Project acronym ABRSEIST
Project Antibiotic Resistance: Socio-Economic Determinants and the Role of Information and Salience in Treatment Choice
Researcher (PI) Hannes ULLRICH
Host Institution (HI) DEUTSCHES INSTITUT FUR WIRTSCHAFTSFORSCHUNG DIW (INSTITUT FUR KONJUNKTURFORSCHUNG) EV
Call Details Starting Grant (StG), SH1, ERC-2018-STG
Summary Antibiotics have contributed to a tremendous increase in human well-being, saving many millions of lives. However, antibiotics become obsolete the more they are used as selection pressure promotes the development of resistant bacteria. The World Health Organization has proclaimed antibiotic resistance as a major global threat to public health. Today, 700,000 deaths per year are due to untreatable infections. To win the battle against antibiotic resistance, new policies affecting the supply and demand of existing and new drugs must be designed. I propose new research to identify and evaluate feasible and effective demand-side policy interventions targeting the relevant decision makers: physicians and patients. ABRSEIST will make use of a broad econometric toolset to identify mechanisms linking antibiotic resistance and consumption exploiting a unique combination of physician-patient-level antibiotic resistance, treatment, and socio-economic data. Using machine learning methods adapted for causal inference, theory-driven structural econometric analysis, and randomization in the field it will provide rigorous evidence on effective intervention designs. This research will improve our understanding of how prescribing, resistance, and the effect of antibiotic use on resistance, are distributed in the general population which has important implications for the design of targeted interventions. It will then estimate a structural model of general practitioners’ acquisition and use of information under uncertainty about resistance in prescription choice, allowing counterfactual analysis of information-improving policies such as mandatory diagnostic testing. The large-scale and structural econometric analyses allow flexible identification of physician heterogeneity, which ABRSEIST will exploit to design and evaluate targeted, randomized information nudges in the field. The result will be improved rational use and a toolset applicable in contexts of antibiotic prescribing.
Summary
Antibiotics have contributed to a tremendous increase in human well-being, saving many millions of lives. However, antibiotics become obsolete the more they are used as selection pressure promotes the development of resistant bacteria. The World Health Organization has proclaimed antibiotic resistance as a major global threat to public health. Today, 700,000 deaths per year are due to untreatable infections. To win the battle against antibiotic resistance, new policies affecting the supply and demand of existing and new drugs must be designed. I propose new research to identify and evaluate feasible and effective demand-side policy interventions targeting the relevant decision makers: physicians and patients. ABRSEIST will make use of a broad econometric toolset to identify mechanisms linking antibiotic resistance and consumption exploiting a unique combination of physician-patient-level antibiotic resistance, treatment, and socio-economic data. Using machine learning methods adapted for causal inference, theory-driven structural econometric analysis, and randomization in the field it will provide rigorous evidence on effective intervention designs. This research will improve our understanding of how prescribing, resistance, and the effect of antibiotic use on resistance, are distributed in the general population which has important implications for the design of targeted interventions. It will then estimate a structural model of general practitioners’ acquisition and use of information under uncertainty about resistance in prescription choice, allowing counterfactual analysis of information-improving policies such as mandatory diagnostic testing. The large-scale and structural econometric analyses allow flexible identification of physician heterogeneity, which ABRSEIST will exploit to design and evaluate targeted, randomized information nudges in the field. The result will be improved rational use and a toolset applicable in contexts of antibiotic prescribing.
Max ERC Funding
1 498 920 €
Duration
Start date: 2019-01-01, End date: 2023-12-31
Project acronym AGALT
Project Asymptotic Geometric Analysis and Learning Theory
Researcher (PI) Shahar Mendelson
Host Institution (HI) TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Call Details Starting Grant (StG), PE1, ERC-2007-StG
Summary In a typical learning problem one tries to approximate an unknown function by a function from a given class using random data, sampled according to an unknown measure. In this project we will be interested in parameters that govern the complexity of a learning problem. It turns out that this complexity is determined by the geometry of certain sets in high dimension that are connected to the given class (random coordinate projections of the class). Thus, one has to understand the structure of these sets as a function of the dimension - which is given by the cardinality of the random sample. The resulting analysis leads to many theoretical questions in Asymptotic Geometric Analysis, Probability (most notably, Empirical Processes Theory) and Combinatorics, which are of independent interest beyond the application to Learning Theory. Our main goal is to describe the role of various complexity parameters involved in a learning problem, to analyze the connections between them and to investigate the way they determine the geometry of the relevant high dimensional sets. Some of the questions we intend to tackle are well known open problems and making progress towards their solution will have a significant theoretical impact. Moreover, this project should lead to a more complete theory of learning and is likely to have some practical impact, for example, in the design of more efficient learning algorithms.
