Project acronym COHEGRAPH
Project Electron quantum optics in Graphene
Researcher (PI) Séverin Preden Roulleau
Host Institution (HI) COMMISSARIAT A L ENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES
Call Details Starting Grant (StG), PE3, ERC-2015-STG
Summary Quantum computing is based on the manipulation of quantum bits (qubits) to enhance the efficiency of information processing. In solid-state systems, two approaches have been explored:
• static qubits, coupled to quantum buses used for manipulation and information transmission,
• flying qubits which are mobile qubits propagating in quantum circuits for further manipulation.
Flying qubits research led to the recent emergence of the field of electron quantum optics, where electrons play the role of photons in quantum optic like experiments. This has recently led to the development of electronic quantum interferometry as well as single electron sources. As of yet, such experiments have only been successfully implemented in semi-conductor heterostructures cooled at extremely low temperatures. Realizing electron quantum optics experiments in graphene, an inexpensive material showing a high degree of quantum coherence even at moderately low temperatures, would be a strong evidence that quantum computing in graphene is within reach.
One of the most elementary building blocks necessary to perform electron quantum optics experiments is the electron beam splitter, which is the electronic analog of a beam splitter for light. However, the usual scheme for electron beam splitters in semi-conductor heterostructures is not available in graphene because of its gapless band structure. I propose a breakthrough in this direction where pn junction plays the role of electron beam splitter. This will lead to the following achievements considered as important steps towards quantum computing:
• electronic Mach Zehnder interferometry used to study the quantum coherence properties of graphene,
• two electrons Aharonov Bohm interferometry used to generate entangled states as an elementary quantum gate,
• the implementation of on-demand electronic sources in the GHz range for graphene flying qubits.
Summary
Quantum computing is based on the manipulation of quantum bits (qubits) to enhance the efficiency of information processing. In solid-state systems, two approaches have been explored:
• static qubits, coupled to quantum buses used for manipulation and information transmission,
• flying qubits which are mobile qubits propagating in quantum circuits for further manipulation.
Flying qubits research led to the recent emergence of the field of electron quantum optics, where electrons play the role of photons in quantum optic like experiments. This has recently led to the development of electronic quantum interferometry as well as single electron sources. As of yet, such experiments have only been successfully implemented in semi-conductor heterostructures cooled at extremely low temperatures. Realizing electron quantum optics experiments in graphene, an inexpensive material showing a high degree of quantum coherence even at moderately low temperatures, would be a strong evidence that quantum computing in graphene is within reach.
One of the most elementary building blocks necessary to perform electron quantum optics experiments is the electron beam splitter, which is the electronic analog of a beam splitter for light. However, the usual scheme for electron beam splitters in semi-conductor heterostructures is not available in graphene because of its gapless band structure. I propose a breakthrough in this direction where pn junction plays the role of electron beam splitter. This will lead to the following achievements considered as important steps towards quantum computing:
• electronic Mach Zehnder interferometry used to study the quantum coherence properties of graphene,
• two electrons Aharonov Bohm interferometry used to generate entangled states as an elementary quantum gate,
• the implementation of on-demand electronic sources in the GHz range for graphene flying qubits.
Max ERC Funding
1 500 000 €
Duration
Start date: 2016-05-01, End date: 2021-04-30
Project acronym LiKo
Project From Liouville to Kolmogorov: 2d quantum gravity, noise sensitivity and turbulent flows
Researcher (PI) Christophe Garban
Host Institution (HI) UNIVERSITE LYON 1 CLAUDE BERNARD
Call Details Starting Grant (StG), PE1, ERC-2015-STG
Summary This research project is organized along three seemingly unrelated directions:
(1) Mathematical Liouville gravity deals with the geometry of large random planar maps. Historically, conformal invariance was a key ingredient in the construction of Liouville gravity in the physics literature. Conformal invariance has been restored recently with an attempt of understanding large random combinatorial planar maps once conformally embedded in the plane. The geometry induced by these embeddings is conjecturally described by the exponential of a highly oscillating distribution, the Gaussian Free Field. This conjecture is part of a broader program aimed at rigorously understanding the celebrated KPZ relation. The first major goal of my project is to make significant progress towards the completion of this program. I will combine for this several tools such as Liouville Brownian motion, circle packings, QLE processes and Bouchaud trap models.
(2) Euclidean statistical physics is closely related to area (1) through the above KPZ relation. I plan to push further the analysis of critical statistical physics models successfully initiated by the works of Schramm and Smirnov. I will focus in particular on dynamics at and near critical points with a special emphasis on the so-called noise sensitivity of these systems.
