Project acronym 3D-E
Project 3D Engineered Environments for Regenerative Medicine
Researcher (PI) Ruth Elizabeth Cameron
Host Institution (HI) THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE
Call Details Advanced Grant (AdG), PE8, ERC-2012-ADG_20120216
Summary "This proposal develops a unified, underpinning technology to create novel, complex and biomimetic 3D environments for the control of tissue growth. As director of Cambridge Centre for Medical Materials, I have recently been approached by medical colleagues to help to solve important problems in the separate therapeutic areas of breast cancer, cardiac disease and blood disorders. In each case, the solution lies in complex 3D engineered environments for cell culture. These colleagues make it clear that existing 3D scaffolds fail to provide the required complex orientational and spatial anisotropy, and are limited in their ability to impart appropriate biochemical and mechanical cues.
I have a strong track record in this area. A particular success has been the use of a freeze drying technology to make collagen based porous implants for the cartilage-bone interface in the knee, which has now been commercialised. The novelty of this proposal lies in the broadening of the established scientific base of this technology to enable biomacromolecular structures with:
(A) controlled and complex pore orientation to mimic many normal multi-oriented tissue structures
(B) compositional and positional control to match varying local biochemical environments,
(C) the attachment of novel peptides designed to control cell behaviour, and
(D) mechanical control at both a local and macroscopic level to provide mechanical cues for cells.
These will be complemented by the development of
(E) robust characterisation methodologies for the structures created.
These advances will then be employed in each of the medical areas above.
This approach is highly interdisciplinary. Existing working relationships with experts in each medical field will guarantee expertise and licensed facilities in the required biological disciplines. Funds for this proposal would therefore establish a rich hub of mutually beneficial research and opportunities for cross-disciplinary sharing of expertise."
Summary
"This proposal develops a unified, underpinning technology to create novel, complex and biomimetic 3D environments for the control of tissue growth. As director of Cambridge Centre for Medical Materials, I have recently been approached by medical colleagues to help to solve important problems in the separate therapeutic areas of breast cancer, cardiac disease and blood disorders. In each case, the solution lies in complex 3D engineered environments for cell culture. These colleagues make it clear that existing 3D scaffolds fail to provide the required complex orientational and spatial anisotropy, and are limited in their ability to impart appropriate biochemical and mechanical cues.
I have a strong track record in this area. A particular success has been the use of a freeze drying technology to make collagen based porous implants for the cartilage-bone interface in the knee, which has now been commercialised. The novelty of this proposal lies in the broadening of the established scientific base of this technology to enable biomacromolecular structures with:
(A) controlled and complex pore orientation to mimic many normal multi-oriented tissue structures
(B) compositional and positional control to match varying local biochemical environments,
(C) the attachment of novel peptides designed to control cell behaviour, and
(D) mechanical control at both a local and macroscopic level to provide mechanical cues for cells.
These will be complemented by the development of
(E) robust characterisation methodologies for the structures created.
These advances will then be employed in each of the medical areas above.
This approach is highly interdisciplinary. Existing working relationships with experts in each medical field will guarantee expertise and licensed facilities in the required biological disciplines. Funds for this proposal would therefore establish a rich hub of mutually beneficial research and opportunities for cross-disciplinary sharing of expertise."
Max ERC Funding
2 486 267 €
Duration
Start date: 2013-04-01, End date: 2018-03-31
Project acronym ABINITIODGA
Project Ab initio Dynamical Vertex Approximation
Researcher (PI) Karsten Held
Host Institution (HI) TECHNISCHE UNIVERSITAET WIEN
Call Details Starting Grant (StG), PE3, ERC-2012-StG_20111012
Summary Some of the most fascinating physical phenomena are experimentally observed in strongly correlated electron systems and, on the theoretical side, only poorly understood hitherto. The aim of the ERC project AbinitioDGA is the development, implementation and application of a new, 21th century method for the ab initio calculation of materials with such strong electronic correlations. AbinitioDGA includes strong electronic correlations on all time and length scales and hence is a big step beyond the state-of-the-art methods, such as the local density approximation, dynamical mean field theory, and the GW approach (Green function G times screened interaction W). It has the potential for an extraordinary high impact not only in the field of computational materials science but also for a better understanding of quantum critical heavy fermion systems, high-temperature superconductors, and transport through nano- and heterostructures. These four physical problems and related materials will be studied within the ERC project, besides the methodological development.