Summary
In a typical learning problem one tries to approximate an unknown function by a function from a given class using random data, sampled according to an unknown measure. In this project we will be interested in parameters that govern the complexity of a learning problem. It turns out that this complexity is determined by the geometry of certain sets in high dimension that are connected to the given class (random coordinate projections of the class). Thus, one has to understand the structure of these sets as a function of the dimension - which is given by the cardinality of the random sample. The resulting analysis leads to many theoretical questions in Asymptotic Geometric Analysis, Probability (most notably, Empirical Processes Theory) and Combinatorics, which are of independent interest beyond the application to Learning Theory. Our main goal is to describe the role of various complexity parameters involved in a learning problem, to analyze the connections between them and to investigate the way they determine the geometry of the relevant high dimensional sets. Some of the questions we intend to tackle are well known open problems and making progress towards their solution will have a significant theoretical impact. Moreover, this project should lead to a more complete theory of learning and is likely to have some practical impact, for example, in the design of more efficient learning algorithms.
Max ERC Funding
750 000 €
Duration
Start date: 2009-03-01, End date: 2014-02-28
Project acronym ANOPTSETCON
Project Analysis of optimal sets and optimal constants: old questions and new results
Researcher (PI) Aldo Pratelli
Host Institution (HI) FRIEDRICH-ALEXANDER-UNIVERSITAET ERLANGEN NUERNBERG
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary The analysis of geometric and functional inequalities naturally leads to consider the extremal cases, thus
looking for optimal sets, or optimal functions, or optimal constants. The most classical examples are the (different versions of the) isoperimetric inequality and the Sobolev-like inequalities. Much is known about equality cases and best constants, but there are still many questions which seem quite natural but yet have no answer. For instance, it is not known, even in the 2-dimensional space, the answer of a question by Brezis: which set,
among those with a given volume, has the biggest Sobolev-Poincaré constant for p=1? This is a very natural problem, and it appears reasonable that the optimal set should be the ball, but this has never been proved. The interest in problems like this relies not only in the extreme simplicity of the questions and in their classical flavour, but also in the new ideas and techniques which are needed to provide the answers.
The main techniques that we aim to use are fine arguments of symmetrization, geometric constructions and tools from mass transportation (which is well known to be deeply connected with functional inequalities). These are the basic tools that we already used to reach, in last years, many results in a specific direction, namely the search of sharp quantitative inequalities. Our first result, together with Fusco and Maggi, showed what follows. Everybody knows that the set which minimizes the perimeter with given volume is the ball.
But is it true that a set which almost minimizes the perimeter must be close to a ball? The question had been posed in the 1920's and many partial result appeared in the years. In our paper (Ann. of Math., 2007) we proved the sharp result. Many other results of this kind were obtained in last two years.
Summary
The analysis of geometric and functional inequalities naturally leads to consider the extremal cases, thus
looking for optimal sets, or optimal functions, or optimal constants. The most classical examples are the (different versions of the) isoperimetric inequality and the Sobolev-like inequalities. Much is known about equality cases and best constants, but there are still many questions which seem quite natural but yet have no answer. For instance, it is not known, even in the 2-dimensional space, the answer of a question by Brezis: which set,
among those with a given volume, has the biggest Sobolev-Poincaré constant for p=1? This is a very natural problem, and it appears reasonable that the optimal set should be the ball, but this has never been proved. The interest in problems like this relies not only in the extreme simplicity of the questions and in their classical flavour, but also in the new ideas and techniques which are needed to provide the answers.
The main techniques that we aim to use are fine arguments of symmetrization, geometric constructions and tools from mass transportation (which is well known to be deeply connected with functional inequalities). These are the basic tools that we already used to reach, in last years, many results in a specific direction, namely the search of sharp quantitative inequalities. Our first result, together with Fusco and Maggi, showed what follows. Everybody knows that the set which minimizes the perimeter with given volume is the ball.
But is it true that a set which almost minimizes the perimeter must be close to a ball? The question had been posed in the 1920's and many partial result appeared in the years. In our paper (Ann. of Math., 2007) we proved the sharp result. Many other results of this kind were obtained in last two years.
