Project acronym AIME
Project An Inquiry into Modes of Existence
Researcher (PI) Bruno Latour
Host Institution (HI) FONDATION NATIONALE DES SCIENCES POLITIQUES
Call Details Advanced Grant (AdG), SH2, ERC-2010-AdG_20100407
Summary "AIME is an inquiry to make more precise what is lumped together into the confusing word ""modernization"". The work done in the field of science studies (STS) on the progress and practice of science and technology has had the consequence of deeply modifying the definition of ""modernity"", resulting into the provocative idea that ""we (meaning the Europeans) have never been modern"". This is, however only a negative definition. To obtain a positive rendering of the European current situation, it is necessary to start an inquiry in the complex and conflicting set of values that have been invented. This inquiry is possible only if there is a clear and shareable way to judge the differences in the set of truth-conditions that make up those conflicting sets of values. AIME offers a grammar of those differences based on the key notion of modes of existence. Then it builds a procedure and an instrument to test this grammar into a selected set of situations where the definitions of the differing modes of existence is redefined and renegotiated. The result is a set of shareable definitions of what modernization has been in practice. This is important just at the moment when Europe has lost its privileged status and needs to be able to present itself in a new ways to the other cultures and civilizations which are making up the world of globalization with very different views on what it is to modernize themselves."
Summary
"AIME is an inquiry to make more precise what is lumped together into the confusing word ""modernization"". The work done in the field of science studies (STS) on the progress and practice of science and technology has had the consequence of deeply modifying the definition of ""modernity"", resulting into the provocative idea that ""we (meaning the Europeans) have never been modern"". This is, however only a negative definition. To obtain a positive rendering of the European current situation, it is necessary to start an inquiry in the complex and conflicting set of values that have been invented. This inquiry is possible only if there is a clear and shareable way to judge the differences in the set of truth-conditions that make up those conflicting sets of values. AIME offers a grammar of those differences based on the key notion of modes of existence. Then it builds a procedure and an instrument to test this grammar into a selected set of situations where the definitions of the differing modes of existence is redefined and renegotiated. The result is a set of shareable definitions of what modernization has been in practice. This is important just at the moment when Europe has lost its privileged status and needs to be able to present itself in a new ways to the other cultures and civilizations which are making up the world of globalization with very different views on what it is to modernize themselves."
Max ERC Funding
1 334 720 €
Duration
Start date: 2011-09-01, End date: 2015-06-30
Project acronym CPDENL
Project Control of partial differential equations and nonlinearity
Researcher (PI) Jean-Michel Coron
Host Institution (HI) UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6
Call Details Advanced Grant (AdG), PE1, ERC-2010-AdG_20100224
Summary The aim of this 5,5 years project is to create around the PI a research group on the control of systems modeled by partial differential equations at the Laboratory Jacques-Louis Lions of the UPMC and to develop with this group an intensive research activity focused on nonlinear phenomena.
With the ERC grant, the PI plans to hire post-doc fellows and PhD students, to offer 1-to-3 months positions to confirmed researchers, a regular seminar and workshops.
A lot is known on finite dimensional control systems and linear control systems modeled by partial differential equations. Much less is known for nonlinear control systems modeled by partial differential equations. In particular, in many important cases, one does not know how to use the classical iterated Lie brackets which are so useful to deal with nonlinear control systems in finite dimension.
In this project, the PI plans to develop, with the research group, methods to deal with the problems of controllability and of stabilization for nonlinear systems modeled by partial differential equations, in the case where the nonlinearity plays a crucial role. This is for example the case where the linearized control system around the equilibrium of interest is not controllable or not stabilizable. This is also the case when the nonlinearity is too big at infinity and one looks for global results. This is also the case if the nonlinearity contains too many derivatives. The PI has already introduced some methods to deal with these cases, but a lot remains to be done. Indeed, many natural important and challenging problems are still open. Precise examples, often coming from physics, are given in this proposal.
Summary
The aim of this 5,5 years project is to create around the PI a research group on the control of systems modeled by partial differential equations at the Laboratory Jacques-Louis Lions of the UPMC and to develop with this group an intensive research activity focused on nonlinear phenomena.
With the ERC grant, the PI plans to hire post-doc fellows and PhD students, to offer 1-to-3 months positions to confirmed researchers, a regular seminar and workshops.
