Project acronym 2D4D
Project Disruptive Digitalization for Decarbonization
Researcher (PI) Elena Verdolini
Host Institution (HI) UNIVERSITA DEGLI STUDI DI BRESCIA
Country Italy
Call Details Starting Grant (StG), SH2, ERC-2019-STG
Summary By 2040, all major sectors of the European economy will be deeply digitalized. By then, the EU aims at reducing greenhouse gas emissions by 60% with respect to 1990 levels. Digitalization will affect decarbonization efforts because of its impacts on energy demand, employment, competitiveness, trade patterns and its distributional, behavioural and ethical implications. Yet, the policy debates around these two transformations are largely disjoint.
The aim of the 2D4D project is ensure that the digital revolution acts as an enabler – and not as a barrier – for decarbonization. The project quantifies the decarbonization implications of three disruptive digitalization technologies in hard-to-decarbonize sectors: (1) Additive Manufacturing in industry, (2) Mobility-as-a-Service in transportation, and (3) Artificial Intelligence in buildings.
The first objective of 2D4D is to generate a one-of-a-kind data collection to investigate the technical and socio-economic dynamics of these technologies, and how they may affect decarbonization narratives and scenarios. This will be achieved through several data collection methods, including desk research, surveys and expert elicitations.
The second objective of 2D4D is to include digitalization dynamics in decarbonization narratives and pathways. On the one hand, this entails enhancing decarbonization narratives (specifically, the Shared Socio-economic Pathways) to describe digitalization dynamics. On the other hand, it requires improving the representation of sector-specific digitalization dynamics in Integrated Assessment Models, one of the main tools available to generate decarbonization pathways.
The third objective of 2D4D is to identify no-regret, robust policy portfolios. These will be designed to ensure that digitalization unfolds in an inclusive, climate-beneficial way, and that decarbonization policies capitalize on digital technologies to support the energy transition.
Summary
By 2040, all major sectors of the European economy will be deeply digitalized. By then, the EU aims at reducing greenhouse gas emissions by 60% with respect to 1990 levels. Digitalization will affect decarbonization efforts because of its impacts on energy demand, employment, competitiveness, trade patterns and its distributional, behavioural and ethical implications. Yet, the policy debates around these two transformations are largely disjoint.
The aim of the 2D4D project is ensure that the digital revolution acts as an enabler – and not as a barrier – for decarbonization. The project quantifies the decarbonization implications of three disruptive digitalization technologies in hard-to-decarbonize sectors: (1) Additive Manufacturing in industry, (2) Mobility-as-a-Service in transportation, and (3) Artificial Intelligence in buildings.
The first objective of 2D4D is to generate a one-of-a-kind data collection to investigate the technical and socio-economic dynamics of these technologies, and how they may affect decarbonization narratives and scenarios. This will be achieved through several data collection methods, including desk research, surveys and expert elicitations.
The second objective of 2D4D is to include digitalization dynamics in decarbonization narratives and pathways. On the one hand, this entails enhancing decarbonization narratives (specifically, the Shared Socio-economic Pathways) to describe digitalization dynamics. On the other hand, it requires improving the representation of sector-specific digitalization dynamics in Integrated Assessment Models, one of the main tools available to generate decarbonization pathways.
The third objective of 2D4D is to identify no-regret, robust policy portfolios. These will be designed to ensure that digitalization unfolds in an inclusive, climate-beneficial way, and that decarbonization policies capitalize on digital technologies to support the energy transition.
