Project acronym ALZSYN
Project Imaging synaptic contributors to dementia
Researcher (PI) Tara Spires-Jones
Host Institution (HI) THE UNIVERSITY OF EDINBURGH
Call Details Consolidator Grant (CoG), LS5, ERC-2015-CoG
Summary Alzheimer's disease, the most common cause of dementia in older people, is a devastating condition that is becoming a public health crisis as our population ages. Despite great progress recently in Alzheimer’s disease research, we have no disease modifying drugs and a decade with a 99.6% failure rate of clinical trials attempting to treat the disease. This project aims to develop relevant therapeutic targets to restore brain function in Alzheimer’s disease by integrating human and model studies of synapses. It is widely accepted in the field that alterations in amyloid beta initiate the disease process. However the cascade leading from changes in amyloid to widespread tau pathology and neurodegeneration remain unclear. Synapse loss is the strongest pathological correlate of dementia in Alzheimer’s, and mounting evidence suggests that synapse degeneration plays a key role in causing cognitive decline. Here I propose to test the hypothesis that the amyloid cascade begins at the synapse leading to tau pathology, synapse dysfunction and loss, and ultimately neural circuit collapse causing cognitive impairment. The team will use cutting-edge multiphoton and array tomography imaging techniques to test mechanisms downstream of amyloid beta at synapses, and determine whether intervening in the cascade allows recovery of synapse structure and function. Importantly, I will combine studies in robust models of familial Alzheimer’s disease with studies in postmortem human brain to confirm relevance of our mechanistic studies to human disease. Finally, human stem cell derived neurons will be used to test mechanisms and potential therapeutics in neurons expressing the human proteome. Together, these experiments are ground-breaking since they have the potential to further our understanding of how synapses are lost in Alzheimer’s disease and to identify targets for effective therapeutic intervention, which is a critical unmet need in today’s health care system.
Summary
Alzheimer's disease, the most common cause of dementia in older people, is a devastating condition that is becoming a public health crisis as our population ages. Despite great progress recently in Alzheimer’s disease research, we have no disease modifying drugs and a decade with a 99.6% failure rate of clinical trials attempting to treat the disease. This project aims to develop relevant therapeutic targets to restore brain function in Alzheimer’s disease by integrating human and model studies of synapses. It is widely accepted in the field that alterations in amyloid beta initiate the disease process. However the cascade leading from changes in amyloid to widespread tau pathology and neurodegeneration remain unclear. Synapse loss is the strongest pathological correlate of dementia in Alzheimer’s, and mounting evidence suggests that synapse degeneration plays a key role in causing cognitive decline. Here I propose to test the hypothesis that the amyloid cascade begins at the synapse leading to tau pathology, synapse dysfunction and loss, and ultimately neural circuit collapse causing cognitive impairment. The team will use cutting-edge multiphoton and array tomography imaging techniques to test mechanisms downstream of amyloid beta at synapses, and determine whether intervening in the cascade allows recovery of synapse structure and function. Importantly, I will combine studies in robust models of familial Alzheimer’s disease with studies in postmortem human brain to confirm relevance of our mechanistic studies to human disease. Finally, human stem cell derived neurons will be used to test mechanisms and potential therapeutics in neurons expressing the human proteome. Together, these experiments are ground-breaking since they have the potential to further our understanding of how synapses are lost in Alzheimer’s disease and to identify targets for effective therapeutic intervention, which is a critical unmet need in today’s health care system.