A lot is known on finite dimensional control systems and linear control systems modeled by partial differential equations. Much less is known for nonlinear control systems modeled by partial differential equations. In particular, in many important cases, one does not know how to use the classical iterated Lie brackets which are so useful to deal with nonlinear control systems in finite dimension.
In this project, the PI plans to develop, with the research group, methods to deal with the problems of controllability and of stabilization for nonlinear systems modeled by partial differential equations, in the case where the nonlinearity plays a crucial role. This is for example the case where the linearized control system around the equilibrium of interest is not controllable or not stabilizable. This is also the case when the nonlinearity is too big at infinity and one looks for global results. This is also the case if the nonlinearity contains too many derivatives. The PI has already introduced some methods to deal with these cases, but a lot remains to be done. Indeed, many natural important and challenging problems are still open. Precise examples, often coming from physics, are given in this proposal.
Max ERC Funding
1 403 100 €
Duration
Start date: 2011-05-01, End date: 2016-09-30
Project acronym CRIMMIGRATION
Project 'Crimmigration': Crime Control in the Borderlands of Europe
Researcher (PI) Katja Franko Aas
Host Institution (HI) UNIVERSITETET I OSLO
Call Details Starting Grant (StG), SH2, ERC-2010-StG_20091209
Summary Control of migration is becoming an increasingly important task of contemporary policing and criminal justice agencies. The purpose of this project is to map the progressive intertwining and merging of crime control and migration control practices in Europe and to examine their implications.
The project is guided by three sets of research questions: 1) How do contemporary police and criminal justice institutions deal with unwanted mobility and the influx of „aliens‟ (i.e. non-citizens) to their territories? 2) What is the relevance of citizenship for European penal systems? and 3) How do contemporary crime control practices support and perform the task of (cultural and territorial) border control?
The project aims to analyse the impact of the growing emphasis on migration control on criminal justice agencies such as the police, prisons and detention facilities. The basic hypothesis of the project is that migration control objectives are contributing to the development of novel forms of punishment and new rationalities of social control termed „crimmigration‟. The project aims to describe these novel hybrid forms of control since they constitute important conceptual challenges for criminal justice scholarship and require new theoretical perspectives. A question will be asked: what kind of break from traditional criminal justice practices and principles do they represent? Is the focus on punishment and reintegration of offenders gradually being replaced by a focus on diversion, immobilisation and deportation? Moreover what kind of legal, organisational and normative responses do they require?
Summary
Control of migration is becoming an increasingly important task of contemporary policing and criminal justice agencies. The purpose of this project is to map the progressive intertwining and merging of crime control and migration control practices in Europe and to examine their implications.
The project is guided by three sets of research questions: 1) How do contemporary police and criminal justice institutions deal with unwanted mobility and the influx of „aliens‟ (i.e. non-citizens) to their territories? 2) What is the relevance of citizenship for European penal systems? and 3) How do contemporary crime control practices support and perform the task of (cultural and territorial) border control?
The project aims to analyse the impact of the growing emphasis on migration control on criminal justice agencies such as the police, prisons and detention facilities. The basic hypothesis of the project is that migration control objectives are contributing to the development of novel forms of punishment and new rationalities of social control termed „crimmigration‟. The project aims to describe these novel hybrid forms of control since they constitute important conceptual challenges for criminal justice scholarship and require new theoretical perspectives. A question will be asked: what kind of break from traditional criminal justice practices and principles do they represent? Is the focus on punishment and reintegration of offenders gradually being replaced by a focus on diversion, immobilisation and deportation? Moreover what kind of legal, organisational and normative responses do they require?
Max ERC Funding
1 309 800 €
Duration
Start date: 2011-04-01, End date: 2016-03-31
Project acronym DISPEQ
Project Qualitative study of nonlinear dispersive equations
Researcher (PI) Nikolay Tzvetkov
Host Institution (HI) UNIVERSITE DE CERGY-PONTOISE
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary We plan to further improve the understanding of the nonlinear dispersive wave propagation phenomena. In particular we plan to develop tools allowing to make a statistical description of the corresponding flows and methods to study transverse stability independently of the very particular arguments based on the inverse scattering. We also plan to study critical problems in strongly non Euclidean geometries.
