Project acronym 3DWATERWAVES
Project Mathematical aspects of three-dimensional water waves with vorticity
Researcher (PI) Erik Torsten Wahlen
Host Institution (HI) LUNDS UNIVERSITET
Country Sweden
Call Details Starting Grant (StG), PE1, ERC-2015-STG
Summary The goal of this project is to develop a mathematical theory for steady three-dimensional water waves with vorticity. The mathematical model consists of the incompressible Euler equations with a free surface, and vorticity is important for modelling the interaction of surface waves with non-uniform currents. In the two-dimensional case, there has been a lot of progress on water waves with vorticity in the last decade. This progress has mainly been based on the stream function formulation, in which the problem is reformulated as a nonlinear elliptic free boundary problem. An analogue of this formulation is not available in three dimensions, and the theory has therefore so far been restricted to irrotational flow. In this project we seek to go beyond this restriction using two different approaches. In the first approach we will adapt methods which have been used to construct three-dimensional ideal flows with vorticity in domains with a fixed boundary to the free boundary context (for example Beltrami flows). In the second approach we will develop methods which are new even in the case of a fixed boundary, by performing a detailed study of the structure of the equations close to a given shear flow using ideas from infinite-dimensional bifurcation theory. This involves handling infinitely many resonances.
Summary
The goal of this project is to develop a mathematical theory for steady three-dimensional water waves with vorticity. The mathematical model consists of the incompressible Euler equations with a free surface, and vorticity is important for modelling the interaction of surface waves with non-uniform currents. In the two-dimensional case, there has been a lot of progress on water waves with vorticity in the last decade. This progress has mainly been based on the stream function formulation, in which the problem is reformulated as a nonlinear elliptic free boundary problem. An analogue of this formulation is not available in three dimensions, and the theory has therefore so far been restricted to irrotational flow. In this project we seek to go beyond this restriction using two different approaches. In the first approach we will adapt methods which have been used to construct three-dimensional ideal flows with vorticity in domains with a fixed boundary to the free boundary context (for example Beltrami flows). In the second approach we will develop methods which are new even in the case of a fixed boundary, by performing a detailed study of the structure of the equations close to a given shear flow using ideas from infinite-dimensional bifurcation theory. This involves handling infinitely many resonances.
Max ERC Funding
1 203 627 €
Duration
Start date: 2016-03-01, End date: 2022-02-28
Project acronym 4D-PET
Project Innovative PET scanner for dynamic imaging
Researcher (PI) Jose MarIa BENLLOCH BAVIERA
Host Institution (HI) AGENCIA ESTATAL CONSEJO SUPERIOR DEINVESTIGACIONES CIENTIFICAS
Country Spain
Call Details Advanced Grant (AdG), LS7, ERC-2015-AdG
Summary The main objective of 4D-PET is to develop an innovative whole-body PET scanner based in a new detector concept that stores 3D position and time of every single gamma interaction with unprecedented resolution. The combination of scanner geometrical design and high timing resolution will enable developing a full sequence of all gamma-ray interactions inside the scanner, including Compton interactions, like in a 3D movie. 4D-PET fully exploits Time Of Flight (TOF) information to obtain a better image quality and to increase scanner sensitivity, through the inclusion in the image formation of all Compton events occurring inside the detector, which are always rejected in state-of-the-art PET scanners. The new PET design will radically improve state-of-the-art PET performance features, overcoming limitations of current PET technology and opening up new diagnostic venues and very valuable physiological information
Summary
The main objective of 4D-PET is to develop an innovative whole-body PET scanner based in a new detector concept that stores 3D position and time of every single gamma interaction with unprecedented resolution. The combination of scanner geometrical design and high timing resolution will enable developing a full sequence of all gamma-ray interactions inside the scanner, including Compton interactions, like in a 3D movie. 4D-PET fully exploits Time Of Flight (TOF) information to obtain a better image quality and to increase scanner sensitivity, through the inclusion in the image formation of all Compton events occurring inside the detector, which are always rejected in state-of-the-art PET scanners. The new PET design will radically improve state-of-the-art PET performance features, overcoming limitations of current PET technology and opening up new diagnostic venues and very valuable physiological information