On the technical side, AbinitioDGA realizes Hedin's idea to include vertex corrections beyond the GW approximation. All vertex corrections which can be traced back to a fully irreducible local vertex and the bare non-local Coulomb interaction are included. This way, AbinitioDGA does not only contain the GW physics of screened exchange and the strong local correlations of dynamical mean field theory but also non-local correlations beyond on all length scales. Through the latter, AbinitioDGA can prospectively describe phenomena such as quantum criticality, spin-fluctuation mediated superconductivity, and weak localization corrections to the conductivity. Nonetheless, the computational effort is still manageable even for realistic materials calculations, making the considerable effort to implement AbinitioDGA worthwhile.
Summary
Some of the most fascinating physical phenomena are experimentally observed in strongly correlated electron systems and, on the theoretical side, only poorly understood hitherto. The aim of the ERC project AbinitioDGA is the development, implementation and application of a new, 21th century method for the ab initio calculation of materials with such strong electronic correlations. AbinitioDGA includes strong electronic correlations on all time and length scales and hence is a big step beyond the state-of-the-art methods, such as the local density approximation, dynamical mean field theory, and the GW approach (Green function G times screened interaction W). It has the potential for an extraordinary high impact not only in the field of computational materials science but also for a better understanding of quantum critical heavy fermion systems, high-temperature superconductors, and transport through nano- and heterostructures. These four physical problems and related materials will be studied within the ERC project, besides the methodological development.
On the technical side, AbinitioDGA realizes Hedin's idea to include vertex corrections beyond the GW approximation. All vertex corrections which can be traced back to a fully irreducible local vertex and the bare non-local Coulomb interaction are included. This way, AbinitioDGA does not only contain the GW physics of screened exchange and the strong local correlations of dynamical mean field theory but also non-local correlations beyond on all length scales. Through the latter, AbinitioDGA can prospectively describe phenomena such as quantum criticality, spin-fluctuation mediated superconductivity, and weak localization corrections to the conductivity. Nonetheless, the computational effort is still manageable even for realistic materials calculations, making the considerable effort to implement AbinitioDGA worthwhile.
Max ERC Funding
1 491 090 €
Duration
Start date: 2013-01-01, End date: 2018-07-31
Project acronym ACOULOMODE
Project Advanced coupling of low order combustor simulations with thermoacoustic modelling and controller design
Researcher (PI) Aimee Morgans
Host Institution (HI) IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE
Call Details Starting Grant (StG), PE8, ERC-2012-StG_20111012
Summary "Combustion is essential to the world’s energy generation and transport needs, and will remain so for the foreseeable future. Mitigating its impact on the climate and human health, by reducing its associated emissions, is thus a priority. One significant challenge for gas-turbine combustion is combustion instability, which is currently inhibiting reductions in NOx emissions (these damage human health via a deterioration in air quality). Combustion instability is caused by a two-way coupling between unsteady combustion and acoustic waves - the large pressure oscillations that result can cause substantial mechanical damage. Currently, the lack of fast, accurate modelling tools for combustion instability, and the lack of reliable ways of suppressing it are severely hindering reductions in NOx emissions.
