Project acronym DISCRETION
Project Discretion and the child´s best interests in child protection
Researcher (PI) Marit Sissel Irene SKIVENES
Host Institution (HI) UNIVERSITETET I BERGEN
Call Details Consolidator Grant (CoG), SH3, ERC-2016-COG
Summary DISCRETION aims to unlock the black box of discretionary decision-making in child protection cases by a comparative-empirical study of how discretionary decisions are made and justified in the best interests of the child. There are huge research gaps in this important area of the welfare state, with a great deal of uncertainty concerning how, when and why discretionary decisions about the child´s best interests are different between decision-makers within and between child protection systems.
The main objectives for this project are to reveal the mechanisms for exercising discretion, and improve the understanding of the principle of the child´s best interests.
These objectives will be reached by systematically examining the role of institutional, organisational and individual factors including regulations of best interest principles; professions involved; type of courts; type of child protection system; demographic factors and individual values; and the populations’ view on children and paternalism. DISCRETION employs an innovative methodological approach, with multilevel and cross-country studies.
DISCRETION will, by conducting the largest cross-national study on decision-making in child protection to date, lift our understanding of international differences in child protection to a new level. By conducting randomized survey experiments with both decision-makers in the system and the general population, DISCRETION generates unique data on the causal mechanisms explaining differences in discretionary decisions.
The outcomes of DISCRETION are important because societies are at a crossroad when it comes to how children are treated and how their rights are respected, which creates tensions in the traditional relationship between the family and the state. DISCRETION will move beyond the field of child protection and provide important insights into the exercise of discretion in all areas where the public interest as well as national interest must be interpreted.
Summary
DISCRETION aims to unlock the black box of discretionary decision-making in child protection cases by a comparative-empirical study of how discretionary decisions are made and justified in the best interests of the child. There are huge research gaps in this important area of the welfare state, with a great deal of uncertainty concerning how, when and why discretionary decisions about the child´s best interests are different between decision-makers within and between child protection systems.
The main objectives for this project are to reveal the mechanisms for exercising discretion, and improve the understanding of the principle of the child´s best interests.
These objectives will be reached by systematically examining the role of institutional, organisational and individual factors including regulations of best interest principles; professions involved; type of courts; type of child protection system; demographic factors and individual values; and the populations’ view on children and paternalism. DISCRETION employs an innovative methodological approach, with multilevel and cross-country studies.
DISCRETION will, by conducting the largest cross-national study on decision-making in child protection to date, lift our understanding of international differences in child protection to a new level. By conducting randomized survey experiments with both decision-makers in the system and the general population, DISCRETION generates unique data on the causal mechanisms explaining differences in discretionary decisions.
The outcomes of DISCRETION are important because societies are at a crossroad when it comes to how children are treated and how their rights are respected, which creates tensions in the traditional relationship between the family and the state. DISCRETION will move beyond the field of child protection and provide important insights into the exercise of discretion in all areas where the public interest as well as national interest must be interpreted.
Max ERC Funding
1 997 918 €
Duration
Start date: 2017-06-01, End date: 2022-05-31
Project acronym EQOP
Project Socioeconomic gaps in language development and school achievement: Mechanisms of inequality and opportunity
Researcher (PI) Henrik ZACHRISSON
Host Institution (HI) UNIVERSITETET I OSLO
Call Details Consolidator Grant (CoG), SH3, ERC-2018-COG
Summary As inequality increases in most developed countries, children from socioeconomically disadvantaged families are at exceptional risk for academic underachievement with lasting consequences for individuals, their communities, and society at large. Among policy makes, early childhood education and care (ECEC) is considered a key to remedy this risk. Yet the science on ECEC effectiveness at a national scale lags behind the excitement.
Exploiting unique Norwegian data, we first seek to identify how and why socioeconomic disadvantage undermines children’s language skills and school achievement. Second, we will investigate whether ECEC can improve opportunities for disadvantaged children to excel. Third, to clarify the policy relevance of these inquiries, we will estimate costs of socioeconomic achievement gaps and the economic benefits of ECEC at scale. We take an investigative approach that is unprecedented in scope—from population level trends down to nuanced assessments of individual children’s growth.
