Project acronym 2-3-AUT
Project Surfaces, 3-manifolds and automorphism groups
Researcher (PI) Nathalie Wahl
Host Institution (HI) KOBENHAVNS UNIVERSITET
Country Denmark
Call Details Starting Grant (StG), PE1, ERC-2009-StG
Summary The scientific goal of the proposal is to answer central questions related to diffeomorphism groups of manifolds of dimension 2 and 3, and to their deformation invariant analogs, the mapping class groups. While the classification of surfaces has been known for more than a century, their automorphism groups have yet to be fully understood. Even less is known about diffeomorphisms of 3-manifolds despite much interest, and the objects here have only been classified recently, by the breakthrough work of Perelman on the Poincar\'e and geometrization conjectures. In dimension 2, I will focus on the relationship between mapping class groups and topological conformal field theories, with applications to Hochschild homology. In dimension 3, I propose to compute the stable homology of classifying spaces of diffeomorphism groups and mapping class groups, as well as study the homotopy type of the space of diffeomorphisms. I propose moreover to establish homological stability theorems in the wider context of automorphism groups and more general families of groups. The project combines breakthrough methods from homotopy theory with methods from differential and geometric topology. The research team will consist of 3 PhD students, and 4 postdocs, which I will lead.
Summary
The scientific goal of the proposal is to answer central questions related to diffeomorphism groups of manifolds of dimension 2 and 3, and to their deformation invariant analogs, the mapping class groups. While the classification of surfaces has been known for more than a century, their automorphism groups have yet to be fully understood. Even less is known about diffeomorphisms of 3-manifolds despite much interest, and the objects here have only been classified recently, by the breakthrough work of Perelman on the Poincar\'e and geometrization conjectures. In dimension 2, I will focus on the relationship between mapping class groups and topological conformal field theories, with applications to Hochschild homology. In dimension 3, I propose to compute the stable homology of classifying spaces of diffeomorphism groups and mapping class groups, as well as study the homotopy type of the space of diffeomorphisms. I propose moreover to establish homological stability theorems in the wider context of automorphism groups and more general families of groups. The project combines breakthrough methods from homotopy theory with methods from differential and geometric topology. The research team will consist of 3 PhD students, and 4 postdocs, which I will lead.
Max ERC Funding
724 992 €
Duration
Start date: 2009-11-01, End date: 2014-10-31
Project acronym 3D-E
Project 3D Engineered Environments for Regenerative Medicine
Researcher (PI) Ruth Elizabeth Cameron
Host Institution (HI) THE CHANCELLOR MASTERS AND SCHOLARSOF THE UNIVERSITY OF CAMBRIDGE
Country United Kingdom
Call Details Advanced Grant (AdG), PE8, ERC-2012-ADG_20120216
Summary "This proposal develops a unified, underpinning technology to create novel, complex and biomimetic 3D environments for the control of tissue growth. As director of Cambridge Centre for Medical Materials, I have recently been approached by medical colleagues to help to solve important problems in the separate therapeutic areas of breast cancer, cardiac disease and blood disorders. In each case, the solution lies in complex 3D engineered environments for cell culture. These colleagues make it clear that existing 3D scaffolds fail to provide the required complex orientational and spatial anisotropy, and are limited in their ability to impart appropriate biochemical and mechanical cues.
I have a strong track record in this area. A particular success has been the use of a freeze drying technology to make collagen based porous implants for the cartilage-bone interface in the knee, which has now been commercialised. The novelty of this proposal lies in the broadening of the established scientific base of this technology to enable biomacromolecular structures with:
(A) controlled and complex pore orientation to mimic many normal multi-oriented tissue structures
(B) compositional and positional control to match varying local biochemical environments,
(C) the attachment of novel peptides designed to control cell behaviour, and
(D) mechanical control at both a local and macroscopic level to provide mechanical cues for cells.
These will be complemented by the development of
(E) robust characterisation methodologies for the structures created.