This proposal aims to make step improvements in both fast, accurate modelling of combustion instability, and in developing reliable active control strategies for its suppression. It will achieve this by coupling low order combustor models (these are fast, simplified models for simulating combustion instability) with advances in analytical modelling, CFD simulation, reduced order modelling and control theory tools. In particular:
* important advances in accurately incorporating the effect of entropy waves (temperature variations resulting from unsteady combustion) and non-linear flame models will be made;
* new active control strategies for achieving reliable suppression of combustion instability, including from within limit cycle oscillations, will be developed;
* an open-source low order combustor modelling tool will be developed and widely disseminated, opening access to researchers worldwide and improving communications between the fields of thermoacoustics and control theory.
Thus the proposal aims to use analytical and computational methods to contribute to achieving low NOx gas-turbine combustion, without the penalty of damaging combustion instability."
Summary
"Combustion is essential to the world’s energy generation and transport needs, and will remain so for the foreseeable future. Mitigating its impact on the climate and human health, by reducing its associated emissions, is thus a priority. One significant challenge for gas-turbine combustion is combustion instability, which is currently inhibiting reductions in NOx emissions (these damage human health via a deterioration in air quality). Combustion instability is caused by a two-way coupling between unsteady combustion and acoustic waves - the large pressure oscillations that result can cause substantial mechanical damage. Currently, the lack of fast, accurate modelling tools for combustion instability, and the lack of reliable ways of suppressing it are severely hindering reductions in NOx emissions.
This proposal aims to make step improvements in both fast, accurate modelling of combustion instability, and in developing reliable active control strategies for its suppression. It will achieve this by coupling low order combustor models (these are fast, simplified models for simulating combustion instability) with advances in analytical modelling, CFD simulation, reduced order modelling and control theory tools. In particular:
* important advances in accurately incorporating the effect of entropy waves (temperature variations resulting from unsteady combustion) and non-linear flame models will be made;
* new active control strategies for achieving reliable suppression of combustion instability, including from within limit cycle oscillations, will be developed;
* an open-source low order combustor modelling tool will be developed and widely disseminated, opening access to researchers worldwide and improving communications between the fields of thermoacoustics and control theory.
Thus the proposal aims to use analytical and computational methods to contribute to achieving low NOx gas-turbine combustion, without the penalty of damaging combustion instability."
Max ERC Funding
1 489 309 €
Duration
Start date: 2013-01-01, End date: 2017-12-31
Project acronym AF and MSOGR
Project Automorphic Forms and Moduli Spaces of Galois Representations
Researcher (PI) Toby Gee
Host Institution (HI) IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE
Call Details Starting Grant (StG), PE1, ERC-2012-StG_20111012
Summary I propose to establish a research group to develop completely new tools in order to solve three important problems on the relationships between automorphic forms and Galois representations, which lie at the heart of the Langlands program. The first is to prove Serre’s conjecture for real quadratic fields. I will use automorphic induction to transfer the problem to U(4) over the rational numbers, where I will use automorphy lifting theorems and results on the weight part of Serre's conjecture that I established in my earlier work to reduce the problem to proving results in small weight and level. I will prove these base cases via integral p-adic Hodge theory and discriminant bounds.
The second is to develop a geometric theory of moduli spaces of mod p and p-adic Galois representations, and to use it to establish the Breuil–Mézard conjecture in arbitrary dimension, by reinterpreting the conjecture in geometric terms. This will transform the subject by building the first connections between the p-adic Langlands program and the geometric Langlands program, providing an entirely new world of techniques for number theorists. As a consequence of the Breuil-Mézard conjecture, I will be able to deduce far stronger automorphy lifting theorems (in arbitrary dimension) than those currently available.
The third is to completely determine the reduction mod p of certain two-dimensional crystalline representations, and as an application prove a strengthened version of the Gouvêa–Mazur conjecture. I will do this by means of explicit computations with the p-adic local Langlands correspondence for GL_2(Q_p), as well as by improving existing arguments which prove multiplicity one theorems via automorphy lifting theorems. This work will show that the existence of counterexamples to the Gouvêa-Mazur conjecture is due to a purely local phenomenon, and that when this local obstruction vanishes, far stronger conjectures of Buzzard on the slopes of the U_p operator hold.