Max ERC Funding
540 000 €
Duration
Start date: 2010-08-01, End date: 2015-07-31
Project acronym ANTHOS
Project Analytic Number Theory: Higher Order Structures
Researcher (PI) Valentin Blomer
Host Institution (HI) GEORG-AUGUST-UNIVERSITAT GOTTINGENSTIFTUNG OFFENTLICHEN RECHTS
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary This is a proposal for research at the interface of analytic number theory, automorphic forms and algebraic geometry. Motivated by fundamental conjectures in number theory, classical problems will be investigated in higher order situations: general number fields, automorphic forms on higher rank groups, the arithmetic of algebraic varieties of higher degree. In particular, I want to focus on
- computation of moments of L-function of degree 3 and higher with applications to subconvexity and/or non-vanishing, as well as subconvexity for multiple L-functions;
- bounds for sup-norms of cusp forms on various spaces and equidistribution of Hecke correspondences;
- automorphic forms on higher rank groups and general number fields, in particular new bounds towards the Ramanujan conjecture;
- a proof of Manin's conjecture for a certain class of singular algebraic varieties.
The underlying methods are closely related; for example, rational points on algebraic varieties
will be counted by a multiple L-series technique.
Summary
This is a proposal for research at the interface of analytic number theory, automorphic forms and algebraic geometry. Motivated by fundamental conjectures in number theory, classical problems will be investigated in higher order situations: general number fields, automorphic forms on higher rank groups, the arithmetic of algebraic varieties of higher degree. In particular, I want to focus on
- computation of moments of L-function of degree 3 and higher with applications to subconvexity and/or non-vanishing, as well as subconvexity for multiple L-functions;
- bounds for sup-norms of cusp forms on various spaces and equidistribution of Hecke correspondences;
- automorphic forms on higher rank groups and general number fields, in particular new bounds towards the Ramanujan conjecture;
- a proof of Manin's conjecture for a certain class of singular algebraic varieties.
The underlying methods are closely related; for example, rational points on algebraic varieties
will be counted by a multiple L-series technique.
Max ERC Funding
1 004 000 €
Duration
Start date: 2010-10-01, End date: 2015-09-30
Project acronym AQSER
Project Automorphic q-series and their application
Researcher (PI) Kathrin Bringmann
Host Institution (HI) UNIVERSITAET ZU KOELN
Call Details Starting Grant (StG), PE1, ERC-2013-StG
Summary This proposal aims to unravel mysteries at the frontier of number theory and other areas of mathematics and physics. The main focus will be to understand and exploit “modularity” of q-hypergeometric series. “Modular forms are functions on the complex plane that are inordinately symmetric.” (Mazur) The motivation comes from the wide-reaching applications of modularity in combinatorics, percolation, Lie theory, and physics (black holes).
The interplay between automorphic forms, q-series, and other areas of mathematics and physics is often two-sided. On the one hand, the other areas provide interesting examples of automorphic objects and predict their behavior. Sometimes these even motivate new classes of automorphic objects which have not been previously studied. On the other hand, knowing that certain generating functions are modular gives one access to deep theoretical tools to prove results in other areas. “Mathematics is a language, and we need that language to understand the physics of our universe.”(Ooguri) Understanding this interplay has attracted attention of researchers from a variety of areas. However, proofs of modularity of q-hypergeometric series currently fall far short of a comprehensive theory to describe the interplay between them and automorphic forms. A recent conjecture of W. Nahm relates the modularity of such series to K-theory. In this proposal I aim to fill this gap and provide a better understanding of this interplay by building a general structural framework enveloping these q-series. For this I will employ new kinds of automorphic objects and embed the functions of interest into bigger families
A successful outcome of the proposed research will open further horizons and also answer open questions, even those in other areas which were not addressed in this proposal; for example the new theory could be applied to better understand Donaldson invariants.
Summary
This proposal aims to unravel mysteries at the frontier of number theory and other areas of mathematics and physics. The main focus will be to understand and exploit “modularity” of q-hypergeometric series. “Modular forms are functions on the complex plane that are inordinately symmetric.” (Mazur) The motivation comes from the wide-reaching applications of modularity in combinatorics, percolation, Lie theory, and physics (black holes).