These advances will then be employed in each of the medical areas above.
This approach is highly interdisciplinary. Existing working relationships with experts in each medical field will guarantee expertise and licensed facilities in the required biological disciplines. Funds for this proposal would therefore establish a rich hub of mutually beneficial research and opportunities for cross-disciplinary sharing of expertise."
Summary
"This proposal develops a unified, underpinning technology to create novel, complex and biomimetic 3D environments for the control of tissue growth. As director of Cambridge Centre for Medical Materials, I have recently been approached by medical colleagues to help to solve important problems in the separate therapeutic areas of breast cancer, cardiac disease and blood disorders. In each case, the solution lies in complex 3D engineered environments for cell culture. These colleagues make it clear that existing 3D scaffolds fail to provide the required complex orientational and spatial anisotropy, and are limited in their ability to impart appropriate biochemical and mechanical cues.
I have a strong track record in this area. A particular success has been the use of a freeze drying technology to make collagen based porous implants for the cartilage-bone interface in the knee, which has now been commercialised. The novelty of this proposal lies in the broadening of the established scientific base of this technology to enable biomacromolecular structures with:
(A) controlled and complex pore orientation to mimic many normal multi-oriented tissue structures
(B) compositional and positional control to match varying local biochemical environments,
(C) the attachment of novel peptides designed to control cell behaviour, and
(D) mechanical control at both a local and macroscopic level to provide mechanical cues for cells.
These will be complemented by the development of
(E) robust characterisation methodologies for the structures created.
These advances will then be employed in each of the medical areas above.
This approach is highly interdisciplinary. Existing working relationships with experts in each medical field will guarantee expertise and licensed facilities in the required biological disciplines. Funds for this proposal would therefore establish a rich hub of mutually beneficial research and opportunities for cross-disciplinary sharing of expertise."
Max ERC Funding
2 486 267 €
Duration
Start date: 2013-04-01, End date: 2018-03-31
Project acronym 3D-QUEST
Project 3D-Quantum Integrated Optical Simulation
Researcher (PI) Fabio Sciarrino
Host Institution (HI) UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA
Country Italy
Call Details Starting Grant (StG), PE2, ERC-2012-StG_20111012
Summary "Quantum information was born from the merging of classical information and quantum physics. Its main objective consists of understanding the quantum nature of information and learning how to process it by using physical systems which operate by following quantum mechanics laws. Quantum simulation is a fundamental instrument to investigate phenomena of quantum systems dynamics, such as quantum transport, particle localizations and energy transfer, quantum-to-classical transition, and even quantum improved computation, all tasks that are hard to simulate with classical approaches. Within this framework integrated photonic circuits have a strong potential to realize quantum information processing by optical systems.
The aim of 3D-QUEST is to develop and implement quantum simulation by exploiting 3-dimensional integrated photonic circuits. 3D-QUEST is structured to demonstrate the potential of linear optics to implement a computational power beyond the one of a classical computer. Such ""hard-to-simulate"" scenario is disclosed when multiphoton-multimode platforms are realized. The 3D-QUEST research program will focus on three tasks of growing difficulty.
A-1. To simulate bosonic-fermionic dynamics with integrated optical systems acting on 2 photon entangled states.
A-2. To pave the way towards hard-to-simulate, scalable quantum linear optical circuits by investigating m-port interferometers acting on n-photon states with n>2.
A-3. To exploit 3-dimensional integrated structures for the observation of new quantum optical phenomena and for the quantum simulation of more complex scenarios.
3D-QUEST will exploit the potential of the femtosecond laser writing integrated waveguides. This technique will be adopted to realize 3-dimensional capabilities and high flexibility, bringing in this way the optical quantum simulation in to new regime."