Summary
We plan to further improve the understanding of the nonlinear dispersive wave propagation phenomena. In particular we plan to develop tools allowing to make a statistical description of the corresponding flows and methods to study transverse stability independently of the very particular arguments based on the inverse scattering. We also plan to study critical problems in strongly non Euclidean geometries.
Max ERC Funding
880 270 €
Duration
Start date: 2010-10-01, End date: 2015-09-30
Project acronym GMODGAMMADYNAMICS
Project Dynamics on homogeneous spaces, spectra and arithmetic
Researcher (PI) Elon Lindenstrauss
Host Institution (HI) THE HEBREW UNIVERSITY OF JERUSALEM
Call Details Advanced Grant (AdG), PE1, ERC-2010-AdG_20100224
Summary We consider the dynamics of actions on homogeneous spaces of algebraic groups,
We propose to tackle the central open problems in the area, including understanding actions of diagonal groups on homogeneous spaces without an entropy assumption, a related conjecture of Furstenberg about measures on R / Z invariant under multiplication by 2 and 3, and obtaining a quantitative understanding of equidistribution properties of unipotent flows and groups generated by unipotents.
This has applications in arithmetic, Diophantine approximations, the spectral theory of homogeneous spaces, mathematical physics, and other fields. Connections to arithmetic combinatorics will be pursued.
Summary
We consider the dynamics of actions on homogeneous spaces of algebraic groups,
We propose to tackle the central open problems in the area, including understanding actions of diagonal groups on homogeneous spaces without an entropy assumption, a related conjecture of Furstenberg about measures on R / Z invariant under multiplication by 2 and 3, and obtaining a quantitative understanding of equidistribution properties of unipotent flows and groups generated by unipotents.
This has applications in arithmetic, Diophantine approximations, the spectral theory of homogeneous spaces, mathematical physics, and other fields. Connections to arithmetic combinatorics will be pursued.
Max ERC Funding
1 229 714 €
Duration
Start date: 2011-01-01, End date: 2016-12-31
Project acronym MATHANA
Project Mathematical modeling of anaesthetic action
Researcher (PI) Axel Hutt
Host Institution (HI) INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary General anaesthesia is an important method in today's hospital practice and especially in surgery. To supervise the depth of anaesthesia during surgery, the anaesthesist applies electroencephalography (EEG) and monitors the brain activity of the subject on the scalp. The applied monitoring machine calculates the change of the power spectrum of the brain signals to indicate the anaesthetic depth. This procedure is based on the finding that the concentration increase of the anaesthetic drug changes the EEG-power spectrum in a significant way. Although this procedure is applied world-wide, the underlying neural mechanism of the spectrum change is still unknown. The project aims to elucidate the underlying neural mechanism by a detailed investigating a mathematical model of neural populations.
The investigation is based on analytical calculations in a neural population model of the cortex involving intrinsic neural properties of brain areas and feedback loops to other areas, such as the loop between the cortex and the thalamus. Currently, there are two proposed mechanisms for the charactertisic change of the power spectrum: a highly nonlinear jump in the activation (so-called phase transition) and a linear behavior. The project mainly focusses on the nonlinear jump to finally rule it out or support it. A subsequent comparison to previous experimenta results aims to fit the physiological parameters. Since the cortex population is embedded into a network of other cortical areas and the thalamus, the corresponding analytical investigations takes into account external stochastic (from other brain areas) and time-periodic (thalamic) forces. To this end it is necessary to develop several novel nonlinear analysis technique of neural populations to derive the power spectrum close to the phase transition and conditions for physiological parameters.
Summary
General anaesthesia is an important method in today's hospital practice and especially in surgery. To supervise the depth of anaesthesia during surgery, the anaesthesist applies electroencephalography (EEG) and monitors the brain activity of the subject on the scalp. The applied monitoring machine calculates the change of the power spectrum of the brain signals to indicate the anaesthetic depth. This procedure is based on the finding that the concentration increase of the anaesthetic drug changes the EEG-power spectrum in a significant way. Although this procedure is applied world-wide, the underlying neural mechanism of the spectrum change is still unknown. The project aims to elucidate the underlying neural mechanism by a detailed investigating a mathematical model of neural populations.