Summary
I propose to establish a research group to develop completely new tools in order to solve three important problems on the relationships between automorphic forms and Galois representations, which lie at the heart of the Langlands program. The first is to prove Serre’s conjecture for real quadratic fields. I will use automorphic induction to transfer the problem to U(4) over the rational numbers, where I will use automorphy lifting theorems and results on the weight part of Serre's conjecture that I established in my earlier work to reduce the problem to proving results in small weight and level. I will prove these base cases via integral p-adic Hodge theory and discriminant bounds.
The second is to develop a geometric theory of moduli spaces of mod p and p-adic Galois representations, and to use it to establish the Breuil–Mézard conjecture in arbitrary dimension, by reinterpreting the conjecture in geometric terms. This will transform the subject by building the first connections between the p-adic Langlands program and the geometric Langlands program, providing an entirely new world of techniques for number theorists. As a consequence of the Breuil-Mézard conjecture, I will be able to deduce far stronger automorphy lifting theorems (in arbitrary dimension) than those currently available.
The third is to completely determine the reduction mod p of certain two-dimensional crystalline representations, and as an application prove a strengthened version of the Gouvêa–Mazur conjecture. I will do this by means of explicit computations with the p-adic local Langlands correspondence for GL_2(Q_p), as well as by improving existing arguments which prove multiplicity one theorems via automorphy lifting theorems. This work will show that the existence of counterexamples to the Gouvêa-Mazur conjecture is due to a purely local phenomenon, and that when this local obstruction vanishes, far stronger conjectures of Buzzard on the slopes of the U_p operator hold.
Max ERC Funding
1 131 339 €
Duration
Start date: 2012-10-01, End date: 2017-09-30
Project acronym ALGAME
Project Algorithms, Games, Mechanisms, and the Price of Anarchy
Researcher (PI) Elias Koutsoupias
Host Institution (HI) THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Call Details Advanced Grant (AdG), PE6, ERC-2012-ADG_20120216
Summary The objective of this proposal is to bring together a local team of young researchers who will work closely with international collaborators to advance the state of the art of Algorithmic Game Theory and open new venues of research at the interface of Computer Science, Game Theory, and Economics. The proposal consists mainly of three intertwined research strands: algorithmic mechanism design, price of anarchy, and online algorithms.
Specifically, we will attempt to resolve some outstanding open problems in algorithmic mechanism design: characterizing the incentive compatible mechanisms for important domains, such as the domain of combinatorial auctions, and resolving the approximation ratio of mechanisms for scheduling unrelated machines. More generally, we will study centralized and distributed algorithms whose inputs are controlled by selfish agents that are interested in the outcome of the computation. We will investigate new notions of mechanisms with strong truthfulness and limited susceptibility to externalities that can facilitate modular design of mechanisms of complex domains.
We will expand the current research on the price of anarchy to time-dependent games where the players can select not only how to act but also when to act. We also plan to resolve outstanding questions on the price of stability and to build a robust approach to these questions, similar to smooth analysis. For repeated games, we will investigate convergence of simple strategies (e.g., fictitious play), online fairness, and strategic considerations (e.g., metagames). More generally, our aim is to find a productive formulation of playing unknown games by drawing on the fields of online algorithms and machine learning.
Summary
The objective of this proposal is to bring together a local team of young researchers who will work closely with international collaborators to advance the state of the art of Algorithmic Game Theory and open new venues of research at the interface of Computer Science, Game Theory, and Economics. The proposal consists mainly of three intertwined research strands: algorithmic mechanism design, price of anarchy, and online algorithms.
Specifically, we will attempt to resolve some outstanding open problems in algorithmic mechanism design: characterizing the incentive compatible mechanisms for important domains, such as the domain of combinatorial auctions, and resolving the approximation ratio of mechanisms for scheduling unrelated machines. More generally, we will study centralized and distributed algorithms whose inputs are controlled by selfish agents that are interested in the outcome of the computation. We will investigate new notions of mechanisms with strong truthfulness and limited susceptibility to externalities that can facilitate modular design of mechanisms of complex domains.