Summary
"Quantum information was born from the merging of classical information and quantum physics. Its main objective consists of understanding the quantum nature of information and learning how to process it by using physical systems which operate by following quantum mechanics laws. Quantum simulation is a fundamental instrument to investigate phenomena of quantum systems dynamics, such as quantum transport, particle localizations and energy transfer, quantum-to-classical transition, and even quantum improved computation, all tasks that are hard to simulate with classical approaches. Within this framework integrated photonic circuits have a strong potential to realize quantum information processing by optical systems.
The aim of 3D-QUEST is to develop and implement quantum simulation by exploiting 3-dimensional integrated photonic circuits. 3D-QUEST is structured to demonstrate the potential of linear optics to implement a computational power beyond the one of a classical computer. Such ""hard-to-simulate"" scenario is disclosed when multiphoton-multimode platforms are realized. The 3D-QUEST research program will focus on three tasks of growing difficulty.
A-1. To simulate bosonic-fermionic dynamics with integrated optical systems acting on 2 photon entangled states.
A-2. To pave the way towards hard-to-simulate, scalable quantum linear optical circuits by investigating m-port interferometers acting on n-photon states with n>2.
A-3. To exploit 3-dimensional integrated structures for the observation of new quantum optical phenomena and for the quantum simulation of more complex scenarios.
3D-QUEST will exploit the potential of the femtosecond laser writing integrated waveguides. This technique will be adopted to realize 3-dimensional capabilities and high flexibility, bringing in this way the optical quantum simulation in to new regime."
Max ERC Funding
1 474 800 €
Duration
Start date: 2012-08-01, End date: 2017-07-31
Project acronym 3DEpi
Project Transgenerational epigenetic inheritance of chromatin states : the role of Polycomb and 3D chromosome architecture
Researcher (PI) Giacomo CAVALLI
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Country France
Call Details Advanced Grant (AdG), LS2, ERC-2017-ADG
Summary Epigenetic inheritance entails transmission of phenotypic traits not encoded in the DNA sequence and, in the most extreme case, Transgenerational Epigenetic Inheritance (TEI) involves transmission of memory through multiple generations. Very little is known on the mechanisms governing TEI and this is the subject of the present proposal. By transiently enhancing long-range chromatin interactions, we recently established isogenic Drosophila epilines that carry stable alternative epialleles, defined by differential levels of the Polycomb-dependent H3K27me3 mark. Furthermore, we extended our paradigm to natural phenotypes. These are ideal systems to study the role of Polycomb group (PcG) proteins and other components in regulating nuclear organization and epigenetic inheritance of chromatin states. The present project conjugates genetics, epigenomics, imaging and molecular biology to reach three critical aims.
Aim 1: Analysis of the molecular mechanisms regulating Polycomb-mediated TEI. We will identify the DNA, protein and RNA components that trigger and maintain transgenerational chromatin inheritance as well as their mechanisms of action.
Aim 2: Role of 3D genome organization in the regulation of TEI. We will analyze the developmental dynamics of TEI-inducing long-range chromatin interactions, identify chromatin components mediating 3D chromatin contacts and characterize their function in the TEI process.
Aim 3: Identification of a broader role of TEI during development. TEI might reflect a normal role of PcG components in the transmission of parental chromatin onto the next embryonic generation. We will explore this possibility by establishing other TEI paradigms and by relating TEI to the normal PcG function in these systems and in normal development.
This research program will unravel the biological significance and the molecular underpinnings of TEI and lead the way towards establishing this area of research into a consolidated scientific discipline.
Summary
Epigenetic inheritance entails transmission of phenotypic traits not encoded in the DNA sequence and, in the most extreme case, Transgenerational Epigenetic Inheritance (TEI) involves transmission of memory through multiple generations. Very little is known on the mechanisms governing TEI and this is the subject of the present proposal. By transiently enhancing long-range chromatin interactions, we recently established isogenic Drosophila epilines that carry stable alternative epialleles, defined by differential levels of the Polycomb-dependent H3K27me3 mark. Furthermore, we extended our paradigm to natural phenotypes. These are ideal systems to study the role of Polycomb group (PcG) proteins and other components in regulating nuclear organization and epigenetic inheritance of chromatin states. The present project conjugates genetics, epigenomics, imaging and molecular biology to reach three critical aims.