Throughout the 2000s, Norway’s child poverty rates increased from about 4% to 10%, while the coverage of public ECEC for toddlers increased from 30% to 80%. Across this unique window of time, we have access to rich survey data on language skills and home environment for 100,000 children, and genetically informative data, linked with administrative records on community- and family level socioeconomic risks and opportunities, and on national achievement test scores. These data allow us powerful analytic opportunities, combining state-of-the-art statistical, econometric, psychometric, and genetic epidemiological methods.
I am well positioned to lead this project, having qualified for a Professorship at the University of Oslo aged 36, and having considerable experience in (a) publishing in highly respected scientific journals, (b) working at the intersection of research and policy, (c) leading research projects, and (d) mentoring younger scholars.
Summary
As inequality increases in most developed countries, children from socioeconomically disadvantaged families are at exceptional risk for academic underachievement with lasting consequences for individuals, their communities, and society at large. Among policy makes, early childhood education and care (ECEC) is considered a key to remedy this risk. Yet the science on ECEC effectiveness at a national scale lags behind the excitement.
Exploiting unique Norwegian data, we first seek to identify how and why socioeconomic disadvantage undermines children’s language skills and school achievement. Second, we will investigate whether ECEC can improve opportunities for disadvantaged children to excel. Third, to clarify the policy relevance of these inquiries, we will estimate costs of socioeconomic achievement gaps and the economic benefits of ECEC at scale. We take an investigative approach that is unprecedented in scope—from population level trends down to nuanced assessments of individual children’s growth.
Throughout the 2000s, Norway’s child poverty rates increased from about 4% to 10%, while the coverage of public ECEC for toddlers increased from 30% to 80%. Across this unique window of time, we have access to rich survey data on language skills and home environment for 100,000 children, and genetically informative data, linked with administrative records on community- and family level socioeconomic risks and opportunities, and on national achievement test scores. These data allow us powerful analytic opportunities, combining state-of-the-art statistical, econometric, psychometric, and genetic epidemiological methods.
I am well positioned to lead this project, having qualified for a Professorship at the University of Oslo aged 36, and having considerable experience in (a) publishing in highly respected scientific journals, (b) working at the intersection of research and policy, (c) leading research projects, and (d) mentoring younger scholars.
Max ERC Funding
1 907 959 €
Duration
Start date: 2019-06-01, End date: 2024-05-31
Project acronym FEEC-A
Project Finite Element Exterior Calculus and Applications
Researcher (PI) Ragnar Winther
Host Institution (HI) UNIVERSITETET I OSLO
Call Details Advanced Grant (AdG), PE1, ERC-2013-ADG
Summary "The finite element method is one of the most successful techniques for designing numerical methods for systems of partial differential equations (PDEs). It is not only a methodology for developing numerical algorithms, but also a mathematical framework in which to explore their behavior. The finite element exterior calculus (FEEC) provides a new structure that produces a deeper understanding of the finite element method and its connections to the partial differential equation being approximated. The goal is to develop discretizations which are compatible with the geometric, topological, and algebraic structures which underlie well-posedness of the partial differential equation. The phrase FEEC was first used in a paper the PI wrote for Acta Numerica in 2006, together with his coworkers, D.N. Arnold and R.S. Falk. The general philosophy of FEEC has led to the design of new algorithms and software developments, also in areas beyond the direct application of the theory. The present project will be devoted to further development of the foundations of FEEC, and to direct or indirect use of FEEC in specific applications. The ambition is to set the scene for a nubmer of new research directions based on FEEC by giving ground-braking contributions to its foundation. The aim is also to use FEEC as a tool, or a guideline, to extend the foundation of numerical PDEs to a variety of problems for which this foundation does not exist. The more application oriented parts of the project includes topics like numerical methods for elasticity, its generalizations to more general models in materials science such as viscoelasticity, poroelasticity, and liquid crystals, and the applications of these models to CO2 storage and deformations of the spinal cord."