Max ERC Funding
2 000 000 €
Duration
Start date: 2016-11-01, End date: 2021-10-31
Project acronym AMPHIBIANS
Project All Optical Manipulation of Photonic Metasurfaces for Biophotonic Applications in Microfluidic Environments
Researcher (PI) Andrea DI FALCO
Host Institution (HI) THE UNIVERSITY COURT OF THE UNIVERSITY OF ST ANDREWS
Call Details Consolidator Grant (CoG), PE7, ERC-2018-COG
Summary The current trend in biophotonics is to try and replicate the same ease and precision that our hands, eyes and ears offer at the macroscopic level, e.g. to hold, observe, squeeze and pull, rotate, cut and probe biological specimens in microfluidic environments. The bidding to get closer and closer to the object of interest has prompted the development of extremely advanced manipulation techniques at scales comparable to that of the wavelength of light. However, the fact that the optical beam can only access the microfluidic chip from the narrow aperture of a microscopic objective limits the versatility of the photonic function that can be realized.
With this project, the applicant proposes to introduce a new biophotonic platform based on the all optical manipulation of flexible photonic metasurfaces. These artificial two-dimensional materials have virtually arbitrary photonic responses and have an intrinsic exceptional mechanical stability. This cross-disciplinary project, bridging photonics, material sciences and biology, will enable the adoption of the most modern and advanced photonic designs in microfluidic environments, with transformative benefits for microscopy and biophotonic applications at the interface of molecular and cell biology.
Summary
The current trend in biophotonics is to try and replicate the same ease and precision that our hands, eyes and ears offer at the macroscopic level, e.g. to hold, observe, squeeze and pull, rotate, cut and probe biological specimens in microfluidic environments. The bidding to get closer and closer to the object of interest has prompted the development of extremely advanced manipulation techniques at scales comparable to that of the wavelength of light. However, the fact that the optical beam can only access the microfluidic chip from the narrow aperture of a microscopic objective limits the versatility of the photonic function that can be realized.
With this project, the applicant proposes to introduce a new biophotonic platform based on the all optical manipulation of flexible photonic metasurfaces. These artificial two-dimensional materials have virtually arbitrary photonic responses and have an intrinsic exceptional mechanical stability. This cross-disciplinary project, bridging photonics, material sciences and biology, will enable the adoption of the most modern and advanced photonic designs in microfluidic environments, with transformative benefits for microscopy and biophotonic applications at the interface of molecular and cell biology.
Max ERC Funding
1 999 524 €
Duration
Start date: 2019-02-01, End date: 2024-01-31
Project acronym BG-BB-AS
Project Birational Geometry, B-branes and Artin Stacks
Researcher (PI) Edward Paul Segal
Host Institution (HI) UNIVERSITY COLLEGE LONDON
Call Details Consolidator Grant (CoG), PE1, ERC-2016-COG
Summary Derived categories of coherent sheaves on a variety are a fundamental tool in algebraic geometry. They also arise in String Theory, as the category of B-branes in a quantum field theory whose target space is the variety. This connection to physics has been extraordinarily fruitful, providing deep insights and conjectures.
An Artin stack is a sophisticated generalization of a variety, they encode the idea of equivariant geometry. A simple example is a vector space carrying a linear action of a Lie group. In String Theory this data defines a Gauged Linear Sigma Model, which is a basic tool in the subject. A GLSM should also give rise to a category of B-branes, but surprisingly it is not yet understood what this should be. An overarching goal of this project is to develop an understanding of this category (more accurately, system of categories), and to extend this understanding to more general Artin stacks.
The basic importance of this question is that in certain limits a GLSM reduces to a sigma model, whose target is a quotient of the vector space by the group. This quotient must be taken using Geometric Invariant Theory. Thus this project is intimately connected with the question of how derived categories change under variation-of-GIT, and birational maps in general.
For GLSMs with abelian groups this approach has already produced spectacular results, in the non-abelian case we understand only a few remarkable examples. We will develop these examples into a wide-ranging general theory.
Our key objectives are to:
- Provide powerful new tools for controlling the behaviour of derived categories under birational maps.
- Understand the category of B-branes on a large class of Artin stacks.
- Prove and apply a striking new duality between GLSMs.
- Construct completely new symmetries of derived categories.