Max ERC Funding
1 498 375 €
Duration
Start date: 2020-10-01, End date: 2025-09-30
Project acronym ABINITIODGA
Project Ab initio Dynamical Vertex Approximation
Researcher (PI) Karsten Held
Host Institution (HI) TECHNISCHE UNIVERSITAET WIEN
Country Austria
Call Details Starting Grant (StG), PE3, ERC-2012-StG_20111012
Summary Some of the most fascinating physical phenomena are experimentally observed in strongly correlated electron systems and, on the theoretical side, only poorly understood hitherto. The aim of the ERC project AbinitioDGA is the development, implementation and application of a new, 21th century method for the ab initio calculation of materials with such strong electronic correlations. AbinitioDGA includes strong electronic correlations on all time and length scales and hence is a big step beyond the state-of-the-art methods, such as the local density approximation, dynamical mean field theory, and the GW approach (Green function G times screened interaction W). It has the potential for an extraordinary high impact not only in the field of computational materials science but also for a better understanding of quantum critical heavy fermion systems, high-temperature superconductors, and transport through nano- and heterostructures. These four physical problems and related materials will be studied within the ERC project, besides the methodological development.
On the technical side, AbinitioDGA realizes Hedin's idea to include vertex corrections beyond the GW approximation. All vertex corrections which can be traced back to a fully irreducible local vertex and the bare non-local Coulomb interaction are included. This way, AbinitioDGA does not only contain the GW physics of screened exchange and the strong local correlations of dynamical mean field theory but also non-local correlations beyond on all length scales. Through the latter, AbinitioDGA can prospectively describe phenomena such as quantum criticality, spin-fluctuation mediated superconductivity, and weak localization corrections to the conductivity. Nonetheless, the computational effort is still manageable even for realistic materials calculations, making the considerable effort to implement AbinitioDGA worthwhile.
Summary
Some of the most fascinating physical phenomena are experimentally observed in strongly correlated electron systems and, on the theoretical side, only poorly understood hitherto. The aim of the ERC project AbinitioDGA is the development, implementation and application of a new, 21th century method for the ab initio calculation of materials with such strong electronic correlations. AbinitioDGA includes strong electronic correlations on all time and length scales and hence is a big step beyond the state-of-the-art methods, such as the local density approximation, dynamical mean field theory, and the GW approach (Green function G times screened interaction W). It has the potential for an extraordinary high impact not only in the field of computational materials science but also for a better understanding of quantum critical heavy fermion systems, high-temperature superconductors, and transport through nano- and heterostructures. These four physical problems and related materials will be studied within the ERC project, besides the methodological development.
On the technical side, AbinitioDGA realizes Hedin's idea to include vertex corrections beyond the GW approximation. All vertex corrections which can be traced back to a fully irreducible local vertex and the bare non-local Coulomb interaction are included. This way, AbinitioDGA does not only contain the GW physics of screened exchange and the strong local correlations of dynamical mean field theory but also non-local correlations beyond on all length scales. Through the latter, AbinitioDGA can prospectively describe phenomena such as quantum criticality, spin-fluctuation mediated superconductivity, and weak localization corrections to the conductivity. Nonetheless, the computational effort is still manageable even for realistic materials calculations, making the considerable effort to implement AbinitioDGA worthwhile.
Max ERC Funding
1 491 090 €
Duration
Start date: 2013-01-01, End date: 2018-07-31
Project acronym ACTIVENP
Project Active and low loss nano photonics (ActiveNP)
Researcher (PI) Thomas Arno Klar
Host Institution (HI) UNIVERSITAT LINZ
Country Austria
Call Details Starting Grant (StG), PE3, ERC-2010-StG_20091028
Summary This project aims at designing novel hybrid nanophotonic devices comprising metallic nanostructures and active elements such as dye molecules or colloidal quantum dots. Three core objectives, each going far beyond the state of the art, shall be tackled: (i) Metamaterials containing gain materials: Metamaterials introduce magnetism to the optical frequency range and hold promise to create entirely novel devices for light manipulation. Since present day metamaterials are extremely absorptive, it is of utmost importance to fight losses. The ground-breaking approach of this proposal is to incorporate fluorescing species into the nanoscale metallic metastructures in order to compensate losses by stimulated emission. (ii) The second objective exceeds the ansatz of compensating losses and will reach out for lasing action. Individual metallic nanostructures such as pairs of nanoparticles will form novel and unusual nanometre sized resonators for laser action. State of the art microresonators still have a volume of at least half of the wavelength cubed. Noble metal nanoparticle resonators scale down this volume by a factor of thousand allowing for truly nanoscale coherent light sources. (iii) A third objective concerns a substantial improvement of nonlinear effects. This will be accomplished by drastically sharpened resonances of nanoplasmonic devices surrounded by active gain materials. An interdisciplinary team of PhD students and a PostDoc will be assembled, each scientist being uniquely qualified to cover one of the expertise fields: Design, spectroscopy, and simulation. The project s outcome is twofold: A substantial expansion of fundamental understanding of nanophotonics and practical devices such as nanoscopic lasers and low loss metamaterials.