Max ERC Funding
2 048 386 €
Duration
Start date: 2017-01-01, End date: 2021-12-31
Project acronym AROMA-CFD
Project Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics
Researcher (PI) Gianluigi Rozza
Host Institution (HI) SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE
Country Italy
Call Details Consolidator Grant (CoG), PE1, ERC-2015-CoG
Summary The aim of AROMA-CFD is to create a team of scientists at SISSA for the development of Advanced Reduced Order Modelling techniques with a focus in Computational Fluid Dynamics (CFD), in order to face and overcome many current limitations of the state of the art and improve the capabilities of reduced order methodologies for more demanding applications in industrial, medical and applied sciences contexts. AROMA-CFD deals with strong methodological developments in numerical analysis, with a special emphasis on mathematical modelling and extensive exploitation of computational science and engineering. Several tasks have been identified to tackle important problems and open questions in reduced order modelling: study of bifurcations and instabilities in flows, increasing Reynolds number and guaranteeing stability, moving towards turbulent flows, considering complex geometrical parametrizations of shapes as computational domains into extended networks. A reduced computational and geometrical framework will be developed for nonlinear inverse problems, focusing on optimal flow control, shape optimization and uncertainty quantification. Further, all the advanced developments in reduced order modelling for CFD will be delivered for applications in multiphysics, such as fluid-structure interaction problems and general coupled phenomena involving inviscid, viscous and thermal flows, solids and porous media. The advanced developed framework within AROMA-CFD will provide attractive capabilities for several industrial and medical applications (e.g. aeronautical, mechanical, naval, off-shore, wind, sport, biomedical engineering, and cardiovascular surgery as well), combining high performance computing (in dedicated supercomputing centers) and advanced reduced order modelling (in common devices) to guarantee real time computing and visualization. A new open source software library for AROMA-CFD will be created: ITHACA, In real Time Highly Advanced Computational Applications.
Summary
The aim of AROMA-CFD is to create a team of scientists at SISSA for the development of Advanced Reduced Order Modelling techniques with a focus in Computational Fluid Dynamics (CFD), in order to face and overcome many current limitations of the state of the art and improve the capabilities of reduced order methodologies for more demanding applications in industrial, medical and applied sciences contexts. AROMA-CFD deals with strong methodological developments in numerical analysis, with a special emphasis on mathematical modelling and extensive exploitation of computational science and engineering. Several tasks have been identified to tackle important problems and open questions in reduced order modelling: study of bifurcations and instabilities in flows, increasing Reynolds number and guaranteeing stability, moving towards turbulent flows, considering complex geometrical parametrizations of shapes as computational domains into extended networks. A reduced computational and geometrical framework will be developed for nonlinear inverse problems, focusing on optimal flow control, shape optimization and uncertainty quantification. Further, all the advanced developments in reduced order modelling for CFD will be delivered for applications in multiphysics, such as fluid-structure interaction problems and general coupled phenomena involving inviscid, viscous and thermal flows, solids and porous media. The advanced developed framework within AROMA-CFD will provide attractive capabilities for several industrial and medical applications (e.g. aeronautical, mechanical, naval, off-shore, wind, sport, biomedical engineering, and cardiovascular surgery as well), combining high performance computing (in dedicated supercomputing centers) and advanced reduced order modelling (in common devices) to guarantee real time computing and visualization. A new open source software library for AROMA-CFD will be created: ITHACA, In real Time Highly Advanced Computational Applications.