Aim 1: Analysis of the molecular mechanisms regulating Polycomb-mediated TEI. We will identify the DNA, protein and RNA components that trigger and maintain transgenerational chromatin inheritance as well as their mechanisms of action.
Aim 2: Role of 3D genome organization in the regulation of TEI. We will analyze the developmental dynamics of TEI-inducing long-range chromatin interactions, identify chromatin components mediating 3D chromatin contacts and characterize their function in the TEI process.
Aim 3: Identification of a broader role of TEI during development. TEI might reflect a normal role of PcG components in the transmission of parental chromatin onto the next embryonic generation. We will explore this possibility by establishing other TEI paradigms and by relating TEI to the normal PcG function in these systems and in normal development.
This research program will unravel the biological significance and the molecular underpinnings of TEI and lead the way towards establishing this area of research into a consolidated scientific discipline.
Max ERC Funding
2 500 000 €
Duration
Start date: 2018-11-01, End date: 2023-10-31
Project acronym 4D IMAGING
Project Towards 4D Imaging of Fundamental Processes on the Atomic and Sub-Atomic Scale
Researcher (PI) Ferenc Krausz
Host Institution (HI) LUDWIG-MAXIMILIANS-UNIVERSITAET MUENCHEN
Country Germany
Call Details Advanced Grant (AdG), PE2, ERC-2009-AdG
Summary State-of-the-art microscopy and diffraction imaging provides insight into the atomic and sub-atomic structure of matter. They permit determination of the positions of atoms in a crystal lattice or in a molecule as well as the distribution of electrons inside atoms. State-of-the-art time-resolved spectroscopy with femtosecond and attosecond resolution provides access to dynamic changes in the atomic and electronic structure of matter. Our proposal aims at combining these two frontier techniques of XXI century science to make a long-standing dream of scientist come true: the direct observation of atoms and electrons in their natural state: in motion. Shifts in the atoms positions by tens to hundreds of picometers can make chemical bonds break apart or newly form, changing the structure and/or chemical composition of matter. Electronic motion on similar scales may result in the emission of light, or the initiation of processes that lead to a change in physical or chemical properties, or biological function. These motions happen within femtoseconds and attoseconds, respectively. To make them observable, we need a 4-dimensional (4D) imaging technique capable of recording freeze-frame snapshots of microscopic systems with picometer spatial resolution and femtosecond to attosecond exposure time. The motion can then be visualized by slow-motion replay of the freeze-frame shots. The goal of this project is to develop a 4D imaging technique that will ultimately offer picometer resolution is space and attosecond resolution in time.
Summary
State-of-the-art microscopy and diffraction imaging provides insight into the atomic and sub-atomic structure of matter. They permit determination of the positions of atoms in a crystal lattice or in a molecule as well as the distribution of electrons inside atoms. State-of-the-art time-resolved spectroscopy with femtosecond and attosecond resolution provides access to dynamic changes in the atomic and electronic structure of matter. Our proposal aims at combining these two frontier techniques of XXI century science to make a long-standing dream of scientist come true: the direct observation of atoms and electrons in their natural state: in motion. Shifts in the atoms positions by tens to hundreds of picometers can make chemical bonds break apart or newly form, changing the structure and/or chemical composition of matter. Electronic motion on similar scales may result in the emission of light, or the initiation of processes that lead to a change in physical or chemical properties, or biological function. These motions happen within femtoseconds and attoseconds, respectively. To make them observable, we need a 4-dimensional (4D) imaging technique capable of recording freeze-frame snapshots of microscopic systems with picometer spatial resolution and femtosecond to attosecond exposure time. The motion can then be visualized by slow-motion replay of the freeze-frame shots. The goal of this project is to develop a 4D imaging technique that will ultimately offer picometer resolution is space and attosecond resolution in time.