Summary
This project aims at designing novel hybrid nanophotonic devices comprising metallic nanostructures and active elements such as dye molecules or colloidal quantum dots. Three core objectives, each going far beyond the state of the art, shall be tackled: (i) Metamaterials containing gain materials: Metamaterials introduce magnetism to the optical frequency range and hold promise to create entirely novel devices for light manipulation. Since present day metamaterials are extremely absorptive, it is of utmost importance to fight losses. The ground-breaking approach of this proposal is to incorporate fluorescing species into the nanoscale metallic metastructures in order to compensate losses by stimulated emission. (ii) The second objective exceeds the ansatz of compensating losses and will reach out for lasing action. Individual metallic nanostructures such as pairs of nanoparticles will form novel and unusual nanometre sized resonators for laser action. State of the art microresonators still have a volume of at least half of the wavelength cubed. Noble metal nanoparticle resonators scale down this volume by a factor of thousand allowing for truly nanoscale coherent light sources. (iii) A third objective concerns a substantial improvement of nonlinear effects. This will be accomplished by drastically sharpened resonances of nanoplasmonic devices surrounded by active gain materials. An interdisciplinary team of PhD students and a PostDoc will be assembled, each scientist being uniquely qualified to cover one of the expertise fields: Design, spectroscopy, and simulation. The project s outcome is twofold: A substantial expansion of fundamental understanding of nanophotonics and practical devices such as nanoscopic lasers and low loss metamaterials.
Max ERC Funding
1 494 756 €
Duration
Start date: 2010-10-01, End date: 2015-09-30
Project acronym AGNES
Project ACTIVE AGEING – RESILIENCE AND EXTERNAL SUPPORT AS MODIFIERS OF THE DISABLEMENT OUTCOME
Researcher (PI) Taina Tuulikki RANTANEN
Host Institution (HI) JYVASKYLAN YLIOPISTO
Country Finland
Call Details Advanced Grant (AdG), SH3, ERC-2015-AdG
Summary The goals are 1. To develop a scale assessing the diversity of active ageing with four dimensions that are ability (what people can do), activity (what people do do), ambition (what are the valued activities that people want to do), and autonomy (how satisfied people are with the opportunity to do valued activities); 2. To examine health and physical and psychological functioning as the determinants and social and build environment, resilience and personal skills as modifiers of active ageing; 3. To develop a multicomponent sustainable intervention aiming to promote active ageing (methods: counselling, information technology, help from volunteers); 4. To test the feasibility and effectiveness on the intervention; and 5. To study cohort effects on the phenotypes on the pathway to active ageing.