Max ERC Funding
1 656 579 €
Duration
Start date: 2016-05-01, End date: 2021-10-31
Project acronym BIGSEA
Project Biogeochemical and ecosystem interactions with socio-economic activity in the global ocean
Researcher (PI) Eric Douglas Galbraith
Host Institution (HI) UNIVERSIDAD AUTONOMA DE BARCELONA
Country Spain
Call Details Consolidator Grant (CoG), PE10, ERC-2015-CoG
Summary The global marine ecosystem is being deeply altered by human activity. On the one hand, rising concentrations of atmospheric greenhouse gases are changing the physical and chemical state of the ocean, exerting pressure from the bottom up. Meanwhile, the global fishery has provided large economic benefits, but in so doing has restructured ecosystems by removing most of the large animal biomass, a major top-down change. Although there has been a tremendous amount of research into isolated aspects of these impacts, the development of a holistic understanding of the full interactions between physics, chemistry, ecology and economic activity might appear impossible, given the myriad complexities. This proposal lays out a strategy to assemble a team of trans-disciplinary expertise, that will develop a unified, data-constrained, grid-based modeling framework to represent the most important interactions of the global human-ocean system. Building this framework requires solving a series of fundamental problems that currently hinder the development of the full model. If these problems can be solved, the resulting model will reveal novel emergent properties and open the doors to a range of previously unexplored questions of high impact across a range of disciplines. Key questions include the ways in which animals interact with oxygen minimum zones with implications for fisheries, the impacts fish harvesting may have on nutrient recycling, spatio-temporal interactions between managed and unmanaged fisheries, and fundamental questions about the relationships between fish price, fishing cost, and multiple markets in a changing world. Just as the first coupled ocean-atmosphere models revealed a wealth of new behaviours, the coupled human-ocean model proposed here has the potential to launch multiple new fields of enquiry. It is hoped that the novel approach will contribute to a paradigm shift that treats human activity as one component within the framework of the Earth System.
Summary
The global marine ecosystem is being deeply altered by human activity. On the one hand, rising concentrations of atmospheric greenhouse gases are changing the physical and chemical state of the ocean, exerting pressure from the bottom up. Meanwhile, the global fishery has provided large economic benefits, but in so doing has restructured ecosystems by removing most of the large animal biomass, a major top-down change. Although there has been a tremendous amount of research into isolated aspects of these impacts, the development of a holistic understanding of the full interactions between physics, chemistry, ecology and economic activity might appear impossible, given the myriad complexities. This proposal lays out a strategy to assemble a team of trans-disciplinary expertise, that will develop a unified, data-constrained, grid-based modeling framework to represent the most important interactions of the global human-ocean system. Building this framework requires solving a series of fundamental problems that currently hinder the development of the full model. If these problems can be solved, the resulting model will reveal novel emergent properties and open the doors to a range of previously unexplored questions of high impact across a range of disciplines. Key questions include the ways in which animals interact with oxygen minimum zones with implications for fisheries, the impacts fish harvesting may have on nutrient recycling, spatio-temporal interactions between managed and unmanaged fisheries, and fundamental questions about the relationships between fish price, fishing cost, and multiple markets in a changing world. Just as the first coupled ocean-atmosphere models revealed a wealth of new behaviours, the coupled human-ocean model proposed here has the potential to launch multiple new fields of enquiry. It is hoped that the novel approach will contribute to a paradigm shift that treats human activity as one component within the framework of the Earth System.
Max ERC Funding
1 600 000 €
Duration
Start date: 2016-07-01, End date: 2021-12-31
Project acronym BioMNP
Project Understanding the interaction between metal nanoparticles and biological membranes
Researcher (PI) Giulia Rossi
Host Institution (HI) UNIVERSITA DEGLI STUDI DI GENOVA
Country Italy
Call Details Starting Grant (StG), PE3, ERC-2015-STG
Summary The BioMNP objective is the molecular-level understanding of the interactions between surface functionalized metal nanoparticles and biological membranes, by means of cutting-edge computational techniques and new molecular models.
Metal nanoparticles (NP) play more and more important roles in pharmaceutical and medical technology as diagnostic or therapeutic devices. Metal NPs can nowadays be engineered in a multitude of shapes, sizes and compositions, and they can be decorated with an almost infinite variety of functionalities. Despite such technological advances, there is still poor understanding of the molecular processes that drive the interactions of metal NPs with cells. Cell membranes are the first barrier encountered by NPs entering living organisms. The understanding and control of the interaction of nanoparticles with biological membranes is therefore of paramount importance to understand the molecular basis of the NP biological effects.