We will expand the current research on the price of anarchy to time-dependent games where the players can select not only how to act but also when to act. We also plan to resolve outstanding questions on the price of stability and to build a robust approach to these questions, similar to smooth analysis. For repeated games, we will investigate convergence of simple strategies (e.g., fictitious play), online fairness, and strategic considerations (e.g., metagames). More generally, our aim is to find a productive formulation of playing unknown games by drawing on the fields of online algorithms and machine learning.
Max ERC Funding
2 461 000 €
Duration
Start date: 2013-04-01, End date: 2019-03-31
Project acronym ANGLE
Project Accelerated design and discovery of novel molecular materials via global lattice energy minimisation
Researcher (PI) Graeme Matthew Day
Host Institution (HI) UNIVERSITY OF SOUTHAMPTON
Call Details Starting Grant (StG), PE4, ERC-2012-StG_20111012
Summary The goal of crystal engineering is the design of functional crystalline materials in which the arrangement of basic structural building blocks imparts desired properties. The engineering of organic molecular crystals has, to date, relied largely on empirical rules governing the intermolecular association of functional groups in the solid state. However, many materials properties depend intricately on the complete crystal structure, i.e. the unit cell, space group and atomic positions, which cannot be predicted solely using such rules. Therefore, the development of computational methods for crystal structure prediction (CSP) from first principles has been a goal of computational chemistry that could significantly accelerate the design of new materials. It is only recently that the necessary advances in the modelling of intermolecular interactions and developments in algorithms for identifying all relevant crystal structures have come together to provide predictive methods that are becoming reliable and affordable on a timescale that could usefully complement an experimental research programme. The principle aim of the proposed work is to establish the use of state-of-the-art crystal structure prediction methods as a means of guiding the discovery and design of novel molecular materials.
This research proposal both continues the development of the computational methods for CSP and, by developing a computational framework for screening of potential molecules, develops the application of these methods for materials design. The areas on which we will focus are organic molecular semiconductors with high charge carrier mobilities and, building on our recently published results in Nature [1], the development of porous organic molecular materials. The project will both deliver novel materials, as well as improvements in the reliability of computational methods that will find widespread applications in materials chemistry.
[1] Nature 2011, 474, 367-371.
Summary
The goal of crystal engineering is the design of functional crystalline materials in which the arrangement of basic structural building blocks imparts desired properties. The engineering of organic molecular crystals has, to date, relied largely on empirical rules governing the intermolecular association of functional groups in the solid state. However, many materials properties depend intricately on the complete crystal structure, i.e. the unit cell, space group and atomic positions, which cannot be predicted solely using such rules. Therefore, the development of computational methods for crystal structure prediction (CSP) from first principles has been a goal of computational chemistry that could significantly accelerate the design of new materials. It is only recently that the necessary advances in the modelling of intermolecular interactions and developments in algorithms for identifying all relevant crystal structures have come together to provide predictive methods that are becoming reliable and affordable on a timescale that could usefully complement an experimental research programme. The principle aim of the proposed work is to establish the use of state-of-the-art crystal structure prediction methods as a means of guiding the discovery and design of novel molecular materials.
This research proposal both continues the development of the computational methods for CSP and, by developing a computational framework for screening of potential molecules, develops the application of these methods for materials design. The areas on which we will focus are organic molecular semiconductors with high charge carrier mobilities and, building on our recently published results in Nature [1], the development of porous organic molecular materials. The project will both deliver novel materials, as well as improvements in the reliability of computational methods that will find widespread applications in materials chemistry.
[1] Nature 2011, 474, 367-371.