(3) 3d turbulence. A more tractable ambition than solving Navier-Stokes equation is to construct explicit stochastic vector fields which combine key features of experimentally observed velocity fields. I will make the mathematical framework precise by identifying four axioms that need to be satisfied. It has been observed recently that the exponential of a certain log-correlated field, as in (1), could be used to create such a realistic velocity field. I plan to construct and analyse this challenging object by relying on techniques from (1) and (2). This would be the first genuine stochastic model of turbulent flow in the spirit of what Kolmogorov was aiming at.
Summary
This research project is organized along three seemingly unrelated directions:
(1) Mathematical Liouville gravity deals with the geometry of large random planar maps. Historically, conformal invariance was a key ingredient in the construction of Liouville gravity in the physics literature. Conformal invariance has been restored recently with an attempt of understanding large random combinatorial planar maps once conformally embedded in the plane. The geometry induced by these embeddings is conjecturally described by the exponential of a highly oscillating distribution, the Gaussian Free Field. This conjecture is part of a broader program aimed at rigorously understanding the celebrated KPZ relation. The first major goal of my project is to make significant progress towards the completion of this program. I will combine for this several tools such as Liouville Brownian motion, circle packings, QLE processes and Bouchaud trap models.
(2) Euclidean statistical physics is closely related to area (1) through the above KPZ relation. I plan to push further the analysis of critical statistical physics models successfully initiated by the works of Schramm and Smirnov. I will focus in particular on dynamics at and near critical points with a special emphasis on the so-called noise sensitivity of these systems.
(3) 3d turbulence. A more tractable ambition than solving Navier-Stokes equation is to construct explicit stochastic vector fields which combine key features of experimentally observed velocity fields. I will make the mathematical framework precise by identifying four axioms that need to be satisfied. It has been observed recently that the exponential of a certain log-correlated field, as in (1), could be used to create such a realistic velocity field. I plan to construct and analyse this challenging object by relying on techniques from (1) and (2). This would be the first genuine stochastic model of turbulent flow in the spirit of what Kolmogorov was aiming at.
Max ERC Funding
935 000 €
Duration
Start date: 2016-09-01, End date: 2021-08-31
Project acronym MALIG
Project A mathematical approach to the liquid-glass transition: kinetically constrained models, cellular automata and mixed order phase transitions
Researcher (PI) cristina Toninelli
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), PE1, ERC-2015-STG
Summary This proposal focuses on the mathematics of three cross-disciplinary, very active and deeply interlaced research themes: interacting particle systems with kinetic constraints, bootstrap percolation cellular automata and mixed order phase transitions. These topics belong to the fertile area of mathematics at the intersection of probability and mathematical statistical mechanics. They are also extremely important in physics. Indeed they are intimately connected to the fundamental problem of understanding the liquid-glass transition, one of the longstanding open questions in condensed matter physics.
The funding of this project will allow the PI to lead a highly qualified team with complementary expertise. Such a diversity will allow a novel, interdisciplinary and potentially groundbreaking approach. Even if research on each one of the above topics has been lately quite lively, very few exchanges and little cross-fertilization occurred among them. One of our main goals is to overcome the barriers among the three different research communities and to explore the interfaces of these yet unconnected fields. We will open two novel and challenging chapters in the mathematics of interacting particle systems and cellular automata: interacting particle glassy systems and bootstrap percolation models with mixed order critical and discontinuous transitions. In order to achieve our groundbreaking goals we will have to go well beyond the present mathematical knowledge. We believe that the novel concepts and the unconventional approaches that we will develop will have a deep impact also in other areas including combinatorics, theory of randomized algorithms and complex systems.
The scientific background and expertise of the PI, with original and groundbreaking contributions in each of the above topics and with a broad and clearcut vision of the mathematics of the proposed research as well as of the fundamental physical questions,make the PI the ideal leader of this project.
Summary
This proposal focuses on the mathematics of three cross-disciplinary, very active and deeply interlaced research themes: interacting particle systems with kinetic constraints, bootstrap percolation cellular automata and mixed order phase transitions. These topics belong to the fertile area of mathematics at the intersection of probability and mathematical statistical mechanics. They are also extremely important in physics. Indeed they are intimately connected to the fundamental problem of understanding the liquid-glass transition, one of the longstanding open questions in condensed matter physics.
