Project acronym 19TH-CENTURY_EUCLID
Project Nineteenth-Century Euclid: Geometry and the Literary Imagination from Wordsworth to Wells
Researcher (PI) Alice Jenkins
Host Institution (HI) UNIVERSITY OF GLASGOW
Call Details Starting Grant (StG), SH4, ERC-2007-StG
Summary This radically interdisciplinary project aims to bring a substantially new field of research – literature and mathematics studies – to prominence as a tool for investigating the culture of nineteenth-century Britain. It will result in three kinds of outcome: a monograph, two interdisciplinary and international colloquia, and a collection of essays. The project focuses on Euclidean geometry as a key element of nineteenth-century literary and scientific culture, showing that it was part of the shared knowledge flowing through elite and popular Romantic and Victorian writing, and figuring notably in the work of very many of the century’s best-known writers. Despite its traditional cultural prestige and educational centrality, geometry has been almost wholly neglected by literary history. This project shows how literature and mathematics studies can draw a new map of nineteenth-century British culture, revitalising our understanding of the Romantic and Victorian imagination through its writing about geometry.
Summary
This radically interdisciplinary project aims to bring a substantially new field of research – literature and mathematics studies – to prominence as a tool for investigating the culture of nineteenth-century Britain. It will result in three kinds of outcome: a monograph, two interdisciplinary and international colloquia, and a collection of essays. The project focuses on Euclidean geometry as a key element of nineteenth-century literary and scientific culture, showing that it was part of the shared knowledge flowing through elite and popular Romantic and Victorian writing, and figuring notably in the work of very many of the century’s best-known writers. Despite its traditional cultural prestige and educational centrality, geometry has been almost wholly neglected by literary history. This project shows how literature and mathematics studies can draw a new map of nineteenth-century British culture, revitalising our understanding of the Romantic and Victorian imagination through its writing about geometry.
Max ERC Funding
323 118 €
Duration
Start date: 2009-01-01, End date: 2011-10-31
Project acronym 2SEXES_1GENOME
Project Sex-specific genetic effects on fitness and human disease
Researcher (PI) Edward Hugh Morrow
Host Institution (HI) THE UNIVERSITY OF SUSSEX
Call Details Starting Grant (StG), LS8, ERC-2011-StG_20101109
Summary Darwin’s theory of natural selection rests on the principle that fitness variation in natural populations has a heritable component, on which selection acts, thereby leading to evolutionary change. A fundamental and so far unresolved question for the field of evolutionary biology is to identify the genetic loci responsible for this fitness variation, thereby coming closer to an understanding of how variation is maintained in the face of continual selection. One important complicating factor in the search for fitness related genes however is the existence of separate sexes – theoretical expectations and empirical data both suggest that sexually antagonistic genes are common. The phrase “two sexes, one genome” nicely sums up the problem; selection may favour alleles in one sex, even if they have detrimental effects on the fitness of the opposite sex, since it is their net effect across both sexes that determine the likelihood that alleles persist in a population. This theoretical framework raises an interesting, and so far entirely unexplored issue: that in one sex the functional performance of some alleles is predicted to be compromised and this effect may account for some common human diseases and conditions which show genotype-sex interactions. I propose to explore the genetic basis of sex-specific fitness in a model organism in both laboratory and natural conditions and to test whether those genes identified as having sexually antagonistic effects can help explain the incidence of human diseases that display sexual dimorphism in prevalence, age of onset or severity. This multidisciplinary project directly addresses some fundamental unresolved questions in evolutionary biology: the genetic basis and maintenance of fitness variation; the evolution of sexual dimorphism; and aims to provide novel insights into the genetic basis of some common human diseases.