“If You Can Measure It, You Can Change It.” Active ageing assessment needs conceptual progress, which I propose to do. A quantifiable scale will be developed that captures the diversity of active ageing stemming from the WHO definition of active ageing as the process of optimizing opportunities for health and participation in the society for all people in line with their needs, goals and capacities as they age. I will collect cross-sectional data (N=1000, ages 75, 80 and 85 years) and model the pathway to active ageing with state-of-the art statistical methods. By doing this I will create novel knowledge on preconditions for active ageing. The collected cohort data will be compared to a pre-existing cohort data that was collected 25 years ago to obtain knowledge about changes over time in functioning of older people. A randomized controlled trial (N=200) will be conducted to assess the effectiveness of the envisioned intervention promoting active ageing through participation. The project will regenerate ageing research by launching a novel scale, by training young scientists, by creating new concepts and theory development and by producing evidence for active ageing promotion
Summary
The goals are 1. To develop a scale assessing the diversity of active ageing with four dimensions that are ability (what people can do), activity (what people do do), ambition (what are the valued activities that people want to do), and autonomy (how satisfied people are with the opportunity to do valued activities); 2. To examine health and physical and psychological functioning as the determinants and social and build environment, resilience and personal skills as modifiers of active ageing; 3. To develop a multicomponent sustainable intervention aiming to promote active ageing (methods: counselling, information technology, help from volunteers); 4. To test the feasibility and effectiveness on the intervention; and 5. To study cohort effects on the phenotypes on the pathway to active ageing.
“If You Can Measure It, You Can Change It.” Active ageing assessment needs conceptual progress, which I propose to do. A quantifiable scale will be developed that captures the diversity of active ageing stemming from the WHO definition of active ageing as the process of optimizing opportunities for health and participation in the society for all people in line with their needs, goals and capacities as they age. I will collect cross-sectional data (N=1000, ages 75, 80 and 85 years) and model the pathway to active ageing with state-of-the art statistical methods. By doing this I will create novel knowledge on preconditions for active ageing. The collected cohort data will be compared to a pre-existing cohort data that was collected 25 years ago to obtain knowledge about changes over time in functioning of older people. A randomized controlled trial (N=200) will be conducted to assess the effectiveness of the envisioned intervention promoting active ageing through participation. The project will regenerate ageing research by launching a novel scale, by training young scientists, by creating new concepts and theory development and by producing evidence for active ageing promotion
Max ERC Funding
2 044 364 €
Duration
Start date: 2016-09-01, End date: 2021-08-31
Project acronym AIDA
Project An Illumination of the Dark Ages: modeling reionization and interpreting observations
Researcher (PI) Andrei Albert Mesinger
Host Institution (HI) SCUOLA NORMALE SUPERIORE
Country Italy
Call Details Starting Grant (StG), PE9, ERC-2014-STG
Summary "Understanding the dawn of the first galaxies and how their light permeated the early Universe is at the very frontier of modern astrophysical cosmology. Generous resources, including ambitions observational programs, are being devoted to studying these epochs of Cosmic Dawn (CD) and Reionization (EoR). In order to interpret these observations, we propose to build on our widely-used, semi-numeric simulation tool, 21cmFAST, and apply it to observations. Using sub-grid, semi-analytic models, we will incorporate additional physical processes governing the evolution of sources and sinks of ionizing photons. The resulting state-of-the-art simulations will be well poised to interpret topical observations of quasar spectra and the cosmic 21cm signal. They would be both physically-motivated and fast, allowing us to rapidly explore astrophysical parameter space. We will statistically quantify the resulting degeneracies and constraints, providing a robust answer to the question, ""What can we learn from EoR/CD observations?"" As an end goal, these investigations will help us understand when the first generations of galaxies formed, how they drove the EoR, and what are the associated large-scale observational signatures."
Summary
"Understanding the dawn of the first galaxies and how their light permeated the early Universe is at the very frontier of modern astrophysical cosmology. Generous resources, including ambitions observational programs, are being devoted to studying these epochs of Cosmic Dawn (CD) and Reionization (EoR). In order to interpret these observations, we propose to build on our widely-used, semi-numeric simulation tool, 21cmFAST, and apply it to observations. Using sub-grid, semi-analytic models, we will incorporate additional physical processes governing the evolution of sources and sinks of ionizing photons. The resulting state-of-the-art simulations will be well poised to interpret topical observations of quasar spectra and the cosmic 21cm signal. They would be both physically-motivated and fast, allowing us to rapidly explore astrophysical parameter space. We will statistically quantify the resulting degeneracies and constraints, providing a robust answer to the question, ""What can we learn from EoR/CD observations?"" As an end goal, these investigations will help us understand when the first generations of galaxies formed, how they drove the EoR, and what are the associated large-scale observational signatures."