Summary
Derived categories of coherent sheaves on a variety are a fundamental tool in algebraic geometry. They also arise in String Theory, as the category of B-branes in a quantum field theory whose target space is the variety. This connection to physics has been extraordinarily fruitful, providing deep insights and conjectures.
An Artin stack is a sophisticated generalization of a variety, they encode the idea of equivariant geometry. A simple example is a vector space carrying a linear action of a Lie group. In String Theory this data defines a Gauged Linear Sigma Model, which is a basic tool in the subject. A GLSM should also give rise to a category of B-branes, but surprisingly it is not yet understood what this should be. An overarching goal of this project is to develop an understanding of this category (more accurately, system of categories), and to extend this understanding to more general Artin stacks.
The basic importance of this question is that in certain limits a GLSM reduces to a sigma model, whose target is a quotient of the vector space by the group. This quotient must be taken using Geometric Invariant Theory. Thus this project is intimately connected with the question of how derived categories change under variation-of-GIT, and birational maps in general.
For GLSMs with abelian groups this approach has already produced spectacular results, in the non-abelian case we understand only a few remarkable examples. We will develop these examples into a wide-ranging general theory.
Our key objectives are to:
- Provide powerful new tools for controlling the behaviour of derived categories under birational maps.
- Understand the category of B-branes on a large class of Artin stacks.
- Prove and apply a striking new duality between GLSMs.
- Construct completely new symmetries of derived categories.
Max ERC Funding
1 358 925 €
Duration
Start date: 2017-09-01, End date: 2022-08-31
Project acronym BHSandAADS
Project The Black Hole Stability Problem and the Analysis of asymptotically anti-de Sitter spacetimes
Researcher (PI) Gustav HOLZEGEL
Host Institution (HI) IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE
Call Details Consolidator Grant (CoG), PE1, ERC-2017-COG
Summary The present proposal is concerned with the analysis of the Einstein equations of general relativity, a non-linear system of geometric partial differential equations describing phenomena from the bending of light to the dynamics of black holes. The theory has recently been confirmed in a spectacular fashion with the detection of gravitational waves.
The main objective of the proposal is to consolidate my research group based at Imperial College by developing novel mathematical techniques that will fundamentally advance our understanding of the Einstein equations. Here the proposal builds on mathematical progress in the last decade resulting from achievements in the fields of partial differential equations, differential geometry, microlocal analysis and theoretical physics.
The Black Hole Stability Problem
A major open problem in general relativity is to prove the non-linear stability of the Kerr family of black hole solutions. Recent advances in the problem of linear stability made by the PI and collaborators open the door to finally address a complete resolution of the stability problem. In this proposal we will describe what non-linear techniques will need to be developed in addition to achieve this goal. A successful resolution of this program would conclude an almost 50-year-old problem.
The Analysis of asymptotically anti-de Sitter (aAdS) spacetimes
We propose to prove the stability of pure AdS if so-called dissipative boundary conditions are imposed at the boundary. This result would align with the well-known stability results for the other maximally-symmetric solutions of the Einstein equations, Minkowski space and de Sitter space.
As a second -- related -- theme we propose to formulate and prove a unique continuation principle for the full non-linear Einstein equations on aAdS spacetimes. This goal will be achieved by advancing techniques that have recently been developed by the PI and collaborators for non-linear wave equations on aAdS spacetimes.
Summary
The present proposal is concerned with the analysis of the Einstein equations of general relativity, a non-linear system of geometric partial differential equations describing phenomena from the bending of light to the dynamics of black holes. The theory has recently been confirmed in a spectacular fashion with the detection of gravitational waves.
The main objective of the proposal is to consolidate my research group based at Imperial College by developing novel mathematical techniques that will fundamentally advance our understanding of the Einstein equations. Here the proposal builds on mathematical progress in the last decade resulting from achievements in the fields of partial differential equations, differential geometry, microlocal analysis and theoretical physics.