BioMNP will go beyond the state of the art by rationalizing the complex interplay of NP size, composition, functionalization and aggregation state during the interaction with model biomembranes. Membranes, in turn, will be modelled at an increasing level of complexity in terms of lipid composition and phase. BioMNP will rely on cutting-edge simulation techniques and facilities, and develop new coarse-grained models grounded on finer-level atomistic simulations, to study the NP-membrane interactions on an extremely large range of length and time scales.
BioMNP will benefit from important and complementary experimental collaborations, will propose interpretations of the available experimental data and make predictions to guide the design of functional, non-toxic metal nanoparticles for biomedical applications. BioMNP aims at answering fundamental questions at the crossroads of physics, biology and chemistry. Its results will have an impact on nanomedicine, toxicology, nanotechnology and material sciences.
Summary
The BioMNP objective is the molecular-level understanding of the interactions between surface functionalized metal nanoparticles and biological membranes, by means of cutting-edge computational techniques and new molecular models.
Metal nanoparticles (NP) play more and more important roles in pharmaceutical and medical technology as diagnostic or therapeutic devices. Metal NPs can nowadays be engineered in a multitude of shapes, sizes and compositions, and they can be decorated with an almost infinite variety of functionalities. Despite such technological advances, there is still poor understanding of the molecular processes that drive the interactions of metal NPs with cells. Cell membranes are the first barrier encountered by NPs entering living organisms. The understanding and control of the interaction of nanoparticles with biological membranes is therefore of paramount importance to understand the molecular basis of the NP biological effects.
BioMNP will go beyond the state of the art by rationalizing the complex interplay of NP size, composition, functionalization and aggregation state during the interaction with model biomembranes. Membranes, in turn, will be modelled at an increasing level of complexity in terms of lipid composition and phase. BioMNP will rely on cutting-edge simulation techniques and facilities, and develop new coarse-grained models grounded on finer-level atomistic simulations, to study the NP-membrane interactions on an extremely large range of length and time scales.
BioMNP will benefit from important and complementary experimental collaborations, will propose interpretations of the available experimental data and make predictions to guide the design of functional, non-toxic metal nanoparticles for biomedical applications. BioMNP aims at answering fundamental questions at the crossroads of physics, biology and chemistry. Its results will have an impact on nanomedicine, toxicology, nanotechnology and material sciences.
Max ERC Funding
1 131 250 €
Duration
Start date: 2016-04-01, End date: 2021-11-30
Project acronym BOOST
Project Biomimetic trick to re-balance Osteblast-Osteoclast loop in osteoporoSis treatment: a Topological and materials driven approach
Researcher (PI) Chiara Silvia Vitale Brovarone
Host Institution (HI) POLITECNICO DI TORINO
Country Italy
Call Details Consolidator Grant (CoG), PE8, ERC-2015-CoG
Summary One out of 5 people in their fifties will experience a bone fracture due to osteoporosis (OP)-induced fragility in their lifetime. The OP socio-economic burden is dramatic and involves tens of millions of people in the EU, with a steadily increasing number due to population ageing. Current treatments entail drug-therapy coupled with a healthy lifestyle but OP fractures need mechanical fixation to rapidly achieve union: the contribution of biomaterial scientists in this field is still far from taking its expected leading role in cutting-edge research. Bone remodelling is a well-coordinated process of bone resorption by osteoclasts followed by the production of new bone by osteoblasts. This process occurs continuously throughout life in a coupling with a positive balance during growth and negative with ageing, which can result in OP. We believe that an architecture driven stimulation of the osteoclast/osteoblast coupling, with an avant-garde focus on osteoclasts activity, is the key to success in treating unbalanced bone remodelling. We aim to manufacture a scaffold that mimics healthy bone features which will establish a new microenvironment favoring a properly stimulated and active population of osteoclasts and osteoblasts, i.e. a well-balanced bone cooperation. After 5 years we will be able to prove the efficacy of this approach. A benchmark will be set up for OP fracture treatment and for the realization of smart bone substitutes that will be able to locally “trick” aged bone cells stimulating them to act as healthy ones. BOOST results will have an unprecedented impact on the scientific research community, opening a new approach to set up smart, biomimetic strategies to treat aged, unbalanced bone tissues and to reduce OP-associated disabilities and financial burdens.