The interplay between automorphic forms, q-series, and other areas of mathematics and physics is often two-sided. On the one hand, the other areas provide interesting examples of automorphic objects and predict their behavior. Sometimes these even motivate new classes of automorphic objects which have not been previously studied. On the other hand, knowing that certain generating functions are modular gives one access to deep theoretical tools to prove results in other areas. “Mathematics is a language, and we need that language to understand the physics of our universe.”(Ooguri) Understanding this interplay has attracted attention of researchers from a variety of areas. However, proofs of modularity of q-hypergeometric series currently fall far short of a comprehensive theory to describe the interplay between them and automorphic forms. A recent conjecture of W. Nahm relates the modularity of such series to K-theory. In this proposal I aim to fill this gap and provide a better understanding of this interplay by building a general structural framework enveloping these q-series. For this I will employ new kinds of automorphic objects and embed the functions of interest into bigger families
A successful outcome of the proposed research will open further horizons and also answer open questions, even those in other areas which were not addressed in this proposal; for example the new theory could be applied to better understand Donaldson invariants.
Max ERC Funding
1 240 500 €
Duration
Start date: 2014-01-01, End date: 2019-04-30
Project acronym BeyondA1
Project Set theory beyond the first uncountable cardinal
Researcher (PI) Assaf Shmuel Rinot
Host Institution (HI) BAR ILAN UNIVERSITY
Call Details Starting Grant (StG), PE1, ERC-2018-STG
Summary We propose to establish a research group that will unveil the combinatorial nature of the second uncountable cardinal. This includes its Ramsey-theoretic, order-theoretic, graph-theoretic and topological features. Among others, we will be directly addressing fundamental problems due to Erdos, Rado, Galvin, and Shelah.
While some of these problems are old and well-known, an unexpected series of breakthroughs from the last three years suggest that now is a promising point in time to carry out such a project. Indeed, through a short period, four previously unattainable problems concerning the second uncountable cardinal were successfully tackled: Aspero on a club-guessing problem of Shelah, Krueger on the club-isomorphism problem for Aronszajn trees, Neeman on the isomorphism problem for dense sets of reals, and the PI on the Souslin problem. Each of these results was obtained through the development of a completely new technical framework, and these frameworks could now pave the way for the solution of some major open questions.
A goal of the highest risk in this project is the discovery of a consistent (possibly, parameterized) forcing axiom that will (preferably, simultaneously) provide structure theorems for stationary sets, linearly ordered sets, trees, graphs, and partition relations, as well as the refutation of various forms of club-guessing principles, all at the level of the second uncountable cardinal. In comparison, at the level of the first uncountable cardinal, a forcing axiom due to Foreman, Magidor and Shelah achieves exactly that.
To approach our goals, the proposed project is divided into four core areas: Uncountable trees, Ramsey theory on ordinals, Club-guessing principles, and Forcing Axioms. There is a rich bilateral interaction between any pair of the four different cores, but the proposed division will allow an efficient allocation of manpower, and will increase the chances of parallel success.
Summary
We propose to establish a research group that will unveil the combinatorial nature of the second uncountable cardinal. This includes its Ramsey-theoretic, order-theoretic, graph-theoretic and topological features. Among others, we will be directly addressing fundamental problems due to Erdos, Rado, Galvin, and Shelah.
While some of these problems are old and well-known, an unexpected series of breakthroughs from the last three years suggest that now is a promising point in time to carry out such a project. Indeed, through a short period, four previously unattainable problems concerning the second uncountable cardinal were successfully tackled: Aspero on a club-guessing problem of Shelah, Krueger on the club-isomorphism problem for Aronszajn trees, Neeman on the isomorphism problem for dense sets of reals, and the PI on the Souslin problem. Each of these results was obtained through the development of a completely new technical framework, and these frameworks could now pave the way for the solution of some major open questions.
A goal of the highest risk in this project is the discovery of a consistent (possibly, parameterized) forcing axiom that will (preferably, simultaneously) provide structure theorems for stationary sets, linearly ordered sets, trees, graphs, and partition relations, as well as the refutation of various forms of club-guessing principles, all at the level of the second uncountable cardinal. In comparison, at the level of the first uncountable cardinal, a forcing axiom due to Foreman, Magidor and Shelah achieves exactly that.
To approach our goals, the proposed project is divided into four core areas: Uncountable trees, Ramsey theory on ordinals, Club-guessing principles, and Forcing Axioms. There is a rich bilateral interaction between any pair of the four different cores, but the proposed division will allow an efficient allocation of manpower, and will increase the chances of parallel success.