The investigation is based on analytical calculations in a neural population model of the cortex involving intrinsic neural properties of brain areas and feedback loops to other areas, such as the loop between the cortex and the thalamus. Currently, there are two proposed mechanisms for the charactertisic change of the power spectrum: a highly nonlinear jump in the activation (so-called phase transition) and a linear behavior. The project mainly focusses on the nonlinear jump to finally rule it out or support it. A subsequent comparison to previous experimenta results aims to fit the physiological parameters. Since the cortex population is embedded into a network of other cortical areas and the thalamus, the corresponding analytical investigations takes into account external stochastic (from other brain areas) and time-periodic (thalamic) forces. To this end it is necessary to develop several novel nonlinear analysis technique of neural populations to derive the power spectrum close to the phase transition and conditions for physiological parameters.
Max ERC Funding
856 500 €
Duration
Start date: 2011-01-01, End date: 2015-10-31
Project acronym MNIQS
Project Mathematics and Numerics of Infinite Quantum Systems
Researcher (PI) Mathieu Lewin
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary The purpose of the project is to study linear and nonlinear models arising in quantum mechanics and which are used to describe
matter at the microscopic and nanoscopic scales. The project focuses on physically-oriented questions (rigorous derivation of a
given model from first principles), analytic problems (existence and properties of bound states, study of solutions to timedependent
equations) and numerical issues (development of reliable algorithmic strategies). Most of the models are nonlinear and
describe physical systems possessing an infinite number of quantum particles, leading to specific difficulties.
The first part of the project is devoted to the study of relativistic atoms and molecules, while taking into account quantum
electrodynamics effects like the polarization of the vacuum. The models are all based on the Dirac operator.
The second part is focused on the study of quantum crystals. The goal is to develop new strategies for describing their behavior in
the presence of defects and local deformations. Both insulators, semiconductors and metals are considered (including graphene).
In the third part, attractive systems are considered (like stars or a few nucleons interacting via strong forces in a nucleus). The
project aims at rigorously understanding some of their specific properties, like Cooper pairing or the possible dynamical collapse of
massive gravitational objects.
Finally, the last part is devoted to general properties of infinite quantum systems, in particular the proof of the existence of the
thermodynamic limit
Summary
The purpose of the project is to study linear and nonlinear models arising in quantum mechanics and which are used to describe
matter at the microscopic and nanoscopic scales. The project focuses on physically-oriented questions (rigorous derivation of a
given model from first principles), analytic problems (existence and properties of bound states, study of solutions to timedependent
equations) and numerical issues (development of reliable algorithmic strategies). Most of the models are nonlinear and
describe physical systems possessing an infinite number of quantum particles, leading to specific difficulties.
The first part of the project is devoted to the study of relativistic atoms and molecules, while taking into account quantum
electrodynamics effects like the polarization of the vacuum. The models are all based on the Dirac operator.
The second part is focused on the study of quantum crystals. The goal is to develop new strategies for describing their behavior in
the presence of defects and local deformations. Both insulators, semiconductors and metals are considered (including graphene).
In the third part, attractive systems are considered (like stars or a few nucleons interacting via strong forces in a nucleus). The
project aims at rigorously understanding some of their specific properties, like Cooper pairing or the possible dynamical collapse of
massive gravitational objects.
Finally, the last part is devoted to general properties of infinite quantum systems, in particular the proof of the existence of the
thermodynamic limit
Max ERC Funding
905 700 €
Duration
Start date: 2010-10-01, End date: 2015-09-30
Project acronym MULTIMOD
Project Multi-Mathematics for Imaging and Optimal Design Under Uncertainty
Researcher (PI) Habib Ammari
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Advanced Grant (AdG), PE1, ERC-2010-AdG_20100224
Summary The aim of this interdisciplinary project is to develop new mathematical and statistical tools, probabilistic approaches, and inversion and optimal design methods to address emerging modalities in medical imaging, nondestructive testing, and environmental inverse problems. It merges the complementary expertise of the investigators in order to make a breakthrough in the field of
mathematical imaging and optimal design by solving the most challenging problems posed by new imaging modalities. The PI and Co-PI are leading experts in their respective fields (applied
analysis and probability) and their researches have very strong interdisciplinary nature.