Summary
Darwin’s theory of natural selection rests on the principle that fitness variation in natural populations has a heritable component, on which selection acts, thereby leading to evolutionary change. A fundamental and so far unresolved question for the field of evolutionary biology is to identify the genetic loci responsible for this fitness variation, thereby coming closer to an understanding of how variation is maintained in the face of continual selection. One important complicating factor in the search for fitness related genes however is the existence of separate sexes – theoretical expectations and empirical data both suggest that sexually antagonistic genes are common. The phrase “two sexes, one genome” nicely sums up the problem; selection may favour alleles in one sex, even if they have detrimental effects on the fitness of the opposite sex, since it is their net effect across both sexes that determine the likelihood that alleles persist in a population. This theoretical framework raises an interesting, and so far entirely unexplored issue: that in one sex the functional performance of some alleles is predicted to be compromised and this effect may account for some common human diseases and conditions which show genotype-sex interactions. I propose to explore the genetic basis of sex-specific fitness in a model organism in both laboratory and natural conditions and to test whether those genes identified as having sexually antagonistic effects can help explain the incidence of human diseases that display sexual dimorphism in prevalence, age of onset or severity. This multidisciplinary project directly addresses some fundamental unresolved questions in evolutionary biology: the genetic basis and maintenance of fitness variation; the evolution of sexual dimorphism; and aims to provide novel insights into the genetic basis of some common human diseases.
Max ERC Funding
1 500 000 €
Duration
Start date: 2012-01-01, End date: 2016-12-31
Project acronym AAMDDR
Project DNA damage response and genome stability: The role of ATM, ATR and the Mre11 complex
Researcher (PI) Vincenzo Costanzo
Host Institution (HI) CANCER RESEARCH UK LBG
Call Details Starting Grant (StG), LS1, ERC-2007-StG
Summary Chromosomal DNA is continuously subjected to exogenous and endogenous damaging insults. In the presence of DNA damage cells activate a multi-faceted checkpoint response that delays cell cycle progression and promotes DNA repair. Failures in this response lead to genomic instability, the main feature of cancer cells. Several cancer-prone human syndromes including the Ataxia teleangiectasia (A-T), the A-T Like Disorder (ATLD) and the Seckel Syndrome reflect defects in the specific genes of the DNA damage response such as ATM, MRE11 and ATR. DNA damage response pathways are poorly understood at biochemical level in vertebrate organisms. We have established a cell-free system based on Xenopus laevis egg extract to study molecular events underlying DNA damage response. This is the first in vitro system that recapitulates different aspects of the DNA damage response in vertebrates. Using this system we propose to study the biochemistry of the ATM, ATR and the Mre11 complex dependent DNA damage response. In particular we will: 1) Dissect the signal transduction pathway that senses DNA damage and promotes cell cycle arrest and DNA damage repair; 2) Analyze at molecular level the role of ATM, ATR, Mre11 in chromosomal DNA replication and mitosis during normal and stressful conditions; 3) Identify substrates of the ATM and ATR dependent DNA damage response using an innovative screening procedure.
Summary
Chromosomal DNA is continuously subjected to exogenous and endogenous damaging insults. In the presence of DNA damage cells activate a multi-faceted checkpoint response that delays cell cycle progression and promotes DNA repair. Failures in this response lead to genomic instability, the main feature of cancer cells. Several cancer-prone human syndromes including the Ataxia teleangiectasia (A-T), the A-T Like Disorder (ATLD) and the Seckel Syndrome reflect defects in the specific genes of the DNA damage response such as ATM, MRE11 and ATR. DNA damage response pathways are poorly understood at biochemical level in vertebrate organisms. We have established a cell-free system based on Xenopus laevis egg extract to study molecular events underlying DNA damage response. This is the first in vitro system that recapitulates different aspects of the DNA damage response in vertebrates. Using this system we propose to study the biochemistry of the ATM, ATR and the Mre11 complex dependent DNA damage response. In particular we will: 1) Dissect the signal transduction pathway that senses DNA damage and promotes cell cycle arrest and DNA damage repair; 2) Analyze at molecular level the role of ATM, ATR, Mre11 in chromosomal DNA replication and mitosis during normal and stressful conditions; 3) Identify substrates of the ATM and ATR dependent DNA damage response using an innovative screening procedure.