Max ERC Funding
1 362 500 €
Duration
Start date: 2018-10-01, End date: 2023-09-30
Project acronym BIOSTRUCT
Project Multiscale mathematical modelling of dynamics of structure formation in cell systems
Researcher (PI) Anna Marciniak-Czochra
Host Institution (HI) RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG
Call Details Starting Grant (StG), PE1, ERC-2007-StG
Summary The aim of this transdisciplinary project is to develop and analyse multiscale mathematical models of pattern formation in multicellular systems controlled by the dynamics of intracellular signalling pathways and cell-to-cell communication and to develop new mathematical methods for the modelling of such complex processes. This aim will be achieved through a close collaboration with experimental groups and comprehensive analytical investigations of the mathematical problems arising in the modelling of these biological processes. The mathematical methods and techniques to be employed will be the analysis of systems of partial differential equations, asymptotic analysis, as well as methods of dynamical systems. These techniques will be used to formulate the models and to study the spatio-temporal behaviour of solutions, especially stability and dependence on characteristic scales, geometry, initial data and key parameters. Advanced numerical methods will be applied to simulate the models. This comprehensive methodology goes beyond the state-of-the-art, since usually the analyses are limited to a single aspect of model behaviour. Groundbreaking impacts envisioned are threefold: (i) The project will contribute to the understanding of mechanisms of structure formation in the developmental process, in the context of recently discovered signalling pathways. In addition, some of the factors and mechanisms playing a role in developmental processes, such as Wnt signalling, are implicated in carcinogenesis, for instance colon and lung cancer. (ii) Accurate quantitative and predictive mathematical models of cell proliferation and differentiation are important for the control of tumour growth and tissue egeneration; (iii) Qualitative analysis of multiscale mathematical models of biological phenomena generates challenging mathematical problems and, therefore, the project will lead to the development of new mathematical theories and tools.
Summary
The aim of this transdisciplinary project is to develop and analyse multiscale mathematical models of pattern formation in multicellular systems controlled by the dynamics of intracellular signalling pathways and cell-to-cell communication and to develop new mathematical methods for the modelling of such complex processes. This aim will be achieved through a close collaboration with experimental groups and comprehensive analytical investigations of the mathematical problems arising in the modelling of these biological processes. The mathematical methods and techniques to be employed will be the analysis of systems of partial differential equations, asymptotic analysis, as well as methods of dynamical systems. These techniques will be used to formulate the models and to study the spatio-temporal behaviour of solutions, especially stability and dependence on characteristic scales, geometry, initial data and key parameters. Advanced numerical methods will be applied to simulate the models. This comprehensive methodology goes beyond the state-of-the-art, since usually the analyses are limited to a single aspect of model behaviour. Groundbreaking impacts envisioned are threefold: (i) The project will contribute to the understanding of mechanisms of structure formation in the developmental process, in the context of recently discovered signalling pathways. In addition, some of the factors and mechanisms playing a role in developmental processes, such as Wnt signalling, are implicated in carcinogenesis, for instance colon and lung cancer. (ii) Accurate quantitative and predictive mathematical models of cell proliferation and differentiation are important for the control of tumour growth and tissue egeneration; (iii) Qualitative analysis of multiscale mathematical models of biological phenomena generates challenging mathematical problems and, therefore, the project will lead to the development of new mathematical theories and tools.
Max ERC Funding
750 000 €
Duration
Start date: 2008-09-01, End date: 2013-08-31
Project acronym Boom & Bust Cycles
Project Boom and Bust Cycles in Asset Prices: Real Implications and Monetary Policy Options
Researcher (PI) Klaus Adam
Host Institution (HI) UNIVERSITAET MANNHEIM
Call Details Starting Grant (StG), SH1, ERC-2011-StG_20101124
Summary I seek increasing our understanding of the origin of asset price booms and bust cycles and propose constructing structural dynamic equilibrium models that allow formalizing their interaction with the dynamics of consumption, hours worked, the current account, stock market trading activity, and monetary policy. For this purpose I propose developing macroeconomic models that relax the assumption of common knowledge of beliefs and preferences, incorporating instead subjective beliefs and learning about market behavior. These features allow for sustained deviations of asset prices from fundamentals in a setting where all agents behave individually rational.