Summary
One out of 5 people in their fifties will experience a bone fracture due to osteoporosis (OP)-induced fragility in their lifetime. The OP socio-economic burden is dramatic and involves tens of millions of people in the EU, with a steadily increasing number due to population ageing. Current treatments entail drug-therapy coupled with a healthy lifestyle but OP fractures need mechanical fixation to rapidly achieve union: the contribution of biomaterial scientists in this field is still far from taking its expected leading role in cutting-edge research. Bone remodelling is a well-coordinated process of bone resorption by osteoclasts followed by the production of new bone by osteoblasts. This process occurs continuously throughout life in a coupling with a positive balance during growth and negative with ageing, which can result in OP. We believe that an architecture driven stimulation of the osteoclast/osteoblast coupling, with an avant-garde focus on osteoclasts activity, is the key to success in treating unbalanced bone remodelling. We aim to manufacture a scaffold that mimics healthy bone features which will establish a new microenvironment favoring a properly stimulated and active population of osteoclasts and osteoblasts, i.e. a well-balanced bone cooperation. After 5 years we will be able to prove the efficacy of this approach. A benchmark will be set up for OP fracture treatment and for the realization of smart bone substitutes that will be able to locally “trick” aged bone cells stimulating them to act as healthy ones. BOOST results will have an unprecedented impact on the scientific research community, opening a new approach to set up smart, biomimetic strategies to treat aged, unbalanced bone tissues and to reduce OP-associated disabilities and financial burdens.
Max ERC Funding
1 977 500 €
Duration
Start date: 2016-05-01, End date: 2022-06-30
Project acronym BOPNIE
Project Boundary value problems for nonlinear integrable equations
Researcher (PI) Jonatan Carl Anders Lenells
Host Institution (HI) KUNGLIGA TEKNISKA HOEGSKOLAN
Country Sweden
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: 2022-02-28
Project acronym BrainBIT
Project All-optical brain-to-brain behaviour and information transfer
Researcher (PI) Francesco PAVONE
Host Institution (HI) UNIVERSITA DEGLI STUDI DI FIRENZE
Country Italy
Call Details Advanced Grant (AdG), PE2, ERC-2015-AdG
Summary Exchange of information between different brains usually takes place through the interaction between bodies and the external environment. The ultimate goal of this project is to establish a novel paradigm of brain-to-brain communication based on direct full-optical recording and controlled stimulation of neuronal activity in different subjects. To pursue this challenging objective, we propose to develop optical technologies well beyond the state of the art for simultaneous neuronal “reading” and “writing” across large volumes and with high spatial and temporal resolution, targeted to the transfer of advantageous behaviour in physiological and pathological conditions.
We will perform whole-brain high-resolution imaging in zebrafish larvae to disentangle the activity patterns related to different tasks. We will then use these patterns as stimulation templates in other larvae to investigate spatio-temporal subject-invariant signatures of specific behavioural states. This ‘pump and probe’ strategy will allow gaining deep insights into the complex relationship between neuronal activity and subject behaviour.
To move towards clinics-oriented studies on brain stimulation therapies, we will complement whole-brain experiments in zebrafish with large area functional imaging and optostimulation in mammals. We will investigate all-optical brain-to-brain information transfer to boost an advantageous behaviour, i.e. motor recovery, in a mouse model of stroke. Mice showing more effective responses to rehabilitation will provide neuronal activity templates to be elicited in other animals, in order to increase rehabilitation efficiency.
We strongly believe that the implementation of new technologies for all-optical transfer of behaviour between different subjects will offer unprecedented views of neuronal activity in healthy and injured brain, paving the way to more effective brain stimulation therapies.
Summary
Exchange of information between different brains usually takes place through the interaction between bodies and the external environment. The ultimate goal of this project is to establish a novel paradigm of brain-to-brain communication based on direct full-optical recording and controlled stimulation of neuronal activity in different subjects. To pursue this challenging objective, we propose to develop optical technologies well beyond the state of the art for simultaneous neuronal “reading” and “writing” across large volumes and with high spatial and temporal resolution, targeted to the transfer of advantageous behaviour in physiological and pathological conditions.