Summary
"The finite element method is one of the most successful techniques for designing numerical methods for systems of partial differential equations (PDEs). It is not only a methodology for developing numerical algorithms, but also a mathematical framework in which to explore their behavior. The finite element exterior calculus (FEEC) provides a new structure that produces a deeper understanding of the finite element method and its connections to the partial differential equation being approximated. The goal is to develop discretizations which are compatible with the geometric, topological, and algebraic structures which underlie well-posedness of the partial differential equation. The phrase FEEC was first used in a paper the PI wrote for Acta Numerica in 2006, together with his coworkers, D.N. Arnold and R.S. Falk. The general philosophy of FEEC has led to the design of new algorithms and software developments, also in areas beyond the direct application of the theory. The present project will be devoted to further development of the foundations of FEEC, and to direct or indirect use of FEEC in specific applications. The ambition is to set the scene for a nubmer of new research directions based on FEEC by giving ground-braking contributions to its foundation. The aim is also to use FEEC as a tool, or a guideline, to extend the foundation of numerical PDEs to a variety of problems for which this foundation does not exist. The more application oriented parts of the project includes topics like numerical methods for elasticity, its generalizations to more general models in materials science such as viscoelasticity, poroelasticity, and liquid crystals, and the applications of these models to CO2 storage and deformations of the spinal cord."
Max ERC Funding
2 059 687 €
Duration
Start date: 2014-02-01, End date: 2019-01-31
Project acronym FUMI
Project Future Migration as Present Fact
Researcher (PI) Jørgen Koren CARLING
Host Institution (HI) INSTITUTT FOR FREDSFORSKNING STIFTELSE
Call Details Consolidator Grant (CoG), SH3, ERC-2018-COG
Summary The springboard for this project is a striking statistic: half of all young adults in West Africa wish to leave their own country and settle elsewhere. Yet, the vast majority never depart. This discrep-ancy raises a fundamental question: if migration is desired, but never materializes, what are the consequences? The project breaks with traditional approaches by shifting the object of study from observed migration in the present to imagined migration in the future. Although such future migration might never occur, it materializes in thoughts, feelings, communication, and behaviour at present. Young people’s priorities are informed by the futures they imagine, and their lives can thus be formed by migration that is imagined but never achieved. Framing the issue in this way renews research on the precursors of migration and opens up a new chapter about the links be-tween migration and development. The project is guided by a bold central hypothesis: Migration that is imagined, yet never takes place, decisively shapes the lives of individuals and the devel-opment of societies. This hypothesis is addressed through a research design that weaves together three streams: theory development, ethnographic fieldwork, and sample surveys. Drawing upon the PI’s proven qualifications in all three fields, the project aims for deep mixed-methods integra-tion. The project’s empirical focus is West Africa. Migration desires are particularly widespread in this region, and internal socio-economic variation can be exploited for theoretical purposes. By investing in theoretical and methodological development, attuned to a poorly understood aspect of global migration challenges, the project holds the promise of sustained impacts on migration research. The project is set within interdisciplinary migration studies, anchored in human geogra-phy and supported by related disciplines including anthropology, economics, and sociology.
Summary
The springboard for this project is a striking statistic: half of all young adults in West Africa wish to leave their own country and settle elsewhere. Yet, the vast majority never depart. This discrep-ancy raises a fundamental question: if migration is desired, but never materializes, what are the consequences? The project breaks with traditional approaches by shifting the object of study from observed migration in the present to imagined migration in the future. Although such future migration might never occur, it materializes in thoughts, feelings, communication, and behaviour at present. Young people’s priorities are informed by the futures they imagine, and their lives can thus be formed by migration that is imagined but never achieved. Framing the issue in this way renews research on the precursors of migration and opens up a new chapter about the links be-tween migration and development. The project is guided by a bold central hypothesis: Migration that is imagined, yet never takes place, decisively shapes the lives of individuals and the devel-opment of societies. This hypothesis is addressed through a research design that weaves together three streams: theory development, ethnographic fieldwork, and sample surveys. Drawing upon the PI’s proven qualifications in all three fields, the project aims for deep mixed-methods integra-tion. The project’s empirical focus is West Africa. Migration desires are particularly widespread in this region, and internal socio-economic variation can be exploited for theoretical purposes. By investing in theoretical and methodological development, attuned to a poorly understood aspect of global migration challenges, the project holds the promise of sustained impacts on migration research. The project is set within interdisciplinary migration studies, anchored in human geogra-phy and supported by related disciplines including anthropology, economics, and sociology.