The first research project derives the derivative price implications of asset price models with learning agents and determines the limits to arbitrage required so that learning models are consistent with the existence of only weak incentives for improving forecasts and beliefs. The second project introduces housing, collateral constraints and open economy features into existing asset pricing models under learning to explain a range of cross-sectional facts about the behavior of the current account that have been observed in the recent housing boom and bust cycle. The third project constructs quantitatively plausible macro asset pricing models that can explain the dynamics of consumption and hours worked jointly with the occurrence of asset price boom and busts cycles. The forth project develops a set of monetary policy models allowing to study the interaction between monetary policies, the real economy and asset prices, and determines how monetary policy should optimally react to asset price movements. The last project explains the aggregate trading patterns on stock exchanges over boom and bust cycles and improves our understanding of the forces supporting the large cross-sectional heterogeneity in return expectations revealed in survey data.
Summary
I seek increasing our understanding of the origin of asset price booms and bust cycles and propose constructing structural dynamic equilibrium models that allow formalizing their interaction with the dynamics of consumption, hours worked, the current account, stock market trading activity, and monetary policy. For this purpose I propose developing macroeconomic models that relax the assumption of common knowledge of beliefs and preferences, incorporating instead subjective beliefs and learning about market behavior. These features allow for sustained deviations of asset prices from fundamentals in a setting where all agents behave individually rational.
The first research project derives the derivative price implications of asset price models with learning agents and determines the limits to arbitrage required so that learning models are consistent with the existence of only weak incentives for improving forecasts and beliefs. The second project introduces housing, collateral constraints and open economy features into existing asset pricing models under learning to explain a range of cross-sectional facts about the behavior of the current account that have been observed in the recent housing boom and bust cycle. The third project constructs quantitatively plausible macro asset pricing models that can explain the dynamics of consumption and hours worked jointly with the occurrence of asset price boom and busts cycles. The forth project develops a set of monetary policy models allowing to study the interaction between monetary policies, the real economy and asset prices, and determines how monetary policy should optimally react to asset price movements. The last project explains the aggregate trading patterns on stock exchanges over boom and bust cycles and improves our understanding of the forces supporting the large cross-sectional heterogeneity in return expectations revealed in survey data.
Max ERC Funding
769 440 €
Duration
Start date: 2011-09-01, End date: 2017-04-30
Project acronym CASe
Project Combinatorics with an analytic structure
Researcher (PI) Karim ADIPRASITO
Host Institution (HI) THE HEBREW UNIVERSITY OF JERUSALEM
Call Details Starting Grant (StG), PE1, ERC-2016-STG
Summary "Combinatorics, and its interplay with geometry, has fascinated our ancestors as shown by early stone carvings in the Neolithic period. Modern combinatorics is motivated by the ubiquity of its structures in both pure and applied mathematics.
The work of Hochster and Stanley, who realized the relation of enumerative questions to commutative algebra and toric geometry made a vital contribution to the development of this subject. Their work was a central contribution to the classification of face numbers of simple polytopes, and the initial success lead to a wealth of research in which combinatorial problems were translated to algebra and geometry and then solved using deep results such as Saito's hard Lefschetz theorem. As a caveat, this also made branches of combinatorics reliant on algebra and geometry to provide new ideas.
In this proposal, I want to reverse this approach and extend our understanding of geometry and algebra guided by combinatorial methods. In this spirit I propose new combinatorial approaches to the interplay of curvature and topology, to isoperimetry, geometric analysis, and intersection theory, to name a few. In addition, while these subjects are interesting by themselves, they are also designed to advance classical topics, for example, the diameter of polyhedra (as in the Hirsch conjecture), arrangement theory (and the study of arrangement complements), Hodge theory (as in Grothendieck's standard conjectures), and realization problems of discrete objects (as in Connes embedding problem for type II factors).
This proposal is supported by the review of some already developed tools, such as relative Stanley--Reisner theory (which is equipped to deal with combinatorial isoperimetries), combinatorial Hodge theory (which extends the ``K\""ahler package'' to purely combinatorial settings), and discrete PDEs (which were used to construct counterexamples to old problems in discrete geometry)."
Summary
"Combinatorics, and its interplay with geometry, has fascinated our ancestors as shown by early stone carvings in the Neolithic period. Modern combinatorics is motivated by the ubiquity of its structures in both pure and applied mathematics.