Max ERC Funding
1 000 000 €
Duration
Start date: 2008-07-01, End date: 2013-06-30
Project acronym AAREA
Project The Archaeology of Agricultural Resilience in Eastern Africa
Researcher (PI) Daryl Stump
Host Institution (HI) UNIVERSITY OF YORK
Call Details Starting Grant (StG), SH6, ERC-2013-StG
Summary "The twin concepts of sustainability and conservation that are so pivotal within current debates regarding economic development and biodiversity protection both contain an inherent temporal dimension, since both refer to the need to balance short-term gains with long-term resource maintenance. Proponents of resilience theory and of development based on ‘indigenous knowledge’ have thus argued for the necessity of including archaeological, historical and palaeoenvironmental components within development project design. Indeed, some have argued that archaeology should lead these interdisciplinary projects on the grounds that it provides the necessary time depth and bridges the social and natural sciences. The project proposed here accepts this logic and endorses this renewed contemporary relevance of archaeological research. However, it also needs to be admitted that moving beyond critiques of the misuse of historical data presents significant hurdles. When presenting results outside the discipline, for example, archaeological projects tend to downplay the poor archaeological visibility of certain agricultural practices, and computer models designed to test sustainability struggle to adequately account for local cultural preferences. This field will therefore not progress unless there is a frank appraisal of archaeology’s strengths and weaknesses. This project will provide this assessment by employing a range of established and groundbreaking archaeological and modelling techniques to examine the development of two east Africa agricultural systems: one at the abandoned site of Engaruka in Tanzania, commonly seen as an example of resource mismanagement and ecological collapse; and another at the current agricultural landscape in Konso, Ethiopia, described by the UN FAO as one of a select few African “lessons from the past”. The project thus aims to assess the sustainability of these systems, but will also assess the role archaeology can play in such debates worldwide."
Summary
"The twin concepts of sustainability and conservation that are so pivotal within current debates regarding economic development and biodiversity protection both contain an inherent temporal dimension, since both refer to the need to balance short-term gains with long-term resource maintenance. Proponents of resilience theory and of development based on ‘indigenous knowledge’ have thus argued for the necessity of including archaeological, historical and palaeoenvironmental components within development project design. Indeed, some have argued that archaeology should lead these interdisciplinary projects on the grounds that it provides the necessary time depth and bridges the social and natural sciences. The project proposed here accepts this logic and endorses this renewed contemporary relevance of archaeological research. However, it also needs to be admitted that moving beyond critiques of the misuse of historical data presents significant hurdles. When presenting results outside the discipline, for example, archaeological projects tend to downplay the poor archaeological visibility of certain agricultural practices, and computer models designed to test sustainability struggle to adequately account for local cultural preferences. This field will therefore not progress unless there is a frank appraisal of archaeology’s strengths and weaknesses. This project will provide this assessment by employing a range of established and groundbreaking archaeological and modelling techniques to examine the development of two east Africa agricultural systems: one at the abandoned site of Engaruka in Tanzania, commonly seen as an example of resource mismanagement and ecological collapse; and another at the current agricultural landscape in Konso, Ethiopia, described by the UN FAO as one of a select few African “lessons from the past”. The project thus aims to assess the sustainability of these systems, but will also assess the role archaeology can play in such debates worldwide."
Max ERC Funding
1 196 701 €
Duration
Start date: 2014-02-01, End date: 2018-01-31
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
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 ACROSS
Project Australasian Colonization Research: Origins of Seafaring to Sahul
Researcher (PI) Rosemary Helen FARR
Host Institution (HI) UNIVERSITY OF SOUTHAMPTON
Call Details Starting Grant (StG), SH6, ERC-2017-STG
Summary One of the most exciting research questions within archaeology is that of the peopling of Australasia by at least c.50,000 years ago. This represents some of the earliest evidence of modern human colonization outside Africa, yet, even at the greatest sea-level lowstand, this migration would have involved seafaring. It is the maritime nature of this dispersal which makes it so important to questions of technological, cognitive and social human development. These issues have traditionally been the preserve of archaeologists, but with a multidisciplinary approach that embraces cutting-edge marine geophysical, hydrodynamic and archaeogenetic analyses, we now have the opportunity to examine the When, Where, Who and How of the earliest seafaring in world history.