Max ERC Funding
1 999 672 €
Duration
Start date: 2019-07-01, End date: 2024-06-30
Project acronym HyLEF
Project Hydrodynamic Limits and Equilibrium Fluctuations: universality from stochastic systems
Researcher (PI) ANA PATRICIA CARVALHO GONÇALVES
Host Institution (HI) INSTITUTO SUPERIOR TECNICO
Call Details Starting Grant (StG), PE1, ERC-2016-STG
Summary A classical problem in the field of interacting particle systems (IPS) is to derive the macroscopic laws of the thermodynamical quantities of a physical system by considering an underlying microscopic dynamics which is composed of particles that move according to some prescribed stochastic, or deterministic, law. The macroscopic laws can be partial differential equations (PDE) or stochastic PDE (SPDE) depending on whether one is looking at the convergence to the mean or to the fluctuations around that mean. One of the purposes of this research project is to give a mathematically rigorous description of the derivation of SPDE from different IPS. We will focus on the derivation of the stochastic Burgers equation (SBE) and its integrated counterpart, namely, the KPZ equation, as well as their fractional versions. The KPZ equation is conjectured to be a universal SPDE describing the fluctuations of randomly growing interfaces of 1d stochastic dynamics close to a stationary state. With this study we want to characterize what is known as the KPZ universality class: the weak and strong conjectures. The latter states that there exists a universal process, namely the KPZ fixed point, which is a fixed point of the renormalization group operator of space-time scaling 1:2:3, for which the KPZ is also invariant. The former states that the fluctuations of a large class of 1d conservative microscopic dynamics are ruled by stationary solutions of the KPZ. Our goal is threefold: first, to derive the KPZ equation from general weakly asymmetric systems, showing its universality; second, to derive new SPDE, which are less studied in the literature, as the fractional KPZ from IPS which allow long jumps, the KPZ with boundary conditions from IPS in contact with reservoirs or with defects, and coupled KPZ from IPS with more than one conserved quantity. Finally, we will analyze the fluctuations of purely strong asymmetric systems, which are conjectured to be given by the KPZ fixed point.
Summary
A classical problem in the field of interacting particle systems (IPS) is to derive the macroscopic laws of the thermodynamical quantities of a physical system by considering an underlying microscopic dynamics which is composed of particles that move according to some prescribed stochastic, or deterministic, law. The macroscopic laws can be partial differential equations (PDE) or stochastic PDE (SPDE) depending on whether one is looking at the convergence to the mean or to the fluctuations around that mean. One of the purposes of this research project is to give a mathematically rigorous description of the derivation of SPDE from different IPS. We will focus on the derivation of the stochastic Burgers equation (SBE) and its integrated counterpart, namely, the KPZ equation, as well as their fractional versions. The KPZ equation is conjectured to be a universal SPDE describing the fluctuations of randomly growing interfaces of 1d stochastic dynamics close to a stationary state. With this study we want to characterize what is known as the KPZ universality class: the weak and strong conjectures. The latter states that there exists a universal process, namely the KPZ fixed point, which is a fixed point of the renormalization group operator of space-time scaling 1:2:3, for which the KPZ is also invariant. The former states that the fluctuations of a large class of 1d conservative microscopic dynamics are ruled by stationary solutions of the KPZ. Our goal is threefold: first, to derive the KPZ equation from general weakly asymmetric systems, showing its universality; second, to derive new SPDE, which are less studied in the literature, as the fractional KPZ from IPS which allow long jumps, the KPZ with boundary conditions from IPS in contact with reservoirs or with defects, and coupled KPZ from IPS with more than one conserved quantity. Finally, we will analyze the fluctuations of purely strong asymmetric systems, which are conjectured to be given by the KPZ fixed point.