We will perform whole-brain high-resolution imaging in zebrafish larvae to disentangle the activity patterns related to different tasks. We will then use these patterns as stimulation templates in other larvae to investigate spatio-temporal subject-invariant signatures of specific behavioural states. This ‘pump and probe’ strategy will allow gaining deep insights into the complex relationship between neuronal activity and subject behaviour.
To move towards clinics-oriented studies on brain stimulation therapies, we will complement whole-brain experiments in zebrafish with large area functional imaging and optostimulation in mammals. We will investigate all-optical brain-to-brain information transfer to boost an advantageous behaviour, i.e. motor recovery, in a mouse model of stroke. Mice showing more effective responses to rehabilitation will provide neuronal activity templates to be elicited in other animals, in order to increase rehabilitation efficiency.
We strongly believe that the implementation of new technologies for all-optical transfer of behaviour between different subjects will offer unprecedented views of neuronal activity in healthy and injured brain, paving the way to more effective brain stimulation therapies.
Max ERC Funding
2 370 250 €
Duration
Start date: 2016-12-01, End date: 2022-05-31
Project acronym BSD
Project Euler systems and the conjectures of Birch and Swinnerton-Dyer, Bloch and Kato
Researcher (PI) Victor Rotger cerda
Host Institution (HI) UNIVERSITAT POLITECNICA DE CATALUNYA
Country Spain
Call Details Consolidator Grant (CoG), PE1, ERC-2015-CoG
Summary In order to celebrate mathematics in the new millennium, the Clay Mathematics Institute established seven $1.000.000 Prize Problems. One of these is the conjecture of Birch and Swinnerton-Dyer (BSD), widely open since the 1960's. The main object of this proposal is developing innovative and unconventional strategies for proving groundbreaking results towards the resolution of this problem and their generalizations by Bloch and Kato (BK).
Breakthroughs on BSD were achieved by Coates-Wiles, Gross, Zagier and Kolyvagin, and Kato. Since then, there have been nearly no new ideas on how to tackle BSD. Only very recently, three independent revolutionary approaches have seen the light: the works of (1) the Fields medalist Bhargava, (2) Skinner and Urban, and (3) myself and my collaborators. In spite of that, our knowledge of BSD is rather poor. In my proposal I suggest innovating strategies for approaching new horizons in BSD and BK that I aim to develop with the team of PhD and postdoctoral researchers that the CoG may allow me to consolidate. The results I plan to prove represent a departure from the achievements obtained with my coauthors during the past years:
I. BSD over totally real number fields. I plan to prove new ground-breaking instances of BSD in rank 0 for elliptic curves over totally real number fields, generalizing the theorem of Kato (by providing a new proof) and covering many new scenarios that have never been considered before.
II. BSD in rank r=2. Most of the literature on BSD applies when r=0 or 1. I expect to prove p-adic versions of the theorems of Gross-Zagier and Kolyvagin in rank 2.
III. Darmon's 2000 conjecture on Stark-Heegner points. I plan to prove Darmon’s striking conjecture announced at the ICM2000 by recasting it in terms of special values of p-adic L-functions.
Summary
In order to celebrate mathematics in the new millennium, the Clay Mathematics Institute established seven $1.000.000 Prize Problems. One of these is the conjecture of Birch and Swinnerton-Dyer (BSD), widely open since the 1960's. The main object of this proposal is developing innovative and unconventional strategies for proving groundbreaking results towards the resolution of this problem and their generalizations by Bloch and Kato (BK).
Breakthroughs on BSD were achieved by Coates-Wiles, Gross, Zagier and Kolyvagin, and Kato. Since then, there have been nearly no new ideas on how to tackle BSD. Only very recently, three independent revolutionary approaches have seen the light: the works of (1) the Fields medalist Bhargava, (2) Skinner and Urban, and (3) myself and my collaborators. In spite of that, our knowledge of BSD is rather poor. In my proposal I suggest innovating strategies for approaching new horizons in BSD and BK that I aim to develop with the team of PhD and postdoctoral researchers that the CoG may allow me to consolidate. The results I plan to prove represent a departure from the achievements obtained with my coauthors during the past years:
I. BSD over totally real number fields. I plan to prove new ground-breaking instances of BSD in rank 0 for elliptic curves over totally real number fields, generalizing the theorem of Kato (by providing a new proof) and covering many new scenarios that have never been considered before.