The Black Hole Stability Problem
A major open problem in general relativity is to prove the non-linear stability of the Kerr family of black hole solutions. Recent advances in the problem of linear stability made by the PI and collaborators open the door to finally address a complete resolution of the stability problem. In this proposal we will describe what non-linear techniques will need to be developed in addition to achieve this goal. A successful resolution of this program would conclude an almost 50-year-old problem.
The Analysis of asymptotically anti-de Sitter (aAdS) spacetimes
We propose to prove the stability of pure AdS if so-called dissipative boundary conditions are imposed at the boundary. This result would align with the well-known stability results for the other maximally-symmetric solutions of the Einstein equations, Minkowski space and de Sitter space.
As a second -- related -- theme we propose to formulate and prove a unique continuation principle for the full non-linear Einstein equations on aAdS spacetimes. This goal will be achieved by advancing techniques that have recently been developed by the PI and collaborators for non-linear wave equations on aAdS spacetimes.
Max ERC Funding
1 999 755 €
Duration
Start date: 2018-11-01, End date: 2023-10-31
Project acronym BOPNIE
Project Boundary value problems for nonlinear integrable equations
Researcher (PI) Jonatan Carl Anders Lenells
Host Institution (HI) KUNGLIGA TEKNISKA HOEGSKOLAN
Call Details Consolidator Grant (CoG), PE1, ERC-2015-CoG
Summary The purpose of this project is to develop new methods for solving boundary value problems (BVPs) for nonlinear integrable partial differential equations (PDEs). Integrable PDEs can be analyzed by means of the Inverse Scattering Transform, whose introduction was one of the most important developments in the theory of nonlinear PDEs in the 20th century. Until the 1990s the inverse scattering methodology was pursued almost entirely for pure initial-value problems. However, in many laboratory and field situations, the solution is generated by what corresponds to the imposition of boundary conditions rather than initial conditions. Thus, an understanding of BVPs is crucial.
In an exciting sequence of events taking place in the last two decades, new tools have become available to deal with BVPs for integrable PDEs. Although some important issues have already been resolved, several major problems remain open.
The aim of this project is to solve a number of these open problems and to find solutions of BVPs which were heretofore not solvable. More precisely, the proposal has eight objectives:
1. Develop methods for solving problems with time-periodic boundary conditions.
2. Answer some long-standing open questions raised by series of wave-tank experiments 35 years ago.
3. Develop a new approach for the study of space-periodic solutions.
4. Develop new approaches for the analysis of BVPs for equations with 3 x 3-matrix Lax pairs.
5. Derive new asymptotic formulas by using a nonlinear version of the steepest descent method.
6. Construct disk and disk/black-hole solutions of the stationary axisymmetric Einstein equations.
7. Solve a BVP in Einstein's theory of relativity describing two colliding gravitational waves.
8. Extend the above methods to BVPs in higher dimensions.
Summary
The purpose of this project is to develop new methods for solving boundary value problems (BVPs) for nonlinear integrable partial differential equations (PDEs). Integrable PDEs can be analyzed by means of the Inverse Scattering Transform, whose introduction was one of the most important developments in the theory of nonlinear PDEs in the 20th century. Until the 1990s the inverse scattering methodology was pursued almost entirely for pure initial-value problems. However, in many laboratory and field situations, the solution is generated by what corresponds to the imposition of boundary conditions rather than initial conditions. Thus, an understanding of BVPs is crucial.
In an exciting sequence of events taking place in the last two decades, new tools have become available to deal with BVPs for integrable PDEs. Although some important issues have already been resolved, several major problems remain open.