The funding of this project will allow the PI to lead a highly qualified team with complementary expertise. Such a diversity will allow a novel, interdisciplinary and potentially groundbreaking approach. Even if research on each one of the above topics has been lately quite lively, very few exchanges and little cross-fertilization occurred among them. One of our main goals is to overcome the barriers among the three different research communities and to explore the interfaces of these yet unconnected fields. We will open two novel and challenging chapters in the mathematics of interacting particle systems and cellular automata: interacting particle glassy systems and bootstrap percolation models with mixed order critical and discontinuous transitions. In order to achieve our groundbreaking goals we will have to go well beyond the present mathematical knowledge. We believe that the novel concepts and the unconventional approaches that we will develop will have a deep impact also in other areas including combinatorics, theory of randomized algorithms and complex systems.
The scientific background and expertise of the PI, with original and groundbreaking contributions in each of the above topics and with a broad and clearcut vision of the mathematics of the proposed research as well as of the fundamental physical questions,make the PI the ideal leader of this project.
Max ERC Funding
883 250 €
Duration
Start date: 2016-09-01, End date: 2021-08-31
Project acronym MicMactin
Project Dissecting active matter: Microscopic origins of macroscopic actomyosin activity
Researcher (PI) Martin Sylvain Peter Lenz
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), PE3, ERC-2015-STG
Summary "Biological motion and forces originate from mechanically active proteins operating at the nanometer scale. These individual active elements interact through the surrounding cellular medium, collectively generating structures spanning tens of micrometers whose mechanical properties are perfectly tuned to their fundamentally out-of-equilibrium biological function. While both individual proteins and the resulting cellular behaviors are well characterized, understanding the relationship between these two scales remains a major challenge in both physics and cell biology.
We will bridge this gap through multiscale models of the emergence of active material properties in the experimentally well-characterized actin cytoskeleton. We will thus investigate unexplored, strongly interacting nonequilibrium regimes. We will develop a complete framework for cytoskeletal activity by separately studying all three fundamental processes driving it out of equilibrium: actin filament assembly and disassembly, force exertion by branched actin networks, and the action of molecular motors. We will then recombine these approaches into a unified understanding of complex cell motility processes.
To tackle the cytoskeleton's disordered geometry and many-body interactions, we will design new nonequilibrium self consistent methods in statistical mechanics and elasticity theory. Our findings will be validated through simulations and close experimental collaborations.
Our work will break new ground in both biology and physics. In the context of biology, it will establish a new framework to understand how the cell controls its achitecture and mechanics through biochemical regulation. On the physics side, it will set up new paradigms for the emergence of original out-of-equilibrium collective behaviors in an experimentally well-characterized system, addressing the foundations of existing macroscopic "active matter" approaches."
Summary
"Biological motion and forces originate from mechanically active proteins operating at the nanometer scale. These individual active elements interact through the surrounding cellular medium, collectively generating structures spanning tens of micrometers whose mechanical properties are perfectly tuned to their fundamentally out-of-equilibrium biological function. While both individual proteins and the resulting cellular behaviors are well characterized, understanding the relationship between these two scales remains a major challenge in both physics and cell biology.
We will bridge this gap through multiscale models of the emergence of active material properties in the experimentally well-characterized actin cytoskeleton. We will thus investigate unexplored, strongly interacting nonequilibrium regimes. We will develop a complete framework for cytoskeletal activity by separately studying all three fundamental processes driving it out of equilibrium: actin filament assembly and disassembly, force exertion by branched actin networks, and the action of molecular motors. We will then recombine these approaches into a unified understanding of complex cell motility processes.
To tackle the cytoskeleton's disordered geometry and many-body interactions, we will design new nonequilibrium self consistent methods in statistical mechanics and elasticity theory. Our findings will be validated through simulations and close experimental collaborations.
Our work will break new ground in both biology and physics. In the context of biology, it will establish a new framework to understand how the cell controls its achitecture and mechanics through biochemical regulation. On the physics side, it will set up new paradigms for the emergence of original out-of-equilibrium collective behaviors in an experimentally well-characterized system, addressing the foundations of existing macroscopic "active matter" approaches."
Max ERC Funding
1 491 868 €
Duration
Start date: 2016-06-01, End date: 2021-05-31
Project acronym ModRed
Project The geometry of modular representations of reductive algebraic groups
Researcher (PI) Simon Riche
Host Institution (HI) UNIVERSITE CLERMONT AUVERGNE
Call Details Starting Grant (StG), PE1, ERC-2015-STG
Summary The main theme of this proposal is the Geometric Representation Theory of reductive algebraic groups over algebraically closed fields of positive characteristic. Our primary goal is to obtain character formulas for simple and for indecomposable tilting representations of such groups, by developing a geometric framework for their categories of representations.