Max ERC Funding
1 468 750 €
Duration
Start date: 2015-05-01, End date: 2021-04-30
Project acronym ALICE
Project Strange Mirrors, Unsuspected Lessons: Leading Europe to a new way of sharing the world experiences
Researcher (PI) Boaventura De Sousa Santos
Host Institution (HI) CENTRO DE ESTUDOS SOCIAIS
Country Portugal
Call Details Advanced Grant (AdG), SH2, ERC-2010-AdG_20100407
Summary Europe sits uncomfortably on the idea that there are no political and cultural alternatives credible enough to respond to the current uneasiness or malaise caused by both a world that is more and more non-European and a Europe that increasingly questions what is European about itself. This project will develop a new grounded theoretical paradigm for contemporary Europe based on two key ideas: the understanding of the world by far exceeds the European understanding of the world; social, political and institutional transformation in Europe may benefit from innovations taking place in regions and countries with which Europe is increasingly interdependent. I will pursue this objective focusing on four main interconnected topics: democratizing democracy, intercultural constitutionalism, the other economy, human rights (right to health in particular).
In a sense that the European challenges are unique but, in one way or another, are being experienced in different corners of the world. The novelty resides in bringing new ideas and experiences into the European conversation, show their relevance to our current uncertainties and aspirations and thereby contribute to face them with new intellectual and political resources. The usefulness and relevance of non-European conceptions and experiences un-thinking the conventional knowledge through two epistemological devices I have developed: the ecology of knowledges and intercultural translation. By resorting to them I will show that there are alternatives but they cannot be made credible and powerful if we go on relying on the modes of theoretical and political thinking that have dominated so far. In other words, the claim put forward by and worked through this project is that in Europe we don’t need alternatives but rather an alternative thinking of alternatives.
Summary
Europe sits uncomfortably on the idea that there are no political and cultural alternatives credible enough to respond to the current uneasiness or malaise caused by both a world that is more and more non-European and a Europe that increasingly questions what is European about itself. This project will develop a new grounded theoretical paradigm for contemporary Europe based on two key ideas: the understanding of the world by far exceeds the European understanding of the world; social, political and institutional transformation in Europe may benefit from innovations taking place in regions and countries with which Europe is increasingly interdependent. I will pursue this objective focusing on four main interconnected topics: democratizing democracy, intercultural constitutionalism, the other economy, human rights (right to health in particular).
In a sense that the European challenges are unique but, in one way or another, are being experienced in different corners of the world. The novelty resides in bringing new ideas and experiences into the European conversation, show their relevance to our current uncertainties and aspirations and thereby contribute to face them with new intellectual and political resources. The usefulness and relevance of non-European conceptions and experiences un-thinking the conventional knowledge through two epistemological devices I have developed: the ecology of knowledges and intercultural translation. By resorting to them I will show that there are alternatives but they cannot be made credible and powerful if we go on relying on the modes of theoretical and political thinking that have dominated so far. In other words, the claim put forward by and worked through this project is that in Europe we don’t need alternatives but rather an alternative thinking of alternatives.
Max ERC Funding
2 423 140 €
Duration
Start date: 2011-07-01, End date: 2016-12-31
Project acronym ANALYTIC
Project ANALYTIC PROPERTIES OF INFINITE GROUPS:
limits, curvature, and randomness
Researcher (PI) Gulnara Arzhantseva
Host Institution (HI) UNIVERSITAT WIEN
Country Austria
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary The overall goal of this project is to develop new concepts and techniques in geometric and asymptotic group theory for a systematic study of the analytic properties of discrete groups. These are properties depending on the unitary representation theory of the group. The fundamental examples are amenability, discovered by von Neumann in 1929, and property (T), introduced by Kazhdan in 1967.