Max ERC Funding
1 499 906 €
Duration
Start date: 2012-10-01, End date: 2017-09-30
Project acronym ANTINEUTRINONOVA
Project Probing Fundamental Physics with Antineutrinos at the NOvA Experiment
Researcher (PI) Jeffrey Hartnell
Host Institution (HI) THE UNIVERSITY OF SUSSEX
Call Details Starting Grant (StG), PE2, ERC-2012-StG_20111012
Summary "This proposal addresses major questions in particle physics that are at the forefront of experimental and theoretical physics research today. The results offered would have far-reaching implications in other fields such as cosmology and could help answer some of the big questions such as why the universe contains so much more matter than antimatter. The research objectives of this proposal are to (i) make world-leading tests of CPT symmetry and (ii) discover the neutrino mass hierarchy and search for indications of leptonic CP violation.
The NOvA long-baseline neutrino oscillation experiment will use a novel ""totally active scintillator design"" for the detector technology and will be exposed to the world's highest power neutrino beam. Building on the first direct observation of muon antineutrino disappearance (that was made by a group founded and led by the PI at the MINOS experiment), tests of CPT symmetry will be performed by looking for differences in the mass squared splittings and mixing angles between neutrinos and antineutrinos. The potential to discover the mass hierarchy is unique to NOvA on the timescale of this proposal due to the long 810 km baseline and the well measured beam of neutrinos and antineutrinos.
This proposal addresses several key challenges in a long-baseline neutrino oscillation experiment with the following tasks: (i) development of a new approach to event energy reconstruction that is expected to have widespread applicability for future neutrino experiments; (ii) undertaking a comprehensive calibration project, exploiting a novel technique developed by the PI, that will be essential to achieving the physics goals; (iii) development of a sophisticated statistical analyses.
The results promised in this proposal surpass the sensitivity to antineutrino oscillation parameters of current 1st generation experiments by at least an order of magnitude, offering wide scope for profound discoveries with implications across disciplines."
Summary
"This proposal addresses major questions in particle physics that are at the forefront of experimental and theoretical physics research today. The results offered would have far-reaching implications in other fields such as cosmology and could help answer some of the big questions such as why the universe contains so much more matter than antimatter. The research objectives of this proposal are to (i) make world-leading tests of CPT symmetry and (ii) discover the neutrino mass hierarchy and search for indications of leptonic CP violation.
The NOvA long-baseline neutrino oscillation experiment will use a novel ""totally active scintillator design"" for the detector technology and will be exposed to the world's highest power neutrino beam. Building on the first direct observation of muon antineutrino disappearance (that was made by a group founded and led by the PI at the MINOS experiment), tests of CPT symmetry will be performed by looking for differences in the mass squared splittings and mixing angles between neutrinos and antineutrinos. The potential to discover the mass hierarchy is unique to NOvA on the timescale of this proposal due to the long 810 km baseline and the well measured beam of neutrinos and antineutrinos.
This proposal addresses several key challenges in a long-baseline neutrino oscillation experiment with the following tasks: (i) development of a new approach to event energy reconstruction that is expected to have widespread applicability for future neutrino experiments; (ii) undertaking a comprehensive calibration project, exploiting a novel technique developed by the PI, that will be essential to achieving the physics goals; (iii) development of a sophisticated statistical analyses.
The results promised in this proposal surpass the sensitivity to antineutrino oscillation parameters of current 1st generation experiments by at least an order of magnitude, offering wide scope for profound discoveries with implications across disciplines."
Max ERC Funding
1 415 848 €
Duration
Start date: 2012-10-01, End date: 2018-09-30
Project acronym APGRAPH
Project Asymptotic Graph Properties
Researcher (PI) Deryk Osthus
Host Institution (HI) THE UNIVERSITY OF BIRMINGHAM
Call Details Starting Grant (StG), PE1, ERC-2012-StG_20111012
Summary Many parts of Graph Theory have witnessed a huge growth over the last years, partly because of their relation to Theoretical Computer Science and Statistical Physics. These connections arise because graphs can be used to model many diverse structures.
