Project acronym CNTM
Project Cryptography on Non-Trusted Machines
Researcher (PI) Stefan Dziembowski
Host Institution (HI) UNIWERSYTET WARSZAWSKI
Call Details Starting Grant (StG), PE5, ERC-2007-StG
Summary This project is about the design of cryptographic schemes that are secure even if implemented on not-secure devices. The motivation for this problem comes from an observation that most of the real-life attacks on cryptographic devices do not break their mathematical foundations, but exploit vulnerabilities of their implementations. This concerns both the cryptographic software executed on PCs (that can be attacked by viruses), and the implementations on hardware (that can be subject to the side-channel attacks). Traditionally fixing this problem was left to the practitioners, since it was a common belief that theory cannot be of any help here. However, new exciting results in cryptography suggest that this view was too pessimistic: there exist methods to design cryptographic protocols in such a way that they are secure even if the hardware on which they are executed cannot be fully trusted. The goal of this project is to investigate these methods further, unify them in a solid mathematical theory (many of them were developed independently), and propose new ideas in this area. The project will be mostly theoretical (although some practical experiments may be performed). Our main interest lies within the theory of private circuits, bounded-retrieval model, physically-observable cryptography, and human-assisted cryptography. We view these theories just as the departing points, since the area is very fresh and we expect to soon witness completely new ideas in this field.
Summary
This project is about the design of cryptographic schemes that are secure even if implemented on not-secure devices. The motivation for this problem comes from an observation that most of the real-life attacks on cryptographic devices do not break their mathematical foundations, but exploit vulnerabilities of their implementations. This concerns both the cryptographic software executed on PCs (that can be attacked by viruses), and the implementations on hardware (that can be subject to the side-channel attacks). Traditionally fixing this problem was left to the practitioners, since it was a common belief that theory cannot be of any help here. However, new exciting results in cryptography suggest that this view was too pessimistic: there exist methods to design cryptographic protocols in such a way that they are secure even if the hardware on which they are executed cannot be fully trusted. The goal of this project is to investigate these methods further, unify them in a solid mathematical theory (many of them were developed independently), and propose new ideas in this area. The project will be mostly theoretical (although some practical experiments may be performed). Our main interest lies within the theory of private circuits, bounded-retrieval model, physically-observable cryptography, and human-assisted cryptography. We view these theories just as the departing points, since the area is very fresh and we expect to soon witness completely new ideas in this field.
Max ERC Funding
872 550 €
Duration
Start date: 2008-11-01, End date: 2013-10-31
Project acronym EPIFISH
Project INNOVATIVE EPIGENETIC MARKERS FOR FISH DOMESTICATION
Researcher (PI) Jorge Manuel De Oliveira Fernandes
Host Institution (HI) NORD UNIVERSITET
Call Details Consolidator Grant (CoG), LS9, ERC-2015-CoG
Summary Aquaculture is the fastest growing food production sector in the world, since there is an increasing demand for fish protein to feed a growing global population, which cannot be met by fisheries. In order to ensure the sustainability of this sector it is critical to domesticate and selectively improve the major commercial fish species. To date, the genetic markers used in selective breeding of fish account only for a fraction of the observed phenotypic variation. EPIFISH is a scientifically innovative and timely project that will address fish domestication and selection from a new perspective using a multidisciplinary approach. The rapid pace of substantial phenotypic changes during adaptation to new environmental conditions in fish undergoing domestication raises the original hypothesis that epigenetic mechanisms are involved in this process. Thus, the overarching aim of EPIFISH is to ascertain the importance of epigenetics in fish domestication using the Nile tilapia (Oreochromis niloticus) as model species. Specific objectives are i) to determine how selection affects the miRNA transcriptome and the epigenetic landscape during domestication, ii) to perform a functional characterization of miRNA variants and epigenetic alleles associated with growth, and iii) to validate them as potential epigenetic markers for future selective breeding programmes. The identification of epigenetic markers will be a ground-breaking element of EPIFISH with major impact on aquaculture biotechnology, since they will enable the development and application of epigenomic selection as a new feature in future selective breeding programmes. Moreover, the project outcomes will provide novel mechanistic insights into the role of epigenetics in fish domestication, which will surely open new horizons for future frontier research in epigenetics, namely transgenerational inheritance and nutritional epigenetics.