Max ERC Funding
1 179 496 €
Duration
Start date: 2016-12-01, End date: 2021-11-30
Project acronym INDEX
Project Rigidity of groups and higher index theory
Researcher (PI) Piotr Wojciech Nowak
Host Institution (HI) INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK
Call Details Starting Grant (StG), PE1, ERC-2015-STG
Summary The Atiyah-Singer index theorem was one of the most spectacular achievements of mathematics in the XXth century, connecting the analytic and topological properties of manifolds. The Baum-Connes conjecture is a hugely successful approach to generalizing the index theorem to a much broader setting. It has remarkable applications in topology and analysis. For instance, it implies the Novikov conjecture on the homotopy invariance of higher signatures of a closed manifold and the Kaplansky-Kadison conjecture on the existence of non-trivial idempotents in the reduced group C*-algebra of a torsion-free group. At present, the Baum-Connes conjecture is known to hold for a large class of groups, including groups admitting metrically proper isometric actions on Hilbert spaces and Gromov hyperbolic groups.
The Baum-Connes conjecture with certain coefficients is known to fail for a class of groups, whose Cayley graphs contain coarsely embedded expander graphs. Nevertheless, the conjecture in full generality remains open and there is a growing need for new examples of groups and group actions, that would be counterexamples to the Baum-Connes conjecture. The main objective of this project is to exhibit such examples.
Our approach relies on strengthening Kazhdan’s property (T), a prominent cohomological rigidity property, from its original setting of Hilbert spaces to much larger classes of Banach spaces. Such properties are an emerging direction in the study of cohomological rigidity and are not yet well-understood. They lie at the intersection of geometric group theory, non-commutative geometry and index theory. In their study we will implement novel approaches, combining geometric and analytic techniques with variety of new cohomological constructions.
Summary
The Atiyah-Singer index theorem was one of the most spectacular achievements of mathematics in the XXth century, connecting the analytic and topological properties of manifolds. The Baum-Connes conjecture is a hugely successful approach to generalizing the index theorem to a much broader setting. It has remarkable applications in topology and analysis. For instance, it implies the Novikov conjecture on the homotopy invariance of higher signatures of a closed manifold and the Kaplansky-Kadison conjecture on the existence of non-trivial idempotents in the reduced group C*-algebra of a torsion-free group. At present, the Baum-Connes conjecture is known to hold for a large class of groups, including groups admitting metrically proper isometric actions on Hilbert spaces and Gromov hyperbolic groups.
The Baum-Connes conjecture with certain coefficients is known to fail for a class of groups, whose Cayley graphs contain coarsely embedded expander graphs. Nevertheless, the conjecture in full generality remains open and there is a growing need for new examples of groups and group actions, that would be counterexamples to the Baum-Connes conjecture. The main objective of this project is to exhibit such examples.
Our approach relies on strengthening Kazhdan’s property (T), a prominent cohomological rigidity property, from its original setting of Hilbert spaces to much larger classes of Banach spaces. Such properties are an emerging direction in the study of cohomological rigidity and are not yet well-understood. They lie at the intersection of geometric group theory, non-commutative geometry and index theory. In their study we will implement novel approaches, combining geometric and analytic techniques with variety of new cohomological constructions.
Max ERC Funding
880 625 €
Duration
Start date: 2016-08-01, End date: 2021-07-31
Project acronym INNOSTOCH
Project INNOVATIONS IN STOCHASTIC ANALYSIS AND APPLICATIONS with emphasis on STOCHASTIC CONTROL AND INFORMATION
Researcher (PI) Bernt Karsten Øksendal
Host Institution (HI) UNIVERSITETET I OSLO
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary "For almost all kinds of dynamic systems modeling real processes in nature or society, most of the mathematical models we can formulate are - at best - inaccurate, and subject to random fluctuations and other types of ""noise"". Therefore it is important to be able to deal with such noisy models in a mathematically rigorous way. This rigorous theory is stochastic analysis. Theoretical progress in stochastic analysis will lead to new and improved applications in a wide range of fields.