The focus of this proposal is on asymptotic results, i.e. the graphs under consideration are large. This often unveils patterns and connections which remain obscure when considering only small graphs.
It also allows for the use of powerful techniques such as probabilistic arguments, which have led to spectacular new developments. In particular, my aim is to make decisive progress on central problems in the following 4 areas:
(1) Factorizations: Factorizations of graphs can be viewed as partitions of the edges of a graph into simple regular structures. They have a rich history and arise in many different settings, such as edge-colouring problems, decomposition problems and in information theory. They also have applications to finding good tours for the famous Travelling salesman problem.
(2) Hamilton cycles: A Hamilton cycle is a cycle which contains all the vertices of the graph. One of the most fundamental problems in Graph Theory/Theoretical Computer Science is to find conditions which guarantee the existence of a Hamilton cycle in a graph.
(3) Embeddings of graphs: This is a natural (but difficult) continuation of the previous question where the aim is to embed more general structures than Hamilton cycles - there has been exciting progress here in recent years which has opened up new avenues.
(4) Resilience of graphs: In many cases, it is important to know whether a graph `strongly’ possesses some property, i.e. one cannot destroy the property by changing a few edges. The systematic study of this notion is a new and rapidly growing area.
I have developed new methods for deep and long-standing problems in these areas which will certainly lead to further applications elsewhere.
Summary
Many parts of Graph Theory have witnessed a huge growth over the last years, partly because of their relation to Theoretical Computer Science and Statistical Physics. These connections arise because graphs can be used to model many diverse structures.
The focus of this proposal is on asymptotic results, i.e. the graphs under consideration are large. This often unveils patterns and connections which remain obscure when considering only small graphs.
It also allows for the use of powerful techniques such as probabilistic arguments, which have led to spectacular new developments. In particular, my aim is to make decisive progress on central problems in the following 4 areas:
(1) Factorizations: Factorizations of graphs can be viewed as partitions of the edges of a graph into simple regular structures. They have a rich history and arise in many different settings, such as edge-colouring problems, decomposition problems and in information theory. They also have applications to finding good tours for the famous Travelling salesman problem.
(2) Hamilton cycles: A Hamilton cycle is a cycle which contains all the vertices of the graph. One of the most fundamental problems in Graph Theory/Theoretical Computer Science is to find conditions which guarantee the existence of a Hamilton cycle in a graph.
(3) Embeddings of graphs: This is a natural (but difficult) continuation of the previous question where the aim is to embed more general structures than Hamilton cycles - there has been exciting progress here in recent years which has opened up new avenues.
(4) Resilience of graphs: In many cases, it is important to know whether a graph `strongly’ possesses some property, i.e. one cannot destroy the property by changing a few edges. The systematic study of this notion is a new and rapidly growing area.
I have developed new methods for deep and long-standing problems in these areas which will certainly lead to further applications elsewhere.
Max ERC Funding
818 414 €
Duration
Start date: 2012-12-01, End date: 2018-11-30
Project acronym ARIPHYHIMO
Project Arithmetic and physics of Higgs moduli spaces
Researcher (PI) Tamas Hausel
Host Institution (HI) INSTITUTE OF SCIENCE AND TECHNOLOGYAUSTRIA
Call Details Advanced Grant (AdG), PE1, ERC-2012-ADG_20120216
Summary The proposal studies problems concerning the geometry and topology of moduli spaces of Higgs bundles on a Riemann surface motivated by parallel considerations in number theory and mathematical physics. In this way the proposal bridges various duality theories in string theory with the Langlands program in number theory.
The heart of the proposal is a circle of precise conjectures relating to the topology of the moduli space of Higgs bundles. The formulation and motivations of the conjectures make direct contact with the Langlands program in number theory, various duality conjectures in string theory, algebraic combinatorics, knot theory and low dimensional topology and representation theory of quivers, finite groups and algebras of Lie type and Cherednik algebras.