My main objective is to establish the precise relations between groups recently appeared in K-theory and topology such as C*-exact groups and groups coarsely embeddable into a Hilbert space, versus those discovered in ergodic theory and operator algebra, for example, sofic and hyperlinear groups. This is a first ever attempt to confront the analytic behavior of so different nature. I plan to work on crucial open questions: Is every coarsely embeddable group C*-exact? Is every group sofic? Is every hyperlinear group sofic?
My motivation is two-fold:
- Many outstanding conjectures were recently solved for these groups, e.g. the Novikov conjecture (1965) for coarsely embeddable groups by Yu in 2000 and the Gottschalk surjunctivity conjecture (1973) for sofic groups by Gromov in 1999. However, their group-theoretical structure remains mysterious.
- In recent years, geometric group theory has undergone significant changes, mainly due to the growing impact of this theory on other branches of mathematics. However, the interplay between geometric, asymptotic, and analytic group properties has not yet been fully understood.
The main innovative contribution of this proposal lies in the interaction between 3 axes: (i) limits of groups, in the space of marked groups or metric ultralimits; (ii) analytic properties of groups with curvature, of lacunary or relatively hyperbolic groups; (iii) random groups, in a topological or statistical meaning. As a result, I will describe the above apparently unrelated classes of groups in a unified way and will detail their algebraic behavior.
Summary
The overall goal of this project is to develop new concepts and techniques in geometric and asymptotic group theory for a systematic study of the analytic properties of discrete groups. These are properties depending on the unitary representation theory of the group. The fundamental examples are amenability, discovered by von Neumann in 1929, and property (T), introduced by Kazhdan in 1967.
My main objective is to establish the precise relations between groups recently appeared in K-theory and topology such as C*-exact groups and groups coarsely embeddable into a Hilbert space, versus those discovered in ergodic theory and operator algebra, for example, sofic and hyperlinear groups. This is a first ever attempt to confront the analytic behavior of so different nature. I plan to work on crucial open questions: Is every coarsely embeddable group C*-exact? Is every group sofic? Is every hyperlinear group sofic?
My motivation is two-fold:
- Many outstanding conjectures were recently solved for these groups, e.g. the Novikov conjecture (1965) for coarsely embeddable groups by Yu in 2000 and the Gottschalk surjunctivity conjecture (1973) for sofic groups by Gromov in 1999. However, their group-theoretical structure remains mysterious.
- In recent years, geometric group theory has undergone significant changes, mainly due to the growing impact of this theory on other branches of mathematics. However, the interplay between geometric, asymptotic, and analytic group properties has not yet been fully understood.
The main innovative contribution of this proposal lies in the interaction between 3 axes: (i) limits of groups, in the space of marked groups or metric ultralimits; (ii) analytic properties of groups with curvature, of lacunary or relatively hyperbolic groups; (iii) random groups, in a topological or statistical meaning. As a result, I will describe the above apparently unrelated classes of groups in a unified way and will detail their algebraic behavior.
Max ERC Funding
1 065 500 €
Duration
Start date: 2011-04-01, End date: 2016-03-31
Project acronym ANGULON
Project Angulon: physics and applications of a new quasiparticle
Researcher (PI) Mikhail Lemeshko
Host Institution (HI) INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA
Country Austria
Call Details Starting Grant (StG), PE3, ERC-2018-STG
Summary This project aims to develop a universal approach to angular momentum in quantum many-body systems based on the angulon quasiparticle recently discovered by the PI. We will establish a general theory of angulons in and out of equilibrium, and apply it to a variety of experimentally studied problems, ranging from chemical dynamics in solvents to solid-state systems (e.g. angular momentum transfer in the Einstein-de Haas effect and ultrafast magnetism).
The concept of angular momentum is ubiquitous across physics, whether one deals with nuclear collisions, chemical reactions, or formation of galaxies. In the microscopic world, quantum rotations are described by non-commuting operators. This makes the angular momentum theory extremely involved, even for systems consisting of only a few interacting particles, such as gas-phase atoms or molecules.