The main purpose of this proposal is to establish a research environment which enhances the creation of new ideas and methods in the research of stochastic analysis and its applications. The emphasis is more on innovation, new models and challenges in the research frontiers, rather than small variations and minor improvements of already established theories and results. We will concentrate on applications in finance and biology, but the theoretical results may as well apply to several other areas.
Utilizing recent results and achievements by PI and a large group of distinguished coworkers, the natural extensions from the present knowledge is to concentrate on the mathematical theory of the interplay between stochastic analysis, stochastic control and information. More precisely, we have ambitions to make fundamental progress in the general theory of stochastic control of random systems and applications in finance and biology, and the explicit relation between the optimal performance and the amount of information available to the controller. Explicit examples of special interest include optimal control under partial or delayed information, and optimal control under inside or advanced information. A success of the present proposal will represent a substantial breakthrough, and in turn bring us a significant step forward in our attempts to understand various aspects of the world better, and it will help us to find optimal, sustainable ways to influence it."
Summary
"For almost all kinds of dynamic systems modeling real processes in nature or society, most of the mathematical models we can formulate are - at best - inaccurate, and subject to random fluctuations and other types of ""noise"". Therefore it is important to be able to deal with such noisy models in a mathematically rigorous way. This rigorous theory is stochastic analysis. Theoretical progress in stochastic analysis will lead to new and improved applications in a wide range of fields.
The main purpose of this proposal is to establish a research environment which enhances the creation of new ideas and methods in the research of stochastic analysis and its applications. The emphasis is more on innovation, new models and challenges in the research frontiers, rather than small variations and minor improvements of already established theories and results. We will concentrate on applications in finance and biology, but the theoretical results may as well apply to several other areas.
Utilizing recent results and achievements by PI and a large group of distinguished coworkers, the natural extensions from the present knowledge is to concentrate on the mathematical theory of the interplay between stochastic analysis, stochastic control and information. More precisely, we have ambitions to make fundamental progress in the general theory of stochastic control of random systems and applications in finance and biology, and the explicit relation between the optimal performance and the amount of information available to the controller. Explicit examples of special interest include optimal control under partial or delayed information, and optimal control under inside or advanced information. A success of the present proposal will represent a substantial breakthrough, and in turn bring us a significant step forward in our attempts to understand various aspects of the world better, and it will help us to find optimal, sustainable ways to influence it."
Max ERC Funding
1 864 800 €
Duration
Start date: 2009-09-01, End date: 2014-08-31
Project acronym KAPIBARA
Project Homotopy Theory of Algebraic Varieties and Wild Ramification
Researcher (PI) Piotr ACHINGER
Host Institution (HI) INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK
Call Details Starting Grant (StG), PE1, ERC-2018-STG
Summary The aim of the proposed research is to study the homotopy theory of algebraic varieties and other algebraically defined geometric objects, especially over fields other than the complex numbers. A noticeable emphasis will be put on fundamental groups and on K(pi, 1) spaces, which serve as building blocks for more complicated objects. The most important source of both motivation and methodology is my recent discovery of the K(pi, 1) property of affine schemes in positive characteristic and its relation to wild ramification phenomena.
The central goal is the study of etale homotopy types in positive characteristic, where we hope to use the aforementioned discovery to yield new results beyond the affine case and a better understanding of the fundamental group of affine schemes. The latter goal is closely tied to Grothendieck's anabelian geometry program, which we would like to extend beyond its usual scope of hyperbolic curves.
There are two bridges going out of this central point. The first is the analogy between wild ramification and irregular singularities of algebraic integrable connections, which prompts us to translate our results to the latter setting, and to define a wild homotopy type whose fundamental group encodes the category of connections.