The aim of this project is to solve a number of these open problems and to find solutions of BVPs which were heretofore not solvable. More precisely, the proposal has eight objectives:
1. Develop methods for solving problems with time-periodic boundary conditions.
2. Answer some long-standing open questions raised by series of wave-tank experiments 35 years ago.
3. Develop a new approach for the study of space-periodic solutions.
4. Develop new approaches for the analysis of BVPs for equations with 3 x 3-matrix Lax pairs.
5. Derive new asymptotic formulas by using a nonlinear version of the steepest descent method.
6. Construct disk and disk/black-hole solutions of the stationary axisymmetric Einstein equations.
7. Solve a BVP in Einstein's theory of relativity describing two colliding gravitational waves.
8. Extend the above methods to BVPs in higher dimensions.
Max ERC Funding
2 000 000 €
Duration
Start date: 2016-05-01, End date: 2021-04-30
Project acronym C9ND
Project C9orf72-mediated neurodegeneration: mechanisms and therapeutics
Researcher (PI) Adrian Michael Isaacs
Host Institution (HI) UNIVERSITY COLLEGE LONDON
Call Details Consolidator Grant (CoG), LS5, ERC-2014-CoG
Summary An expanded GGGGCC repeat in a non-coding region of the C9orf72 gene is the most common known cause of frontotemporal dementia (FTD) and amyotrophic lateral sclerosis (ALS). The repeat RNA is transcribed and accumulates in neuronal RNA aggregates, implicating RNA toxicity as a key pathogenic mechanism. However, the pathways that lead to neurodegeneration are unknown. My lab has made pioneering contributions to the understanding of C9orf72 FTD/ALS, and reported the first structure of the repeat RNA, and the first description of both sense and antisense RNA aggregates in patient brain. We have now developed new disease models that allow, for the first time, the dissection of RNA toxicity both in vivo and in sophisticated neuronal culture models. We have also used our knowledge of the repeat structure to identify novel small molecules that show very strong binding to the repeats. We will utilise our innovative disease models in a multidisciplinary approach to fully dissect the cellular pathways underlying C9orf72 repeat RNA toxicity in vivo, on a genome-wide scale. Altered RNA metabolism has been implicated in a wide range of neurodegenerative diseases, indicating that our findings will provide profound new insight into fundamental mechanisms of neuronal maintenance and survival. This research programme will also deliver a step change in our understanding of C9orf72 FTD/ALS pathogenesis and provide essential insight for the identification of small molecules with genuine therapeutic potential. RNA-mediated mechanisms are now known to be a common theme in neurodegeneration, suggesting these findings will have broad significance.
Summary
An expanded GGGGCC repeat in a non-coding region of the C9orf72 gene is the most common known cause of frontotemporal dementia (FTD) and amyotrophic lateral sclerosis (ALS). The repeat RNA is transcribed and accumulates in neuronal RNA aggregates, implicating RNA toxicity as a key pathogenic mechanism. However, the pathways that lead to neurodegeneration are unknown. My lab has made pioneering contributions to the understanding of C9orf72 FTD/ALS, and reported the first structure of the repeat RNA, and the first description of both sense and antisense RNA aggregates in patient brain. We have now developed new disease models that allow, for the first time, the dissection of RNA toxicity both in vivo and in sophisticated neuronal culture models. We have also used our knowledge of the repeat structure to identify novel small molecules that show very strong binding to the repeats. We will utilise our innovative disease models in a multidisciplinary approach to fully dissect the cellular pathways underlying C9orf72 repeat RNA toxicity in vivo, on a genome-wide scale. Altered RNA metabolism has been implicated in a wide range of neurodegenerative diseases, indicating that our findings will provide profound new insight into fundamental mechanisms of neuronal maintenance and survival. This research programme will also deliver a step change in our understanding of C9orf72 FTD/ALS pathogenesis and provide essential insight for the identification of small molecules with genuine therapeutic potential. RNA-mediated mechanisms are now known to be a common theme in neurodegeneration, suggesting these findings will have broad significance.