Max ERC Funding
2 500 000 €
Duration
Start date: 2010-03-01, End date: 2015-02-28
Project acronym 4D-GenEx
Project Spatio-temporal Organization and Expression of the Genome
Researcher (PI) Antoine COULON
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Country France
Call Details Starting Grant (StG), LS2, ERC-2017-STG
Summary This project investigates the two-way relationship between spatio-temporal genome organization and coordinated gene regulation, through an approach at the interface between physics, computer science and biology.
In the nucleus, preferred positions are observed from chromosomes to single genes, in relation to normal and pathological cellular states. Evidence indicates a complex spatio-temporal coupling between co-regulated genes: e.g. certain genes cluster spatially when responding to similar factors and transcriptional noise patterns suggest domain-wide mechanisms. Yet, no individual experiment allows probing transcriptional coordination in 4 dimensions (FISH, live locus tracking, Hi-C...). Interpreting such data also critically requires theory (stochastic processes, statistical physics…). A lack of appropriate experimental/analytical approaches is impairing our understanding of the 4D genome.
Our proposal combines cutting-edge single-molecule imaging, signal-theory data analysis and physical modeling to study how genes coordinate in space and time in a single nucleus. Our objectives are to understand (a) competition/recycling of shared resources between genes within subnuclear compartments, (b) how enhancers communicate with genes domain-wide, and (c) the role of local conformational dynamics and supercoiling in gene co-regulation. Our organizing hypothesis is that, by acting on their microenvironment, genes shape their co-expression with other genes.
Building upon my expertise, we will use dual-color MS2/PP7 RNA labeling to visualize for the first time transcription and motion of pairs of hormone-responsive genes in real time. With our innovative signal analysis tools, we will extract spatio-temporal signatures of underlying processes, which we will investigate with stochastic modeling and validate through experimental perturbations. We expect to uncover how the functional organization of the linear genome relates to its physical properties and dynamics in 4D.
Summary
This project investigates the two-way relationship between spatio-temporal genome organization and coordinated gene regulation, through an approach at the interface between physics, computer science and biology.
In the nucleus, preferred positions are observed from chromosomes to single genes, in relation to normal and pathological cellular states. Evidence indicates a complex spatio-temporal coupling between co-regulated genes: e.g. certain genes cluster spatially when responding to similar factors and transcriptional noise patterns suggest domain-wide mechanisms. Yet, no individual experiment allows probing transcriptional coordination in 4 dimensions (FISH, live locus tracking, Hi-C...). Interpreting such data also critically requires theory (stochastic processes, statistical physics…). A lack of appropriate experimental/analytical approaches is impairing our understanding of the 4D genome.
Our proposal combines cutting-edge single-molecule imaging, signal-theory data analysis and physical modeling to study how genes coordinate in space and time in a single nucleus. Our objectives are to understand (a) competition/recycling of shared resources between genes within subnuclear compartments, (b) how enhancers communicate with genes domain-wide, and (c) the role of local conformational dynamics and supercoiling in gene co-regulation. Our organizing hypothesis is that, by acting on their microenvironment, genes shape their co-expression with other genes.
Building upon my expertise, we will use dual-color MS2/PP7 RNA labeling to visualize for the first time transcription and motion of pairs of hormone-responsive genes in real time. With our innovative signal analysis tools, we will extract spatio-temporal signatures of underlying processes, which we will investigate with stochastic modeling and validate through experimental perturbations. We expect to uncover how the functional organization of the linear genome relates to its physical properties and dynamics in 4D.