The voyage from Sunda (South East Asia) to Sahul (Australasia) provides evidence for the earliest ‘open water’ crossing in the world. A combination of the sparse number of early archaeological finds and the significant changes in the palaeolandscape and submergence of the broad north western Australian continental shelf, mean that little is known about the routes taken and what these crossings may have entailed.
This project will combine research of the submerged palaeolandscape of the continental shelf to refine our knowledge of the onshore/offshore environment, identify potential submerged prehistoric sites and enhance our understanding of the palaeoshoreline and tidal regime. This will be combined with archaeogenetic research targeting mtDNA and Y-chromosome data to resolve questions of demography and dating.
For the first time this project takes a truly multidisciplinary approach to address the colonization of Sahul, providing an unique opportunity to tackle some of the most important questions about human origins, the relationship between humans and the changing environment, population dynamics and migration, seafaring technology, social organisation and cognition.
Summary
One of the most exciting research questions within archaeology is that of the peopling of Australasia by at least c.50,000 years ago. This represents some of the earliest evidence of modern human colonization outside Africa, yet, even at the greatest sea-level lowstand, this migration would have involved seafaring. It is the maritime nature of this dispersal which makes it so important to questions of technological, cognitive and social human development. These issues have traditionally been the preserve of archaeologists, but with a multidisciplinary approach that embraces cutting-edge marine geophysical, hydrodynamic and archaeogenetic analyses, we now have the opportunity to examine the When, Where, Who and How of the earliest seafaring in world history.
The voyage from Sunda (South East Asia) to Sahul (Australasia) provides evidence for the earliest ‘open water’ crossing in the world. A combination of the sparse number of early archaeological finds and the significant changes in the palaeolandscape and submergence of the broad north western Australian continental shelf, mean that little is known about the routes taken and what these crossings may have entailed.
This project will combine research of the submerged palaeolandscape of the continental shelf to refine our knowledge of the onshore/offshore environment, identify potential submerged prehistoric sites and enhance our understanding of the palaeoshoreline and tidal regime. This will be combined with archaeogenetic research targeting mtDNA and Y-chromosome data to resolve questions of demography and dating.
For the first time this project takes a truly multidisciplinary approach to address the colonization of Sahul, providing an unique opportunity to tackle some of the most important questions about human origins, the relationship between humans and the changing environment, population dynamics and migration, seafaring technology, social organisation and cognition.
Max ERC Funding
1 134 928 €
Duration
Start date: 2018-02-01, End date: 2023-01-31
Project acronym ACTIVE_NEUROGENESIS
Project Activity-dependent signaling in radial glial cells and their neuronal progeny
Researcher (PI) Colin Akerman
Host Institution (HI) THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Call Details Starting Grant (StG), LS5, ERC-2009-StG
Summary A significant advance in the field of development has been the appreciation that radial glial cells are progenitors and give birth to neurons in the brain. In order to advance this exciting area of biology, we need approaches that combine structural and functional studies of these cells. This is reflected by the emerging realisation that dynamic interactions involving radial glia may be critical for the regulation of their proliferative behaviour. It has been observed that radial glia experience transient elevations in intracellular Ca2+ but the nature of these signals, and the information that they convey, is not known. The inability to observe these cells in vivo and over the course of their development has also meant that basic questions remain unexplored. For instance, how does the behaviour of a radial glial cell at one point in development, influence the final identity of its progeny? I propose to build a research team that will capitalise upon methods we have developed for observing individual radial glia and their progeny in an intact vertebrate nervous system. The visual system of Xenopus Laevis tadpoles offers non-invasive optical access to the brain, making time-lapse imaging of single cells feasible over minutes and weeks. The system s anatomy lends itself to techniques that measure the activity of the cells in a functional sensory network. We will use this to examine signalling mechanisms in radial glia and how a radial glial cell s experience influences its proliferative behaviour and the types of neuron it generates. We will also examine the interactions that continue between a radial glial cell and its daughter neurons. Finally, we will explore the relationships that exist within neuronal progeny derived from a single radial glial cell.