Max ERC Funding
1 985 699 €
Duration
Start date: 2015-10-01, End date: 2020-09-30
Project acronym CC
Project Combinatorial Construction
Researcher (PI) Peter Keevash
Host Institution (HI) THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Call Details Consolidator Grant (CoG), PE1, ERC-2014-CoG
Summary Combinatorial Construction is a mathematical challenge with many applications. Examples include the construction of networks that are very sparse but highly connected, or codes that can correct many transmission errors with little overhead in communication costs. For a general class of combinatorial objects, and some desirable property, the fundamental question in Combinatorial Construction is to demonstrate the existence of an object with the property, preferably via an explicit algorithmic construction. Thus it is ubiquitous in Computer Science, including applications to expanders, sorting networks, distributed communication, data storage, codes, cryptography and derandomisation. In popular culture it appears as the unsolved `lottery problem' of determining the minimum number of tickets that guarantee a prize. In a recent preprint I prove the Existence Conjecture for combinatorial designs, via a new method of Randomised Algebraic Constructions; this result has already attracted considerable attention in the mathematical community. The significance is not only in the solution of a problem posed by Steiner in 1852, but also in the discovery of a powerful new method, that promises to have many further applications in Combinatorics, and more widely in Mathematics and Theoretical Computer Science. I am now poised to resolve many other problems of combinatorial construction.
Summary
Combinatorial Construction is a mathematical challenge with many applications. Examples include the construction of networks that are very sparse but highly connected, or codes that can correct many transmission errors with little overhead in communication costs. For a general class of combinatorial objects, and some desirable property, the fundamental question in Combinatorial Construction is to demonstrate the existence of an object with the property, preferably via an explicit algorithmic construction. Thus it is ubiquitous in Computer Science, including applications to expanders, sorting networks, distributed communication, data storage, codes, cryptography and derandomisation. In popular culture it appears as the unsolved `lottery problem' of determining the minimum number of tickets that guarantee a prize. In a recent preprint I prove the Existence Conjecture for combinatorial designs, via a new method of Randomised Algebraic Constructions; this result has already attracted considerable attention in the mathematical community. The significance is not only in the solution of a problem posed by Steiner in 1852, but also in the discovery of a powerful new method, that promises to have many further applications in Combinatorics, and more widely in Mathematics and Theoretical Computer Science. I am now poised to resolve many other problems of combinatorial construction.
Max ERC Funding
1 706 729 €
Duration
Start date: 2016-01-01, End date: 2020-12-31
Project acronym Clock Mechanics
Project Mechanosensation and the circadian clock: a reciprocal analysis
Researcher (PI) Joerg Albert
Host Institution (HI) UNIVERSITY COLLEGE LONDON
Call Details Consolidator Grant (CoG), LS5, ERC-2014-CoG
Summary All forms of life adjust themselves to the daily rhythms of their environments using endogenous oscillators collectively referred to as circadian clocks. Peripheral and central body clocks exist, which both require extrinsic information (e.g. light or temperature changes) to keep in sync with the geophysical cycle (entrainment). In addition, intrinsic cues (e.g. activity levels) have been linked to clock entrainment. Recently, we could show that activation of proprioceptors is sufficient to entrain the central clock of the fruit fly Drosophila melanogaster. Proprioceptors are mechanosensors that monitor the positions, and relative movements, of an animal’s own body parts. The existence of proprioceptive entrainment pathways has significant implications; it implies that an animal’s ‘clock time’ is computed by integrating, and weighting, various external and internal conditions, suggesting the existence of external and internal time.
Using Drosophila, I will investigate the relationship between mechanosensory and circadian systems in a dual, and bidirectional, approach. The project’s first aim is to dissect the neurobiological bases of proprioceptive clock entrainment (i) identifying the specific stimulus requirements for effective entrainment, (ii) determining its mechanosensory pathways and, in a combined computational and experimental strategy, (iii) quantifying the precise contributions of an animal’s activity to its sense of time. The project’s second aim, in turn, is to unravel the roles of the clock, and clock genes, for the function of mechanosensory systems. Previous studies have linked the clock to noise vulnerability in mammalian ears, and clock genes to regeneration in avian ears. Our own preliminary data reveal severe mechanosensory defects in flies mutant for core clock genes. I will use the Drosophila ear as a unifying model to analyse the specific roles of the clock, and clock genes, for the function of mechanotransducer systems.