The second bridge is the theory of perfectoid spaces, allowing one to pass between characteristic p and p-adic geometry, which we plan to use to shed some new light on the homotopy theory of adic spaces. At the same time, we address the related question: when is the universal cover of a p-adic variety a perfectoid space? We expect a connection between this question and the Shafarevich conjecture and varieties with large fundamental group.
The last part of the project deals with varieties over the field of formal Laurent series over C, where we want to construct a Betti homotopy realization using logarithmic geometry. The need for such a construction is motivated by certain questions in mirror symmetry.
Summary
The aim of the proposed research is to study the homotopy theory of algebraic varieties and other algebraically defined geometric objects, especially over fields other than the complex numbers. A noticeable emphasis will be put on fundamental groups and on K(pi, 1) spaces, which serve as building blocks for more complicated objects. The most important source of both motivation and methodology is my recent discovery of the K(pi, 1) property of affine schemes in positive characteristic and its relation to wild ramification phenomena.
The central goal is the study of etale homotopy types in positive characteristic, where we hope to use the aforementioned discovery to yield new results beyond the affine case and a better understanding of the fundamental group of affine schemes. The latter goal is closely tied to Grothendieck's anabelian geometry program, which we would like to extend beyond its usual scope of hyperbolic curves.
There are two bridges going out of this central point. The first is the analogy between wild ramification and irregular singularities of algebraic integrable connections, which prompts us to translate our results to the latter setting, and to define a wild homotopy type whose fundamental group encodes the category of connections.
The second bridge is the theory of perfectoid spaces, allowing one to pass between characteristic p and p-adic geometry, which we plan to use to shed some new light on the homotopy theory of adic spaces. At the same time, we address the related question: when is the universal cover of a p-adic variety a perfectoid space? We expect a connection between this question and the Shafarevich conjecture and varieties with large fundamental group.
The last part of the project deals with varieties over the field of formal Laurent series over C, where we want to construct a Betti homotopy realization using logarithmic geometry. The need for such a construction is motivated by certain questions in mirror symmetry.
Max ERC Funding
1 007 500 €
Duration
Start date: 2019-06-01, End date: 2024-05-31
Project acronym NCGQG
Project Noncommutative geometry and quantum groups
Researcher (PI) Sergiy Neshveyev
Host Institution (HI) UNIVERSITETET I OSLO
Call Details Starting Grant (StG), PE1, ERC-2012-StG_20111012
Summary "The goal of the project is to make fundamental contributions to the study of quantum groups in the operator algebraic setting. Two main directions it aims to explore are noncommutative differential geometry and boundary theory of quantum random walks.
The idea behind noncommutative geometry is to bring geometric insight to the study of noncommutative algebras and to analyze spaces which are beyond the reach via classical means. It has been particularly successful in the latter, for example, in the study of the spaces of leaves of foliations. Quantum groups supply plenty of examples of noncommutative algebras, but the question how they fit into noncommutative geometry remains complicated. A successful union of these two areas is important for testing ideas of noncommutative geometry and for its development in new directions. One of the main goals of the project is to use the momentum created by our recent work in the area in order to further expand the boundaries of our understanding. Specifically, we are going to study such problems as the local index formula, equivariance of Dirac operators with respect to the dual group action (with an eye towards the Baum-Connes conjecture for discrete quantum groups), construction of Dirac operators on quantum homogeneous spaces, structure of quantized C*-algebras of continuous functions, computation of dual cohomology of compact quantum groups.
The boundary theory of quantum random walks was created around ten years ago. In the recent years there has been a lot of progress on the “measure-theoretic” side of the theory, while the questions largely remain open on the “topological” side. A significant progress in this area can have a great influence on understanding of quantum groups, construction of new examples and development of quantum probability. The main problems we are going to study are boundary convergence of quantum random walks and computation of Martin boundaries."
Summary
"The goal of the project is to make fundamental contributions to the study of quantum groups in the operator algebraic setting. Two main directions it aims to explore are noncommutative differential geometry and boundary theory of quantum random walks.