Summary
A significant advance in the field of development has been the appreciation that radial glial cells are progenitors and give birth to neurons in the brain. In order to advance this exciting area of biology, we need approaches that combine structural and functional studies of these cells. This is reflected by the emerging realisation that dynamic interactions involving radial glia may be critical for the regulation of their proliferative behaviour. It has been observed that radial glia experience transient elevations in intracellular Ca2+ but the nature of these signals, and the information that they convey, is not known. The inability to observe these cells in vivo and over the course of their development has also meant that basic questions remain unexplored. For instance, how does the behaviour of a radial glial cell at one point in development, influence the final identity of its progeny? I propose to build a research team that will capitalise upon methods we have developed for observing individual radial glia and their progeny in an intact vertebrate nervous system. The visual system of Xenopus Laevis tadpoles offers non-invasive optical access to the brain, making time-lapse imaging of single cells feasible over minutes and weeks. The system s anatomy lends itself to techniques that measure the activity of the cells in a functional sensory network. We will use this to examine signalling mechanisms in radial glia and how a radial glial cell s experience influences its proliferative behaviour and the types of neuron it generates. We will also examine the interactions that continue between a radial glial cell and its daughter neurons. Finally, we will explore the relationships that exist within neuronal progeny derived from a single radial glial cell.
Max ERC Funding
1 284 808 €
Duration
Start date: 2010-02-01, End date: 2015-01-31
Project acronym ACTSELECTCONTEXT
Project Action Selection under Contextual Uncertainty: the Role of Learning and Effective Connectivity in the Human Brain
Researcher (PI) Sven Bestmann
Host Institution (HI) UNIVERSITY COLLEGE LONDON
Call Details Starting Grant (StG), LS5, ERC-2010-StG_20091118
Summary In a changing world, one hallmark feature of human behaviour is the ability to learn about the statistics of the environment and use this prior information for action selection. Knowing about a forthcoming event allows for adjusting our actions pre-emptively, which can optimize survival.
This proposal studies how the human brain learns about the uncertainty in the environment, and how this leads to flexible and efficient action selection.
I hypothesise that the accumulation of evidence for future movements through learning reflects a fundamental organisational principle for action control. This explains widely distributed perceptual-, learning-, decision-, and movement-related signals in the human brain. However, little is known about the concerted interplay between brain regions in terms of effective connectivity which is required for flexible behaviour.
My proposal seeks to shed light on this unresolved issue. To this end, I will use i) a multi-disciplinary neuroimaging approach, together with model-based analyses and Bayesian model comparison, adapted to human reaching behaviour as occurring in daily life; and ii) two novel approaches for testing effective connectivity: dynamic causal modelling (DCM) and concurrent transcranial magnetic stimulation-functional magnetic resonance imaging.
My prediction is that action selection relies on effective connectivity changes, which are a function of the prior information that the brain has to learn about.
If true, this will provide novel insight into the human ability to select actions, based on learning about the uncertainty which is inherent in contextual information. This is relevant for understanding action selection during development and ageing, and for pathologies of action such as Parkinson s disease or stroke.
Summary
In a changing world, one hallmark feature of human behaviour is the ability to learn about the statistics of the environment and use this prior information for action selection. Knowing about a forthcoming event allows for adjusting our actions pre-emptively, which can optimize survival.
This proposal studies how the human brain learns about the uncertainty in the environment, and how this leads to flexible and efficient action selection.
I hypothesise that the accumulation of evidence for future movements through learning reflects a fundamental organisational principle for action control. This explains widely distributed perceptual-, learning-, decision-, and movement-related signals in the human brain. However, little is known about the concerted interplay between brain regions in terms of effective connectivity which is required for flexible behaviour.
My proposal seeks to shed light on this unresolved issue. To this end, I will use i) a multi-disciplinary neuroimaging approach, together with model-based analyses and Bayesian model comparison, adapted to human reaching behaviour as occurring in daily life; and ii) two novel approaches for testing effective connectivity: dynamic causal modelling (DCM) and concurrent transcranial magnetic stimulation-functional magnetic resonance imaging.