Summary
Aquaculture is the fastest growing food production sector in the world, since there is an increasing demand for fish protein to feed a growing global population, which cannot be met by fisheries. In order to ensure the sustainability of this sector it is critical to domesticate and selectively improve the major commercial fish species. To date, the genetic markers used in selective breeding of fish account only for a fraction of the observed phenotypic variation. EPIFISH is a scientifically innovative and timely project that will address fish domestication and selection from a new perspective using a multidisciplinary approach. The rapid pace of substantial phenotypic changes during adaptation to new environmental conditions in fish undergoing domestication raises the original hypothesis that epigenetic mechanisms are involved in this process. Thus, the overarching aim of EPIFISH is to ascertain the importance of epigenetics in fish domestication using the Nile tilapia (Oreochromis niloticus) as model species. Specific objectives are i) to determine how selection affects the miRNA transcriptome and the epigenetic landscape during domestication, ii) to perform a functional characterization of miRNA variants and epigenetic alleles associated with growth, and iii) to validate them as potential epigenetic markers for future selective breeding programmes. The identification of epigenetic markers will be a ground-breaking element of EPIFISH with major impact on aquaculture biotechnology, since they will enable the development and application of epigenomic selection as a new feature in future selective breeding programmes. Moreover, the project outcomes will provide novel mechanistic insights into the role of epigenetics in fish domestication, which will surely open new horizons for future frontier research in epigenetics, namely transgenerational inheritance and nutritional epigenetics.
Max ERC Funding
1 996 189 €
Duration
Start date: 2016-07-01, End date: 2021-06-30
Project acronym FattyCyanos
Project Fatty acid incorporation and modification in cyanobacterial natural products
Researcher (PI) Pedro LEÃO
Host Institution (HI) CIIMAR - Centro Interdisciplinar de Investigação Marinha e Ambiental
Call Details Starting Grant (StG), PE5, ERC-2017-STG
Summary Known, but mostly novel natural products (NPs) are in high demand – these are used in drugs, cosmetics and agrochemicals and serve also as research tools to probe biological systems. NP structures inspire chemists to develop new syntheses, and NP biosynthetic enzymes add to the metabolic engineer’s toolbox. The advent of next generation DNA-sequencing has revealed a vastly rich pool of NP biosynthetic gene clusters (BGCs) among bacterial genomes, most of which with no corresponding NP. Hence, opportunities abound for the discovery of new chemistry and enzymology that has the potential to push the boundaries of chemical space and enzymatic reactivity. Still, we cannot reliably predict chemistry from BGCs with unusual organization or encoding unknown functionalities, and, for molecules of unorthodox architecture, it is difficult to anticipate how their BGCs are organized. It is the valuable, truly novel chemistry and biochemistry that lies on these unexplored connections, that we aim to reveal with this proposal. To achieve it, we will work with a chemically-talented group of organisms – cyanobacteria, and with a specific structural class – fatty acids (FAs) – that is metabolized in a quite peculiar fashion by these organisms, paving the way for NP and enzyme discovery. On one hand, we will exploit the unique FA metabolism of cyanobacteria to develop a feeding strategy that will quickly reveal unprecedented FA-incorporating NPs. On the other, we will scrutinize the intriguing biosynthesis of three unique classes of metabolites that we have isolated recently and that incorporate and modify FA-moieties. We will find the BGCs for these compounds and dissect the functionality involved in such puzzling modifications to uncover important underlying enzymatic chemistry. This proposal is a blend of discovery- and hypothesis-driven research at the NP chemistry/biosynthesis interface that draws on the experience of the PI’s work on different aspects of cyanobacterial NPs.