Max ERC Funding
1 499 750 €
Duration
Start date: 2018-04-01, End date: 2023-03-31
Project acronym 4TH-NU-AVENUE
Project Search for a fourth neutrino with a PBq anti-neutrino source
Researcher (PI) Thierry Michel Rene Lasserre
Host Institution (HI) COMMISSARIAT A L ENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES
Country France
Call Details Starting Grant (StG), PE2, ERC-2012-StG_20111012
Summary Several observed anomalies in neutrino oscillation data can be explained by a hypothetical fourth neutrino separated from the three standard neutrinos by a squared mass difference of a few eV2. This hypothesis can be tested with a PBq (ten kilocurie scale) 144Ce antineutrino beta-source deployed at the center of a large low background liquid scintillator detector, such like Borexino, KamLAND, and SNO+. In particular, the compact size of such a source could yield an energy-dependent oscillating pattern in event spatial distribution that would unambiguously determine neutrino mass differences and mixing angles.
The proposed program aims to perform the necessary research and developments to produce and deploy an intense antineutrino source in a large liquid scintillator detector. Our program will address the definition of the production process of the neutrino source as well as its experimental characterization, the detailed physics simulation of both signal and backgrounds, the complete design and the realization of the thick shielding, the preparation of the interfaces with the antineutrino detector, including the safety and security aspects.
Summary
Several observed anomalies in neutrino oscillation data can be explained by a hypothetical fourth neutrino separated from the three standard neutrinos by a squared mass difference of a few eV2. This hypothesis can be tested with a PBq (ten kilocurie scale) 144Ce antineutrino beta-source deployed at the center of a large low background liquid scintillator detector, such like Borexino, KamLAND, and SNO+. In particular, the compact size of such a source could yield an energy-dependent oscillating pattern in event spatial distribution that would unambiguously determine neutrino mass differences and mixing angles.
The proposed program aims to perform the necessary research and developments to produce and deploy an intense antineutrino source in a large liquid scintillator detector. Our program will address the definition of the production process of the neutrino source as well as its experimental characterization, the detailed physics simulation of both signal and backgrounds, the complete design and the realization of the thick shielding, the preparation of the interfaces with the antineutrino detector, including the safety and security aspects.
Max ERC Funding
1 500 000 €
Duration
Start date: 2012-10-01, End date: 2018-09-30
Project acronym ABEP
Project Asset Bubbles and Economic Policy
Researcher (PI) Jaume Ventura Fontanet
Host Institution (HI) Centre de Recerca en Economia Internacional (CREI)
Country Spain
Call Details Advanced Grant (AdG), SH1, ERC-2009-AdG
Summary Advanced capitalist economies experience large and persistent movements in asset prices that are difficult to justify with economic fundamentals. The internet bubble of the 1990s and the real state market bubble of the 2000s are two recent examples. The predominant view is that these bubbles are a market failure, and are caused by some form of individual irrationality on the part of market participants. This project is based instead on the view that market participants are individually rational, although this does not preclude sometimes collectively sub-optimal outcomes. Bubbles are thus not a source of market failure by themselves but instead arise as a result of a pre-existing market failure, namely, the existence of pockets of dynamically inefficient investments. Under some conditions, bubbles partly solve this problem, increasing market efficiency and welfare. It is also possible however that bubbles do not solve the underlying problem and, in addition, create negative side-effects. The main objective of this project is to develop this view of asset bubbles, and produce an empirically-relevant macroeconomic framework that allows us to address the following questions: (i) What is the relationship between bubbles and financial market frictions? Special emphasis is given to how the globalization of financial markets and the development of new financial products affect the size and effects of bubbles. (ii) What is the relationship between bubbles, economic growth and unemployment? The theory suggests the presence of virtuous and vicious cycles, as economic growth creates the conditions for bubbles to pop up, while bubbles create incentives for economic growth to happen. (iii) What is the optimal policy to manage bubbles? We need to develop the tools that allow policy makers to sustain those bubbles that have positive effects and burst those that have negative effects.