The work of Hochster and Stanley, who realized the relation of enumerative questions to commutative algebra and toric geometry made a vital contribution to the development of this subject. Their work was a central contribution to the classification of face numbers of simple polytopes, and the initial success lead to a wealth of research in which combinatorial problems were translated to algebra and geometry and then solved using deep results such as Saito's hard Lefschetz theorem. As a caveat, this also made branches of combinatorics reliant on algebra and geometry to provide new ideas.
In this proposal, I want to reverse this approach and extend our understanding of geometry and algebra guided by combinatorial methods. In this spirit I propose new combinatorial approaches to the interplay of curvature and topology, to isoperimetry, geometric analysis, and intersection theory, to name a few. In addition, while these subjects are interesting by themselves, they are also designed to advance classical topics, for example, the diameter of polyhedra (as in the Hirsch conjecture), arrangement theory (and the study of arrangement complements), Hodge theory (as in Grothendieck's standard conjectures), and realization problems of discrete objects (as in Connes embedding problem for type II factors).
This proposal is supported by the review of some already developed tools, such as relative Stanley--Reisner theory (which is equipped to deal with combinatorial isoperimetries), combinatorial Hodge theory (which extends the ``K\""ahler package'' to purely combinatorial settings), and discrete PDEs (which were used to construct counterexamples to old problems in discrete geometry)."
Max ERC Funding
1 337 200 €
Duration
Start date: 2016-12-01, End date: 2021-11-30
Project acronym CIVICS
Project Criminality, Victimization and Social Interactions
Researcher (PI) Katrine Vellesen LOKEN
Host Institution (HI) NORGES HANDELSHOYSKOLE
Call Details Starting Grant (StG), SH1, ERC-2017-STG
Summary A large social science literature tries to describe and understand the causes and consequences of crime, usually focusing on individuals’ criminal activity in isolation. The ambitious aim of this research project is to establish a broader perspective of crime that takes into account the social context in which it takes place. The findings will inform policymakers on how to better use funds both for crime prevention and the rehabilitation of incarcerated criminals.
Criminal activity is often a group phenomenon, yet little is known about how criminal networks form and what can be done to break them up or prevent them from forming in the first place. Overlooking victims of crime and their relationships to criminals has led to an incomplete and distorted view of crime and its individual and social costs. While a better understanding of these social interactions is crucial for designing more effective anti-crime policy, existing research in criminology, sociology and economics has struggled to identify causal effects due to data limitations and difficult statistical identification issues.
This project will push the research frontier by combining register datasets that have never been merged before, and by using several state-of-the-art statistical methods to estimate causal effects related to criminal peer groups and their victims. More specifically, we aim to do the following:
-Use recent advances in network modelling to describe the structure and density of various criminal networks and study network dynamics following the arrest/incarceration or death of a central player in a network.
-Obtain a more accurate measure of the societal costs of crime, including actual measures for lost earnings and physical and mental health problems, following victims and their offenders both before and after a crime takes place.
-Conduct a randomized controlled trial within a prison system to better understand how current rehabilitation programs affect criminal and victim networks.
Summary
A large social science literature tries to describe and understand the causes and consequences of crime, usually focusing on individuals’ criminal activity in isolation. The ambitious aim of this research project is to establish a broader perspective of crime that takes into account the social context in which it takes place. The findings will inform policymakers on how to better use funds both for crime prevention and the rehabilitation of incarcerated criminals.
Criminal activity is often a group phenomenon, yet little is known about how criminal networks form and what can be done to break them up or prevent them from forming in the first place. Overlooking victims of crime and their relationships to criminals has led to an incomplete and distorted view of crime and its individual and social costs. While a better understanding of these social interactions is crucial for designing more effective anti-crime policy, existing research in criminology, sociology and economics has struggled to identify causal effects due to data limitations and difficult statistical identification issues.
This project will push the research frontier by combining register datasets that have never been merged before, and by using several state-of-the-art statistical methods to estimate causal effects related to criminal peer groups and their victims. More specifically, we aim to do the following:
-Use recent advances in network modelling to describe the structure and density of various criminal networks and study network dynamics following the arrest/incarceration or death of a central player in a network.
-Obtain a more accurate measure of the societal costs of crime, including actual measures for lost earnings and physical and mental health problems, following victims and their offenders both before and after a crime takes place.
-Conduct a randomized controlled trial within a prison system to better understand how current rehabilitation programs affect criminal and victim networks.
Max ERC Funding
1 187 046 €
Duration
Start date: 2018-03-01, End date: 2023-02-28