Summary
Known, but mostly novel natural products (NPs) are in high demand – these are used in drugs, cosmetics and agrochemicals and serve also as research tools to probe biological systems. NP structures inspire chemists to develop new syntheses, and NP biosynthetic enzymes add to the metabolic engineer’s toolbox. The advent of next generation DNA-sequencing has revealed a vastly rich pool of NP biosynthetic gene clusters (BGCs) among bacterial genomes, most of which with no corresponding NP. Hence, opportunities abound for the discovery of new chemistry and enzymology that has the potential to push the boundaries of chemical space and enzymatic reactivity. Still, we cannot reliably predict chemistry from BGCs with unusual organization or encoding unknown functionalities, and, for molecules of unorthodox architecture, it is difficult to anticipate how their BGCs are organized. It is the valuable, truly novel chemistry and biochemistry that lies on these unexplored connections, that we aim to reveal with this proposal. To achieve it, we will work with a chemically-talented group of organisms – cyanobacteria, and with a specific structural class – fatty acids (FAs) – that is metabolized in a quite peculiar fashion by these organisms, paving the way for NP and enzyme discovery. On one hand, we will exploit the unique FA metabolism of cyanobacteria to develop a feeding strategy that will quickly reveal unprecedented FA-incorporating NPs. On the other, we will scrutinize the intriguing biosynthesis of three unique classes of metabolites that we have isolated recently and that incorporate and modify FA-moieties. We will find the BGCs for these compounds and dissect the functionality involved in such puzzling modifications to uncover important underlying enzymatic chemistry. This proposal is a blend of discovery- and hypothesis-driven research at the NP chemistry/biosynthesis interface that draws on the experience of the PI’s work on different aspects of cyanobacterial NPs.
Max ERC Funding
1 462 938 €
Duration
Start date: 2018-01-01, End date: 2022-12-31
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 FUNDMS
Project Functionalisation of Diluted Magnetic Semiconductors
Researcher (PI) Tomasz Dietl
Host Institution (HI) INSTYTUT FIZYKI POLSKIEJ AKADEMII NAUK
Call Details Advanced Grant (AdG), PE3, ERC-2008-AdG
Summary Low-temperature studies of transition metal doped III-V and II-VI compounds carried out over the last decade have demonstrated the unprecedented opportunity offered by these systems for exploring physical phenomena and device concepts in previously unavailable combinations of quantum structures and ferromagnetism in semiconductors. The work proposed here aims at combining and at advancing epitaxial methods, spatially-resolved nano-characterisation tools, and theoretical modelling in order to understand the intricate interplay between carrier localisation, magnetism, and magnetic ion distribution in DMS, and to develop functional DMS structures. To accomplish these goals we will take advantage of two recent breakthroughs in materials engineering. First, the attainment of high-k oxides makes now possible to generate interfacial hole densities up to 10^21 cm-3. We will exploit gated thin layers of DMS phosphides, nitrides, and oxides, in which hole delocalization and thus high temperature ferromagnetism is to be expected under gate bias. Furthermore we will systematically investigate how the Curie temperature of (Ga,Mn)As can be risen above 180 K. Second, the progress in nanoscale chemical analysis has allowed demonstrating that high temperature ferromagnetism of semiconductors results from nanoscale crystallographic or chemical phase separations into regions containing a large concentration of the magnetic constituent. We will elaborate experimentally and theoretically epitaxy and co-doping protocols for controlling the self-organised growth of magnetic nanostructures, utilizing broadly synchrotron radiation and nanoscopic characterisation tools. The established methods will allow us to obtain on demand either magnetic nano-dots or magnetic nano-columns embedded in a semiconductor host, for which we predict, and will demonstrate, ground-breaking functionalities. We will also assess reports on the possibility of high-temperature ferromagnetism without magnetic ions.