Furthermore, in most experiments the behavior of quantum particles is inevitably altered by a many-body environment of some kind. For example, molecular rotation – and therefore reactivity – depends on the presence of a solvent, electronic angular momentum in solids is coupled to lattice phonons, highly excited atomic levels can be perturbed by a surrounding ultracold gas. If approached in a brute-force fashion, understanding angular momentum in such systems is an impossible task, since a macroscopic number of particles is involved.
Recently, the PI and his team have shown that this challenge can be met by introducing a new quasiparticle – the angulon. In 2017, the PI has demonstrated the existence of angulons by comparing his theory with 20 years of measurements on molecules rotating in superfluids. Most importantly, the angulon concept allows one to gain analytical insights inaccessible to the state-of-the-art techniques of condensed matter and chemical physics. The angulon approach holds the promise of opening up a new interdisciplinary research area with applications reaching far beyond what is proposed here.
Summary
This project aims to develop a universal approach to angular momentum in quantum many-body systems based on the angulon quasiparticle recently discovered by the PI. We will establish a general theory of angulons in and out of equilibrium, and apply it to a variety of experimentally studied problems, ranging from chemical dynamics in solvents to solid-state systems (e.g. angular momentum transfer in the Einstein-de Haas effect and ultrafast magnetism).
The concept of angular momentum is ubiquitous across physics, whether one deals with nuclear collisions, chemical reactions, or formation of galaxies. In the microscopic world, quantum rotations are described by non-commuting operators. This makes the angular momentum theory extremely involved, even for systems consisting of only a few interacting particles, such as gas-phase atoms or molecules.
Furthermore, in most experiments the behavior of quantum particles is inevitably altered by a many-body environment of some kind. For example, molecular rotation – and therefore reactivity – depends on the presence of a solvent, electronic angular momentum in solids is coupled to lattice phonons, highly excited atomic levels can be perturbed by a surrounding ultracold gas. If approached in a brute-force fashion, understanding angular momentum in such systems is an impossible task, since a macroscopic number of particles is involved.
Recently, the PI and his team have shown that this challenge can be met by introducing a new quasiparticle – the angulon. In 2017, the PI has demonstrated the existence of angulons by comparing his theory with 20 years of measurements on molecules rotating in superfluids. Most importantly, the angulon concept allows one to gain analytical insights inaccessible to the state-of-the-art techniques of condensed matter and chemical physics. The angulon approach holds the promise of opening up a new interdisciplinary research area with applications reaching far beyond what is proposed here.
Max ERC Funding
1 499 588 €
Duration
Start date: 2019-02-01, End date: 2024-01-31
Project acronym ANPROB
Project Analytic-probabilistic methods for borderline singular integrals
Researcher (PI) Tuomas Pentinpoika Hytoenen
Host Institution (HI) HELSINGIN YLIOPISTO
Country Finland
Call Details Starting Grant (StG), PE1, ERC-2011-StG_20101014
Summary The proposal consists of an extensive research program to advance the understanding of singular integral operators of Harmonic Analysis in various situations on the borderline of the existing theory. This is to be achieved by a creative combination of techniques from Analysis and Probability. On top of the standard arsenal of modern Harmonic Analysis, the main probabilistic tools are the martingale transform inequalities of Burkholder, and random geometric constructions in the spirit of the random dyadic cubes introduced to Nonhomogeneous Analysis by Nazarov, Treil and Volberg.
The problems to be addressed fall under the following subtitles, with many interconnections and overlap: (i) sharp weighted inequalities; (ii) nonhomogeneous singular integrals on metric spaces; (iii) local Tb theorems with borderline assumptions; (iv) functional calculus of rough differential operators; and (v) vector-valued singular integrals.
Topic (i) is a part of Classical Analysis, where new methods have led to substantial recent progress, culminating in my solution in July 2010 of a celebrated problem on the linear dependence of the weighted operator norm on the Muckenhoupt norm of the weight. The proof should be extendible to several related questions, and the aim is to also address some outstanding open problems in the area.