Summary
All forms of life adjust themselves to the daily rhythms of their environments using endogenous oscillators collectively referred to as circadian clocks. Peripheral and central body clocks exist, which both require extrinsic information (e.g. light or temperature changes) to keep in sync with the geophysical cycle (entrainment). In addition, intrinsic cues (e.g. activity levels) have been linked to clock entrainment. Recently, we could show that activation of proprioceptors is sufficient to entrain the central clock of the fruit fly Drosophila melanogaster. Proprioceptors are mechanosensors that monitor the positions, and relative movements, of an animal’s own body parts. The existence of proprioceptive entrainment pathways has significant implications; it implies that an animal’s ‘clock time’ is computed by integrating, and weighting, various external and internal conditions, suggesting the existence of external and internal time.
Using Drosophila, I will investigate the relationship between mechanosensory and circadian systems in a dual, and bidirectional, approach. The project’s first aim is to dissect the neurobiological bases of proprioceptive clock entrainment (i) identifying the specific stimulus requirements for effective entrainment, (ii) determining its mechanosensory pathways and, in a combined computational and experimental strategy, (iii) quantifying the precise contributions of an animal’s activity to its sense of time. The project’s second aim, in turn, is to unravel the roles of the clock, and clock genes, for the function of mechanosensory systems. Previous studies have linked the clock to noise vulnerability in mammalian ears, and clock genes to regeneration in avian ears. Our own preliminary data reveal severe mechanosensory defects in flies mutant for core clock genes. I will use the Drosophila ear as a unifying model to analyse the specific roles of the clock, and clock genes, for the function of mechanotransducer systems.
Max ERC Funding
1 899 549 €
Duration
Start date: 2015-09-01, End date: 2021-08-31
Project acronym Critical
Project Behaviour near criticality
Researcher (PI) Martin Hairer
Host Institution (HI) THE UNIVERSITY OF WARWICK
Call Details Consolidator Grant (CoG), PE1, ERC-2013-CoG
Summary "One of the main challenges of modern mathematical physics is to understand the behaviour of systems at or near criticality. In a number of cases, one can argue heuristically that this behaviour should be described by a nonlinear stochastic partial differential equation. Some examples of systems of interest are models of phase coexistence near the critical temperature, one-dimensional interface growth models, and models of absorption of a diffusing particle by random impurities. Unfortunately, the equations arising in all of these contexts are mathematically ill-posed. This is to the extent that they defeat not only ""standard"" stochastic PDE techniques (as developed by Da Prato / Zabczyk / Röckner / Walsh / Krylov / etc), but also more recent approaches based on Wick renormalisation of nonlinearities (Da Prato / Debussche / etc).
Over the past year or so, I have been developing a theory of regularity structures that allows to give a rigorous mathematical interpretation to such equations, which therefore allows to build the mathematical objects conjectured to describe the abovementioned systems near criticality. The aim of the proposal is to study the convergence of a variety of concrete microscopic models to these limiting objects. The main fundamental mathematical tools to be developed in this endeavour are a discrete analogue to the theory of regularity structures, as well as a number of nonlinear invariance principles.
If successful, the project will yield unique insight in the large-scale behaviour of a number of physically relevant systems in regimes where both nonlinear effects and random fluctuations compete with equal strength."
Summary
"One of the main challenges of modern mathematical physics is to understand the behaviour of systems at or near criticality. In a number of cases, one can argue heuristically that this behaviour should be described by a nonlinear stochastic partial differential equation. Some examples of systems of interest are models of phase coexistence near the critical temperature, one-dimensional interface growth models, and models of absorption of a diffusing particle by random impurities. Unfortunately, the equations arising in all of these contexts are mathematically ill-posed. This is to the extent that they defeat not only ""standard"" stochastic PDE techniques (as developed by Da Prato / Zabczyk / Röckner / Walsh / Krylov / etc), but also more recent approaches based on Wick renormalisation of nonlinearities (Da Prato / Debussche / etc).