The goal of this project is to synergize asymptotic imaging, stochastic modelling, and analysis of both deterministic and stochastic wave propagation phenomena. We want to throw a bridge across the deterministic and stochastic aspects and tools of mathematical imaging. This requires a deep understanding of the different scales in the physical problem, an accurate modelling of the noise sources, and fine mathematical analysis of complex phenomena. The emphasis of this project will be put on deriving for each of the challenging imaging problems that we will consider, the best possible imaging functionals in the sense of stability and resolution. For optimal design problems, we
will evaluate the effect of uncertainties on the geometrical or physical parameters and design accurate optimal design methodologies.
In this project, we will build an exceptional interdisciplinary research and an innovative approach to training in applied mathematics. We will train a new generation of applied mathematicians who will master both the probabilistic and analytical tools to best meet the challenges of emerging technologies.
Summary
The aim of this interdisciplinary project is to develop new mathematical and statistical tools, probabilistic approaches, and inversion and optimal design methods to address emerging modalities in medical imaging, nondestructive testing, and environmental inverse problems. It merges the complementary expertise of the investigators in order to make a breakthrough in the field of
mathematical imaging and optimal design by solving the most challenging problems posed by new imaging modalities. The PI and Co-PI are leading experts in their respective fields (applied
analysis and probability) and their researches have very strong interdisciplinary nature.
The goal of this project is to synergize asymptotic imaging, stochastic modelling, and analysis of both deterministic and stochastic wave propagation phenomena. We want to throw a bridge across the deterministic and stochastic aspects and tools of mathematical imaging. This requires a deep understanding of the different scales in the physical problem, an accurate modelling of the noise sources, and fine mathematical analysis of complex phenomena. The emphasis of this project will be put on deriving for each of the challenging imaging problems that we will consider, the best possible imaging functionals in the sense of stability and resolution. For optimal design problems, we
will evaluate the effect of uncertainties on the geometrical or physical parameters and design accurate optimal design methodologies.
In this project, we will build an exceptional interdisciplinary research and an innovative approach to training in applied mathematics. We will train a new generation of applied mathematicians who will master both the probabilistic and analytical tools to best meet the challenges of emerging technologies.
Max ERC Funding
1 920 000 €
Duration
Start date: 2011-04-01, End date: 2016-03-31
Project acronym MULTIRIGHTS
Project The Legitimacy of Multi-level Human Rights Judiciary
Researcher (PI) Andreas Follesdal
Host Institution (HI) UNIVERSITETET I OSLO
Call Details Advanced Grant (AdG), SH2, ERC-2010-AdG_20100407
Summary The proliferation of human rights treaties at regional and global levels may offer moral foundations for international law. However, many worry that this growth of supervisory organs is illegitimate. Consider, for instance
• The European Court of Human Rights (ECtHR) is overburdened.
• The human rights organs may disagree e.g. on how to balance freedom of expression against protection from hate speech. Which should be obeyed?
• Citizens of well-functioning democracies ask: why should such international organs intervene?
The MultiRights team of international lawyers and political theorists will first scrutinize the claims of legitimacy deficits. We then consider reform proposals for global and European human rights organs: We develop four plausible models, ranging from Primacy of National Courts to a World Court of Human Rights. We will assess the models by four Contested Constitutional Principles of legitimacy, revised for our multilevel legal order: Human Rights values, the Rule of Law, Subsidiarity, and Democracy.
MultiRights thereby provides reasoned comparative assessment of models for human rights regime reforms, and contributes to better standards of legitimacy for international institutions. The findings also help us understand and assess the alleged ‘Constitutionalisation of International Law” - an urgent topic under globalization, when governance beyond states increases in density and impact.
The academic contributions of MultiRights will also benefit several reforms:
• the Interlaken Process on how to improve the ECtHR,
• the accession of the EU to the European Convention on Human Rights under the Lisbon Treaty,
• the UN Secretary General’s calls to reform the Human Rights treaty body system, and
• challenges to the democratic credentials of such human rights review.
Summary
The proliferation of human rights treaties at regional and global levels may offer moral foundations for international law. However, many worry that this growth of supervisory organs is illegitimate. Consider, for instance
• The European Court of Human Rights (ECtHR) is overburdened.
• The human rights organs may disagree e.g. on how to balance freedom of expression against protection from hate speech. Which should be obeyed?
• Citizens of well-functioning democracies ask: why should such international organs intervene?