II. BSD in rank r=2. Most of the literature on BSD applies when r=0 or 1. I expect to prove p-adic versions of the theorems of Gross-Zagier and Kolyvagin in rank 2.
III. Darmon's 2000 conjecture on Stark-Heegner points. I plan to prove Darmon’s striking conjecture announced at the ICM2000 by recasting it in terms of special values of p-adic L-functions.
Max ERC Funding
1 428 588 €
Duration
Start date: 2016-09-01, End date: 2021-08-31
Project acronym CATA-LUX
Project Light-Driven Asymmetric Organocatalysis
Researcher (PI) Paolo Melchiorre
Host Institution (HI) FUNDACIO PRIVADA INSTITUT CATALA D'INVESTIGACIO QUIMICA
Country Spain
Call Details Consolidator Grant (CoG), PE5, ERC-2015-CoG
Summary Visible light photocatalysis and metal-free organocatalytic processes are powerful strategies of modern chemical research with extraordinary potential for the sustainable preparation of organic molecules. However, these environmentally respectful approaches have to date remained largely unrelated. The proposed research seeks to merge these fields of molecule activation to redefine their synthetic potential.
Light-driven processes considerably enrich the modern synthetic repertoire, offering a potent way to build complex organic frameworks. In contrast, it is extremely challenging to develop asymmetric catalytic photoreactions that can create chiral molecules with a well-defined three-dimensional arrangement. By developing innovative methodologies to effectively address this issue, I will provide a novel reactivity framework for conceiving light-driven enantioselective organocatalytic processes.
I will translate the effective tools governing the success of ground state asymmetric organocatalysis into the realm of photochemical reactivity, exploiting the potential of key organocatalytic intermediates to directly participate in the photoexcitation of substrates. At the same time, the chiral organocatalyst will ensure effective stereochemical control. This single catalyst system, where stereoinduction and photoactivation merge in a sole organocatalyst, will serve for developing novel enantioselective photoreactions. In a complementary dual catalytic approach, the synergistic activities of an organocatalyst and a metal-free photosensitiser will combine to realise asymmetric variants of venerable photochemical processes, which have never before succumbed to a stereocontrolled approach.
This proposal challenges the current perception that photochemistry is too unselective to parallel the impressive levels of efficiency reached by the asymmetric catalysis of thermal reactions, expanding the way chemists think about making chiral molecules
Summary
Visible light photocatalysis and metal-free organocatalytic processes are powerful strategies of modern chemical research with extraordinary potential for the sustainable preparation of organic molecules. However, these environmentally respectful approaches have to date remained largely unrelated. The proposed research seeks to merge these fields of molecule activation to redefine their synthetic potential.
Light-driven processes considerably enrich the modern synthetic repertoire, offering a potent way to build complex organic frameworks. In contrast, it is extremely challenging to develop asymmetric catalytic photoreactions that can create chiral molecules with a well-defined three-dimensional arrangement. By developing innovative methodologies to effectively address this issue, I will provide a novel reactivity framework for conceiving light-driven enantioselective organocatalytic processes.
I will translate the effective tools governing the success of ground state asymmetric organocatalysis into the realm of photochemical reactivity, exploiting the potential of key organocatalytic intermediates to directly participate in the photoexcitation of substrates. At the same time, the chiral organocatalyst will ensure effective stereochemical control. This single catalyst system, where stereoinduction and photoactivation merge in a sole organocatalyst, will serve for developing novel enantioselective photoreactions. In a complementary dual catalytic approach, the synergistic activities of an organocatalyst and a metal-free photosensitiser will combine to realise asymmetric variants of venerable photochemical processes, which have never before succumbed to a stereocontrolled approach.
This proposal challenges the current perception that photochemistry is too unselective to parallel the impressive levels of efficiency reached by the asymmetric catalysis of thermal reactions, expanding the way chemists think about making chiral molecules
Max ERC Funding
2 000 000 €
Duration
Start date: 2016-11-01, End date: 2021-10-31
