland studies, multi-level governance and the everyday state.
Max ERC Funding
2 491 364 €
Duration
Start date: 2016-01-01, End date: 2021-12-31