Summary
The proposal studies problems concerning the geometry and topology of moduli spaces of Higgs bundles on a Riemann surface motivated by parallel considerations in number theory and mathematical physics. In this way the proposal bridges various duality theories in string theory with the Langlands program in number theory.
The heart of the proposal is a circle of precise conjectures relating to the topology of the moduli space of Higgs bundles. The formulation and motivations of the conjectures make direct contact with the Langlands program in number theory, various duality conjectures in string theory, algebraic combinatorics, knot theory and low dimensional topology and representation theory of quivers, finite groups and algebras of Lie type and Cherednik algebras.
Max ERC Funding
1 304 945 €
Duration
Start date: 2013-04-01, End date: 2018-08-31
Project acronym ARTIMATTER
Project "Lego-Style Materials, Structures and Devices Assembled on Demand from Isolated Atomic Planes"
Researcher (PI) Andre Geim
Host Institution (HI) THE UNIVERSITY OF MANCHESTER
Call Details Advanced Grant (AdG), PE3, ERC-2012-ADG_20120216
Summary "Following the advent of graphene with its wide range of unique properties, several other one-atom-thick crystals have been isolated and their preliminary studies have been undertaken. They range from semiconducting monolayers of MoS2 and NbSe2, which similar to graphene exhibit the electric field effect and relatively high electronic quality, to wide-gap insulators such as boron-nitride monolayers that can serve as atomically-thin tunnel barriers.
This library of two-dimensional crystals opens a possibility to construct various 3D structures with on-demand properties, which do not exist in nature but can be assembled in Lego style by stacking individual atomic planes on top of each other in a desired sequence. This project is to explore this new avenue.
We will design, fabricate and study multilayer materials ranging from basic heterostructures that consist of a few alternating layers of graphene and boron nitride and already exhibit a rich spectrum of new phenomena, as recently demonstrated by the applicant’s group, to complex artificial materials containing many layers of different 2D crystals and mimicking, for example, layered superconductors. In a similar manner, various electronic, optoelectronic, micromechanical and other devices will be developed and investigated. The applicant’s aim is to search for new materials with unique properties, novel devices with better characteristics and new physics that is likely to emerge along the way.
The proposed research offers many exciting opportunities and can lead to the development of a large unexplored field with impact exceeding even that of graphene research. This presents a unique, once-in-decade, opportunity to make a very significant breakthrough in condensed matter physics and materials science."
Summary
"Following the advent of graphene with its wide range of unique properties, several other one-atom-thick crystals have been isolated and their preliminary studies have been undertaken. They range from semiconducting monolayers of MoS2 and NbSe2, which similar to graphene exhibit the electric field effect and relatively high electronic quality, to wide-gap insulators such as boron-nitride monolayers that can serve as atomically-thin tunnel barriers.
This library of two-dimensional crystals opens a possibility to construct various 3D structures with on-demand properties, which do not exist in nature but can be assembled in Lego style by stacking individual atomic planes on top of each other in a desired sequence. This project is to explore this new avenue.
We will design, fabricate and study multilayer materials ranging from basic heterostructures that consist of a few alternating layers of graphene and boron nitride and already exhibit a rich spectrum of new phenomena, as recently demonstrated by the applicant’s group, to complex artificial materials containing many layers of different 2D crystals and mimicking, for example, layered superconductors. In a similar manner, various electronic, optoelectronic, micromechanical and other devices will be developed and investigated. The applicant’s aim is to search for new materials with unique properties, novel devices with better characteristics and new physics that is likely to emerge along the way.
The proposed research offers many exciting opportunities and can lead to the development of a large unexplored field with impact exceeding even that of graphene research. This presents a unique, once-in-decade, opportunity to make a very significant breakthrough in condensed matter physics and materials science."
Max ERC Funding
2 200 000 €
Duration
Start date: 2013-05-01, End date: 2018-04-30