The MultiRights team of international lawyers and political theorists will first scrutinize the claims of legitimacy deficits. We then consider reform proposals for global and European human rights organs: We develop four plausible models, ranging from Primacy of National Courts to a World Court of Human Rights. We will assess the models by four Contested Constitutional Principles of legitimacy, revised for our multilevel legal order: Human Rights values, the Rule of Law, Subsidiarity, and Democracy.
MultiRights thereby provides reasoned comparative assessment of models for human rights regime reforms, and contributes to better standards of legitimacy for international institutions. The findings also help us understand and assess the alleged ‘Constitutionalisation of International Law” - an urgent topic under globalization, when governance beyond states increases in density and impact.
The academic contributions of MultiRights will also benefit several reforms:
• the Interlaken Process on how to improve the ECtHR,
• the accession of the EU to the European Convention on Human Rights under the Lisbon Treaty,
• the UN Secretary General’s calls to reform the Human Rights treaty body system, and
• challenges to the democratic credentials of such human rights review.
Max ERC Funding
2 430 000 €
Duration
Start date: 2011-06-01, End date: 2016-05-31
Project acronym PAGAP
Project Periods in Algebraic Geometry and Physics
Researcher (PI) Francis Clement Sais Brown
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary Periods are the integrals of algebraic differential forms over domains defined by polynomial inequalities, and are ubiquitous in mathematics and physics. One of the simplest classes of periods are given by multiple zeta values, which are the periods of moduli spaces M_{0,n} of curves of genus zero. They have recently undergone a huge revival of interest, and occur in number theory, the theory of mixed Tate motives, knot invariants, quantum groups, deformation quantization and many more branches of mathematics and physics.
Remarkably, it has been observed experimentally that Feynman amplitudes in quantum field theories typically evaluate numerically to multiple zeta values and polylogarithms (which are the iterated integrals on M_{0,n}), and a huge amount of effort is presently devoted to computations of such amplitudes in order to provide predictions for particle collider experiments. A deeper understanding of the reason for the appearance of the same mathematical objects in algebraic geometry and physics is essential to streamline these computations, and ultimately tackle the outstanding problems in particle physics.
The proposal has two parts: firstly to undertake a systematic study of the periods and iterated integrals on higher genus moduli spaces M_{g,n} and related varieties, and secondly to relate these fundamental mathematical objects to quantum field theories, bringing to bear modern techniques from algebraic geometry, Hodge theory, and motives to this emerging interdisciplinary area. Part of this would involve the implementation (with the assistance of future postdoc. team members) of an algorithm for the evaluation of Feynman diagrams which is due to the author and goes several orders beyond what has previously been possible, in order eventually to deduce concrete predictions for the Large Hadron Collider.
Summary
Periods are the integrals of algebraic differential forms over domains defined by polynomial inequalities, and are ubiquitous in mathematics and physics. One of the simplest classes of periods are given by multiple zeta values, which are the periods of moduli spaces M_{0,n} of curves of genus zero. They have recently undergone a huge revival of interest, and occur in number theory, the theory of mixed Tate motives, knot invariants, quantum groups, deformation quantization and many more branches of mathematics and physics.
Remarkably, it has been observed experimentally that Feynman amplitudes in quantum field theories typically evaluate numerically to multiple zeta values and polylogarithms (which are the iterated integrals on M_{0,n}), and a huge amount of effort is presently devoted to computations of such amplitudes in order to provide predictions for particle collider experiments. A deeper understanding of the reason for the appearance of the same mathematical objects in algebraic geometry and physics is essential to streamline these computations, and ultimately tackle the outstanding problems in particle physics.
The proposal has two parts: firstly to undertake a systematic study of the periods and iterated integrals on higher genus moduli spaces M_{g,n} and related varieties, and secondly to relate these fundamental mathematical objects to quantum field theories, bringing to bear modern techniques from algebraic geometry, Hodge theory, and motives to this emerging interdisciplinary area. Part of this would involve the implementation (with the assistance of future postdoc. team members) of an algorithm for the evaluation of Feynman diagrams which is due to the author and goes several orders beyond what has previously been possible, in order eventually to deduce concrete predictions for the Large Hadron Collider.
Max ERC Funding
1 068 540 €
Duration
Start date: 2010-11-01, End date: 2015-10-31