My prediction is that action selection relies on effective connectivity changes, which are a function of the prior information that the brain has to learn about.
If true, this will provide novel insight into the human ability to select actions, based on learning about the uncertainty which is inherent in contextual information. This is relevant for understanding action selection during development and ageing, and for pathologies of action such as Parkinson s disease or stroke.
Max ERC Funding
1 341 805 €
Duration
Start date: 2011-06-01, End date: 2016-05-31
Project acronym ADaPTIVE
Project Analysing Diversity with a Phenomic approach: Trends in Vertebrate Evolution
Researcher (PI) Anjali Goswami
Host Institution (HI) NATURAL HISTORY MUSEUM
Call Details Starting Grant (StG), LS8, ERC-2014-STG
Summary What processes shape vertebrate diversity through deep time? Approaches to this question can focus on many different factors, from life history and ecology to large-scale environmental change and extinction. To date, the majority of studies on the evolution of vertebrate diversity have focused on relatively simple metrics, specifically taxon counts or univariate measures, such as body size. However, multivariate morphological data provides a more complete picture of evolutionary and palaeoecological change. Morphological data can also bridge deep-time palaeobiological analyses with studies of the genetic and developmental factors that shape variation and must also influence large-scale patterns of evolutionary change. Thus, accurately reconstructing the patterns and processes underlying evolution requires an approach that can fully represent an organism’s phenome, the sum total of their observable traits.
Recent advances in imaging and data analysis allow large-scale study of phenomic evolution. In this project, I propose to quantitatively analyse the deep-time evolutionary diversity of tetrapods (amphibians, reptiles, birds, and mammals). Specifically, I will apply and extend new imaging, morphometric, and analytical tools to construct a multivariate phenomic dataset for living and extinct tetrapods from 3-D scans. I will use these data to rigorously compare extinction selectivity, timing, pace, and shape of adaptive radiations, and ecomorphological response to large-scale climatic shifts across all tetrapod clades. To do so, I will quantify morphological diversity (disparity) and rates of evolution spanning over 300 million years of tetrapod history. I will further analyse the evolution of phenotypic integration by quantifying not just the traits themselves, but changes in the relationships among traits, which reflect the genetic, developmental, and functional interactions that shape variation, the raw material for natural selection.
Summary
What processes shape vertebrate diversity through deep time? Approaches to this question can focus on many different factors, from life history and ecology to large-scale environmental change and extinction. To date, the majority of studies on the evolution of vertebrate diversity have focused on relatively simple metrics, specifically taxon counts or univariate measures, such as body size. However, multivariate morphological data provides a more complete picture of evolutionary and palaeoecological change. Morphological data can also bridge deep-time palaeobiological analyses with studies of the genetic and developmental factors that shape variation and must also influence large-scale patterns of evolutionary change. Thus, accurately reconstructing the patterns and processes underlying evolution requires an approach that can fully represent an organism’s phenome, the sum total of their observable traits.
Recent advances in imaging and data analysis allow large-scale study of phenomic evolution. In this project, I propose to quantitatively analyse the deep-time evolutionary diversity of tetrapods (amphibians, reptiles, birds, and mammals). Specifically, I will apply and extend new imaging, morphometric, and analytical tools to construct a multivariate phenomic dataset for living and extinct tetrapods from 3-D scans. I will use these data to rigorously compare extinction selectivity, timing, pace, and shape of adaptive radiations, and ecomorphological response to large-scale climatic shifts across all tetrapod clades. To do so, I will quantify morphological diversity (disparity) and rates of evolution spanning over 300 million years of tetrapod history. I will further analyse the evolution of phenotypic integration by quantifying not just the traits themselves, but changes in the relationships among traits, which reflect the genetic, developmental, and functional interactions that shape variation, the raw material for natural selection.
Max ERC Funding
1 482 818 €
Duration
Start date: 2015-06-01, End date: 2020-05-31
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
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