Summary
Low-temperature studies of transition metal doped III-V and II-VI compounds carried out over the last decade have demonstrated the unprecedented opportunity offered by these systems for exploring physical phenomena and device concepts in previously unavailable combinations of quantum structures and ferromagnetism in semiconductors. The work proposed here aims at combining and at advancing epitaxial methods, spatially-resolved nano-characterisation tools, and theoretical modelling in order to understand the intricate interplay between carrier localisation, magnetism, and magnetic ion distribution in DMS, and to develop functional DMS structures. To accomplish these goals we will take advantage of two recent breakthroughs in materials engineering. First, the attainment of high-k oxides makes now possible to generate interfacial hole densities up to 10^21 cm-3. We will exploit gated thin layers of DMS phosphides, nitrides, and oxides, in which hole delocalization and thus high temperature ferromagnetism is to be expected under gate bias. Furthermore we will systematically investigate how the Curie temperature of (Ga,Mn)As can be risen above 180 K. Second, the progress in nanoscale chemical analysis has allowed demonstrating that high temperature ferromagnetism of semiconductors results from nanoscale crystallographic or chemical phase separations into regions containing a large concentration of the magnetic constituent. We will elaborate experimentally and theoretically epitaxy and co-doping protocols for controlling the self-organised growth of magnetic nanostructures, utilizing broadly synchrotron radiation and nanoscopic characterisation tools. The established methods will allow us to obtain on demand either magnetic nano-dots or magnetic nano-columns embedded in a semiconductor host, for which we predict, and will demonstrate, ground-breaking functionalities. We will also assess reports on the possibility of high-temperature ferromagnetism without magnetic ions.
Max ERC Funding
2 440 000 €
Duration
Start date: 2009-01-01, End date: 2013-12-31
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 INSULATRONICS
Project Controlling Electric Signals with Insulating Antiferromagnets and Insulating Ferromagnets
Researcher (PI) Arne Brataas
Host Institution (HI) NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET NTNU
Call Details Advanced Grant (AdG), PE3, ERC-2014-ADG
Summary The proposal aims to facilitate a revolution of information and communication technologies by controlling electric signals with antiferromagnetic insulators and ferromagnetic insulators. We recently discovered that antiferromagnets can be active components in spintronics devices despite their lack of a macroscopic magnetic moment, and even when they are insulating.
Conventional electronics- and spintronics-based logic and memory devices, interconnects, and microwave oscillators are based on (spin-polarized) charge transport, which inherently dissipates power due to ohmic losses. The research proposed seeks to determine the extents to which “Insulatronics” has the potential to control the electric and thermal signal generation, transmission, and detection in more power-efficient ways.
Insulatronics is profoundly different because there are no moving charges involved so the power reduction is significant. We hope to establish the extents to which spin-waves and coherent magnons in antiferromagnetic insulators and ferromagnetic insulators can be strongly coupled to electric and thermal currents in adjacent conductors and utilize this coupling to control electric signals. The coupling will be facilitated by spin-transfer torques and spin-pumping – a technique we pioneered – as well as spin-orbit torques and its reciprocal process of charge-pumping.
The core of this project focuses on the theoretical and fundamental challenges facing Insulatronics. Beyond the duration of the project, if we are successful, the use of spin signals in insulators with extremely low power dissipation may enable superior low-power technologies such as oscillators, logic devices, interconnects, non-volatile random access memories, and perhaps even quantum information processing.
Summary
The proposal aims to facilitate a revolution of information and communication technologies by controlling electric signals with antiferromagnetic insulators and ferromagnetic insulators. We recently discovered that antiferromagnets can be active components in spintronics devices despite their lack of a macroscopic magnetic moment, and even when they are insulating.
Conventional electronics- and spintronics-based logic and memory devices, interconnects, and microwave oscillators are based on (spin-polarized) charge transport, which inherently dissipates power due to ohmic losses. The research proposed seeks to determine the extents to which “Insulatronics” has the potential to control the electric and thermal signal generation, transmission, and detection in more power-efficient ways.
Insulatronics is profoundly different because there are no moving charges involved so the power reduction is significant. We hope to establish the extents to which spin-waves and coherent magnons in antiferromagnetic insulators and ferromagnetic insulators can be strongly coupled to electric and thermal currents in adjacent conductors and utilize this coupling to control electric signals. The coupling will be facilitated by spin-transfer torques and spin-pumping – a technique we pioneered – as well as spin-orbit torques and its reciprocal process of charge-pumping.
The core of this project focuses on the theoretical and fundamental challenges facing Insulatronics. Beyond the duration of the project, if we are successful, the use of spin signals in insulators with extremely low power dissipation may enable superior low-power technologies such as oscillators, logic devices, interconnects, non-volatile random access memories, and perhaps even quantum information processing.
Max ERC Funding
2 140 503 €
Duration
Start date: 2015-12-01, End date: 2020-11-30
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