The idea behind noncommutative geometry is to bring geometric insight to the study of noncommutative algebras and to analyze spaces which are beyond the reach via classical means. It has been particularly successful in the latter, for example, in the study of the spaces of leaves of foliations. Quantum groups supply plenty of examples of noncommutative algebras, but the question how they fit into noncommutative geometry remains complicated. A successful union of these two areas is important for testing ideas of noncommutative geometry and for its development in new directions. One of the main goals of the project is to use the momentum created by our recent work in the area in order to further expand the boundaries of our understanding. Specifically, we are going to study such problems as the local index formula, equivariance of Dirac operators with respect to the dual group action (with an eye towards the Baum-Connes conjecture for discrete quantum groups), construction of Dirac operators on quantum homogeneous spaces, structure of quantized C*-algebras of continuous functions, computation of dual cohomology of compact quantum groups.
The boundary theory of quantum random walks was created around ten years ago. In the recent years there has been a lot of progress on the “measure-theoretic” side of the theory, while the questions largely remain open on the “topological” side. A significant progress in this area can have a great influence on understanding of quantum groups, construction of new examples and development of quantum probability. The main problems we are going to study are boundary convergence of quantum random walks and computation of Martin boundaries."
Max ERC Funding
1 144 930 €
Duration
Start date: 2013-01-01, End date: 2017-12-31
Project acronym OPENFLUX
Project Societal openness, normative flux, and the social modification of heritability
Researcher (PI) Torkild Hovde Lyngstad
Host Institution (HI) UNIVERSITETET I OSLO
Call Details Consolidator Grant (CoG), SH3, ERC-2018-COG
Summary In this project, we will use social modifications of heritability as measurement devices for assessing how social conditions shape opportunity structures, and how human potential is either constrained or enabled. Major themes in family demography and social stratification such as equality of opportunity in the age of mass education, changing family structures in the 20th century, development of life courses and careers, and intergenerational transmission processes all motivate an important role for human genetics. Up to recently, little of these efforts have directly engaged with genetic research. A common criticism of genetic methods is that they are silent on social context and environmental interactions. We turn these criticisms into tools, by assessing how genetic effects vary across contexts and environments. First, we study social change across cohorts, as influential theory suggests heritable dispositions will increase in importance when opportunity structures expand or social norms are in flux. We will test these ideas on the recent decades of family and fertility changes, and the expanding opportunity structures in education and labor markets. Second, we ask whether genetic and environmental influences on social stratification and family demographic outcomes change over the life course as the consequences of individual choice and social structures accumulate. Third, we will examine the similarity in outcomes of parents and their offspring from a genetically informed standpoint. A synergy combining state-of-the-art techniques from molecular and behavior genetics with high-quality population register data and strong theorization and measurement of socio-environmental factors from the social sciences is highly innovative cross-fertilization of research that will yield major new insights.
Summary
In this project, we will use social modifications of heritability as measurement devices for assessing how social conditions shape opportunity structures, and how human potential is either constrained or enabled. Major themes in family demography and social stratification such as equality of opportunity in the age of mass education, changing family structures in the 20th century, development of life courses and careers, and intergenerational transmission processes all motivate an important role for human genetics. Up to recently, little of these efforts have directly engaged with genetic research. A common criticism of genetic methods is that they are silent on social context and environmental interactions. We turn these criticisms into tools, by assessing how genetic effects vary across contexts and environments. First, we study social change across cohorts, as influential theory suggests heritable dispositions will increase in importance when opportunity structures expand or social norms are in flux. We will test these ideas on the recent decades of family and fertility changes, and the expanding opportunity structures in education and labor markets. Second, we ask whether genetic and environmental influences on social stratification and family demographic outcomes change over the life course as the consequences of individual choice and social structures accumulate. Third, we will examine the similarity in outcomes of parents and their offspring from a genetically informed standpoint. A synergy combining state-of-the-art techniques from molecular and behavior genetics with high-quality population register data and strong theorization and measurement of socio-environmental factors from the social sciences is highly innovative cross-fertilization of research that will yield major new insights.
Max ERC Funding
1 987 231 €
Duration
Start date: 2019-07-01, End date: 2024-06-30