Over the past year or so, I have been developing a theory of regularity structures that allows to give a rigorous mathematical interpretation to such equations, which therefore allows to build the mathematical objects conjectured to describe the abovementioned systems near criticality. The aim of the proposal is to study the convergence of a variety of concrete microscopic models to these limiting objects. The main fundamental mathematical tools to be developed in this endeavour are a discrete analogue to the theory of regularity structures, as well as a number of nonlinear invariance principles.
If successful, the project will yield unique insight in the large-scale behaviour of a number of physically relevant systems in regimes where both nonlinear effects and random fluctuations compete with equal strength."
Max ERC Funding
1 526 234 €
Duration
Start date: 2014-09-01, End date: 2019-08-31
Project acronym DarkComb
Project Dark-Soliton Engineering in Microresonator Frequency Combs
Researcher (PI) Victor TORRES COMPANY
Host Institution (HI) CHALMERS TEKNISKA HOEGSKOLA AB
Call Details Consolidator Grant (CoG), PE7, ERC-2017-COG
Summary The continuing increase in Internet data traffic is pushing the capacity of single-mode fiber to its fundamental limits. Space division multiplexing (SDM) offers the only remaining physical degree of freedom – the space dimension in the transmission channel – to substantially increase the capacity in lightwave communication systems.
The microresonator comb is an emerging technology platform that enables the generation of an optical frequency comb in a micrometer-scale cavity. Its compact size and compatibility with established semiconductor fabrication techniques promises to revolutionize the fields of frequency synthesis and metrology, and create new mass-market applications.
I envision significant scaling advantages in future fiber-optic communications by merging SDM with microresonator frequency combs. One major obstacle to overcome here is the poor conversion efficiency that can be fundamentally obtained using the most stable and broadest combs generated in microresonators today. I propose to look into the generation of dark, as opposed to bright, temporal solitons in linearly coupled microresonators. The goal is to achieve reliable microresonator combs with exceptionally high power conversion efficiency, resulting in optimal characteristics for SDM applications. The scientific and technological possibilities of this achievement promise significant impact beyond the realm of fiber-optic communications.
My broad international experience, unique background in fiber communications, photonic waveguides and ultrafast photonics, the preliminary results of my group and the available infrastructure at my university place me in an outstanding position to pioneer this new direction of research.
Summary
The continuing increase in Internet data traffic is pushing the capacity of single-mode fiber to its fundamental limits. Space division multiplexing (SDM) offers the only remaining physical degree of freedom – the space dimension in the transmission channel – to substantially increase the capacity in lightwave communication systems.
The microresonator comb is an emerging technology platform that enables the generation of an optical frequency comb in a micrometer-scale cavity. Its compact size and compatibility with established semiconductor fabrication techniques promises to revolutionize the fields of frequency synthesis and metrology, and create new mass-market applications.
I envision significant scaling advantages in future fiber-optic communications by merging SDM with microresonator frequency combs. One major obstacle to overcome here is the poor conversion efficiency that can be fundamentally obtained using the most stable and broadest combs generated in microresonators today. I propose to look into the generation of dark, as opposed to bright, temporal solitons in linearly coupled microresonators. The goal is to achieve reliable microresonator combs with exceptionally high power conversion efficiency, resulting in optimal characteristics for SDM applications. The scientific and technological possibilities of this achievement promise significant impact beyond the realm of fiber-optic communications.
My broad international experience, unique background in fiber communications, photonic waveguides and ultrafast photonics, the preliminary results of my group and the available infrastructure at my university place me in an outstanding position to pioneer this new direction of research.
Max ERC Funding
2 259 523 €
Duration
Start date: 2018-05-01, End date: 2023-04-30