Summary
Advanced capitalist economies experience large and persistent movements in asset prices that are difficult to justify with economic fundamentals. The internet bubble of the 1990s and the real state market bubble of the 2000s are two recent examples. The predominant view is that these bubbles are a market failure, and are caused by some form of individual irrationality on the part of market participants. This project is based instead on the view that market participants are individually rational, although this does not preclude sometimes collectively sub-optimal outcomes. Bubbles are thus not a source of market failure by themselves but instead arise as a result of a pre-existing market failure, namely, the existence of pockets of dynamically inefficient investments. Under some conditions, bubbles partly solve this problem, increasing market efficiency and welfare. It is also possible however that bubbles do not solve the underlying problem and, in addition, create negative side-effects. The main objective of this project is to develop this view of asset bubbles, and produce an empirically-relevant macroeconomic framework that allows us to address the following questions: (i) What is the relationship between bubbles and financial market frictions? Special emphasis is given to how the globalization of financial markets and the development of new financial products affect the size and effects of bubbles. (ii) What is the relationship between bubbles, economic growth and unemployment? The theory suggests the presence of virtuous and vicious cycles, as economic growth creates the conditions for bubbles to pop up, while bubbles create incentives for economic growth to happen. (iii) What is the optimal policy to manage bubbles? We need to develop the tools that allow policy makers to sustain those bubbles that have positive effects and burst those that have negative effects.
Max ERC Funding
1 000 000 €
Duration
Start date: 2010-04-01, End date: 2015-03-31
Project acronym ACB
Project The Analytic Conformal Bootstrap
Researcher (PI) Luis Fernando ALDAY
Host Institution (HI) THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Country United Kingdom
Call Details Advanced Grant (AdG), PE2, ERC-2017-ADG
Summary The aim of the present proposal is to establish a research team developing and exploiting innovative techniques to study conformal field theories (CFT) analytically. Our approach does not rely on a Lagrangian description but on symmetries and consistency conditions. As such it applies to any CFT, offering a unified framework to study generic CFTs analytically. The initial implementation of this program has already led to striking new results and insights for both Lagrangian and non-Lagrangian CFTs.
The overarching aims of my team will be: To develop an analytic bootstrap program for CFTs in general dimensions; to complement these techniques with more traditional methods and develop a systematic machinery to obtain analytic results for generic CFTs; and to use these results to gain new insights into the mathematical structure of the space of quantum field theories.
The proposal will bring together researchers from different areas. The objectives in brief are:
1) Develop an alternative to Feynman diagram computations for Lagrangian CFTs.
2) Develop a machinery to compute loops for QFT on AdS, with and without gravity.
3) Develop an analytic approach to non-perturbative N=4 SYM and other CFTs.
4) Determine the space of all CFTs.
5) Gain new insights into the mathematical structure of the space of quantum field theories.
The outputs of this proposal will include a new way of doing perturbative computations based on symmetries; a constructive derivation of the AdS/CFT duality; new analytic techniques to attack strongly coupled systems and invaluable new lessons about the space of CFTs and QFTs.
Success in this research will lead to a completely new, unified way to view and solve CFTs, with a huge impact on several branches of physics and mathematics.
Summary
The aim of the present proposal is to establish a research team developing and exploiting innovative techniques to study conformal field theories (CFT) analytically. Our approach does not rely on a Lagrangian description but on symmetries and consistency conditions. As such it applies to any CFT, offering a unified framework to study generic CFTs analytically. The initial implementation of this program has already led to striking new results and insights for both Lagrangian and non-Lagrangian CFTs.
The overarching aims of my team will be: To develop an analytic bootstrap program for CFTs in general dimensions; to complement these techniques with more traditional methods and develop a systematic machinery to obtain analytic results for generic CFTs; and to use these results to gain new insights into the mathematical structure of the space of quantum field theories.
The proposal will bring together researchers from different areas. The objectives in brief are:
1) Develop an alternative to Feynman diagram computations for Lagrangian CFTs.
2) Develop a machinery to compute loops for QFT on AdS, with and without gravity.