Topics (ii) and (v) deal with extensions of the theory of singular integrals to functions with more general domain and range spaces, allowing them to be abstract metric and Banach spaces, respectively. In case (ii), I have recently been able to relax the requirements on the space compared to the established theories, opening a new research direction here. Topics (iii) and (iv) are concerned with weakening the assumptions on singular integrals in the usual Euclidean space, to allow certain applications in the theory of Partial Differential Equations. The goal is to maintain a close contact and exchange of ideas between such abstract and concrete questions.
Summary
The proposal consists of an extensive research program to advance the understanding of singular integral operators of Harmonic Analysis in various situations on the borderline of the existing theory. This is to be achieved by a creative combination of techniques from Analysis and Probability. On top of the standard arsenal of modern Harmonic Analysis, the main probabilistic tools are the martingale transform inequalities of Burkholder, and random geometric constructions in the spirit of the random dyadic cubes introduced to Nonhomogeneous Analysis by Nazarov, Treil and Volberg.
The problems to be addressed fall under the following subtitles, with many interconnections and overlap: (i) sharp weighted inequalities; (ii) nonhomogeneous singular integrals on metric spaces; (iii) local Tb theorems with borderline assumptions; (iv) functional calculus of rough differential operators; and (v) vector-valued singular integrals.
Topic (i) is a part of Classical Analysis, where new methods have led to substantial recent progress, culminating in my solution in July 2010 of a celebrated problem on the linear dependence of the weighted operator norm on the Muckenhoupt norm of the weight. The proof should be extendible to several related questions, and the aim is to also address some outstanding open problems in the area.
Topics (ii) and (v) deal with extensions of the theory of singular integrals to functions with more general domain and range spaces, allowing them to be abstract metric and Banach spaces, respectively. In case (ii), I have recently been able to relax the requirements on the space compared to the established theories, opening a new research direction here. Topics (iii) and (iv) are concerned with weakening the assumptions on singular integrals in the usual Euclidean space, to allow certain applications in the theory of Partial Differential Equations. The goal is to maintain a close contact and exchange of ideas between such abstract and concrete questions.
Max ERC Funding
1 100 000 €
Duration
Start date: 2011-11-01, End date: 2016-10-31
Project acronym ANTEGEFI
Project Analytic Techniques for Geometric and Functional Inequalities
Researcher (PI) Nicola Fusco
Host Institution (HI) UNIVERSITA DEGLI STUDI DI NAPOLI FEDERICO II
Country Italy
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary Isoperimetric and Sobolev inequalities are the best known examples of geometric-functional inequalities. In recent years the PI and collaborators have obtained new and sharp quantitative versions of these and other important related inequalities. These results have been obtained by the combined use of classical symmetrization methods, new tools coming from mass transportation theory, deep geometric measure tools and ad hoc symmetrizations. The objective of this project is to further develop thes techniques in order to get: sharp quantitative versions of Faber-Krahn inequality, Gaussian isoperimetric inequality, Brunn-Minkowski inequality, Poincaré and Sobolev logarithm inequalities; sharp decay rates for the quantitative Sobolev inequalities and Polya-Szegö inequality.
Summary
Isoperimetric and Sobolev inequalities are the best known examples of geometric-functional inequalities. In recent years the PI and collaborators have obtained new and sharp quantitative versions of these and other important related inequalities. These results have been obtained by the combined use of classical symmetrization methods, new tools coming from mass transportation theory, deep geometric measure tools and ad hoc symmetrizations. The objective of this project is to further develop thes techniques in order to get: sharp quantitative versions of Faber-Krahn inequality, Gaussian isoperimetric inequality, Brunn-Minkowski inequality, Poincaré and Sobolev logarithm inequalities; sharp decay rates for the quantitative Sobolev inequalities and Polya-Szegö inequality.
Max ERC Funding
600 000 €
Duration
Start date: 2009-01-01, End date: 2013-12-31