3) Develop an analytic approach to non-perturbative N=4 SYM and other CFTs.
4) Determine the space of all CFTs.
5) Gain new insights into the mathematical structure of the space of quantum field theories.
The outputs of this proposal will include a new way of doing perturbative computations based on symmetries; a constructive derivation of the AdS/CFT duality; new analytic techniques to attack strongly coupled systems and invaluable new lessons about the space of CFTs and QFTs.
Success in this research will lead to a completely new, unified way to view and solve CFTs, with a huge impact on several branches of physics and mathematics.
Max ERC Funding
2 171 483 €
Duration
Start date: 2018-12-01, End date: 2023-11-30
Project acronym ACCOPT
Project ACelerated COnvex OPTimization
Researcher (PI) Yurii NESTEROV
Host Institution (HI) UNIVERSITE CATHOLIQUE DE LOUVAIN
Country Belgium
Call Details Advanced Grant (AdG), PE1, ERC-2017-ADG
Summary The amazing rate of progress in the computer technologies and telecommunications presents many new challenges for Optimization Theory. New problems are usually very big in size, very special in structure and possibly have a distributed data support. This makes them unsolvable by the standard optimization methods. In these situations, old theoretical models, based on the hidden Black-Box information, cannot work. New theoretical and algorithmic solutions are urgently needed. In this project we will concentrate on development of fast optimization methods for problems of big and very big size. All the new methods will be endowed with provable efficiency guarantees for large classes of optimization problems, arising in practical applications. Our main tool is the acceleration technique developed for the standard Black-Box methods as applied to smooth convex functions. However, we will have to adapt it to deal with different situations.
The first line of development will be based on the smoothing technique as applied to a non-smooth functions. We propose to substantially extend this approach to generate approximate solutions in relative scale. The second line of research will be related to applying acceleration techniques to the second-order methods minimizing functions with sparse Hessians. Finally, we aim to develop fast gradient methods for huge-scale problems. The size of these problems is so big that even the usual vector operations are extremely expensive. Thus, we propose to develop new methods with sublinear iteration costs. In our approach, the main source for achieving improvements will be the proper use of problem structure.
Our overall aim is to be able to solve in a routine way many important problems, which currently look unsolvable. Moreover, the theoretical development of Convex Optimization will reach the state, when there is no gap between theory and practice: the theoretically most efficient methods will definitely outperform any homebred heuristics.
Summary
The amazing rate of progress in the computer technologies and telecommunications presents many new challenges for Optimization Theory. New problems are usually very big in size, very special in structure and possibly have a distributed data support. This makes them unsolvable by the standard optimization methods. In these situations, old theoretical models, based on the hidden Black-Box information, cannot work. New theoretical and algorithmic solutions are urgently needed. In this project we will concentrate on development of fast optimization methods for problems of big and very big size. All the new methods will be endowed with provable efficiency guarantees for large classes of optimization problems, arising in practical applications. Our main tool is the acceleration technique developed for the standard Black-Box methods as applied to smooth convex functions. However, we will have to adapt it to deal with different situations.
The first line of development will be based on the smoothing technique as applied to a non-smooth functions. We propose to substantially extend this approach to generate approximate solutions in relative scale. The second line of research will be related to applying acceleration techniques to the second-order methods minimizing functions with sparse Hessians. Finally, we aim to develop fast gradient methods for huge-scale problems. The size of these problems is so big that even the usual vector operations are extremely expensive. Thus, we propose to develop new methods with sublinear iteration costs. In our approach, the main source for achieving improvements will be the proper use of problem structure.
Our overall aim is to be able to solve in a routine way many important problems, which currently look unsolvable. Moreover, the theoretical development of Convex Optimization will reach the state, when there is no gap between theory and practice: the theoretically most efficient methods will definitely outperform any homebred heuristics.
Max ERC Funding
2 090 038 €
Duration
Start date: 2018-09-01, End date: 2023-08-31