Obtaining such formulas has been one of the main problems in this area since the 1980's. A program outlined by G. Lusztig in the 1990's has lead to a formula for the characters of simple representations in the case the characteristic of the base field is bigger than an explicit but huge bound. A recent breakthrough due to G. Williamson has shown that this formula cannot hold for smaller characteristics, however. Nothing is known about characters of tilting modules in general (except for a conjectural formula for some characters, due to Andersen). Our main tools include a new perspective on Soergel bimodules offered by the study of parity sheaves (introduced by Juteau-Mautner-Williamson) and a diagrammatic presentation of their category (due to Elias-Williamson).
Summary
The main theme of this proposal is the Geometric Representation Theory of reductive algebraic groups over algebraically closed fields of positive characteristic. Our primary goal is to obtain character formulas for simple and for indecomposable tilting representations of such groups, by developing a geometric framework for their categories of representations.
Obtaining such formulas has been one of the main problems in this area since the 1980's. A program outlined by G. Lusztig in the 1990's has lead to a formula for the characters of simple representations in the case the characteristic of the base field is bigger than an explicit but huge bound. A recent breakthrough due to G. Williamson has shown that this formula cannot hold for smaller characteristics, however. Nothing is known about characters of tilting modules in general (except for a conjectural formula for some characters, due to Andersen). Our main tools include a new perspective on Soergel bimodules offered by the study of parity sheaves (introduced by Juteau-Mautner-Williamson) and a diagrammatic presentation of their category (due to Elias-Williamson).
Max ERC Funding
882 844 €
Duration
Start date: 2016-09-01, End date: 2021-08-31
Project acronym STAQAMOF
Project Statistical modelling across price and time scales: a quantitative approach to modern financial regulation
Researcher (PI) Mathieu Felix Rosenbaum
Host Institution (HI) ECOLE POLYTECHNIQUE
Call Details Starting Grant (StG), PE1, ERC-2015-STG
Summary This project aims at providing a new quantitative approach to financial regulation, notably in the context of high frequency trading. The key idea of our method is to build relevant statistical models through price and time scales, connecting the microstructure of financial markets to the long term behavior of prices. Doing so, we will be able to understand and quantify the macroscopic consequences of regulatory measures modifying the microscopic design of the market. Succeeding in this modelling task will require to address several intricate statistical problems. In particular new results will be needed in the fields of limit theory for semi-martingales, multifractal processes, rough stochastic differential equations, Hawkes processes and high-dimensional statistics. Hence, through this project, we not only have the hope to provide groundbreaking tools for worldwide regulation of financial markets but, concurrently, to answer important and challenging mathematical problems. In term of analyzing concrete regulatory measures, particular attention will be devoted to the issue of the choice of a proper tick value, that is the minimal price increment allowed on a financial market. Indeed, the tick value is the tool which seems to be favored by most policy makers in order to regulate high frequency trading.
Summary
This project aims at providing a new quantitative approach to financial regulation, notably in the context of high frequency trading. The key idea of our method is to build relevant statistical models through price and time scales, connecting the microstructure of financial markets to the long term behavior of prices. Doing so, we will be able to understand and quantify the macroscopic consequences of regulatory measures modifying the microscopic design of the market. Succeeding in this modelling task will require to address several intricate statistical problems. In particular new results will be needed in the fields of limit theory for semi-martingales, multifractal processes, rough stochastic differential equations, Hawkes processes and high-dimensional statistics. Hence, through this project, we not only have the hope to provide groundbreaking tools for worldwide regulation of financial markets but, concurrently, to answer important and challenging mathematical problems. In term of analyzing concrete regulatory measures, particular attention will be devoted to the issue of the choice of a proper tick value, that is the minimal price increment allowed on a financial market. Indeed, the tick value is the tool which seems to be favored by most policy makers in order to regulate high frequency trading.
Max ERC Funding
1 165 625 €
Duration
Start date: 2016-10-01, End date: 2021-09-30
Project acronym TibArmy
Project The Tibetan Army of the Dalai Lamas (1642-1959)
Researcher (PI) Alice Travers
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), SH6, ERC-2015-STG
Summary TibArmy proposes to undertake a study of a previously unresearched subject: the Tibetan army during the period of the Buddhist government of the Dalai Lamas, known as the Ganden Phodrang, from 1642 to 1959. This government was the heir to a robust military culture with long experience in the defence of Buddhism since the Tibetan Imperial Period (7th-9th centuries); however, from its inception it decided to rely on foreign armies for its protection. On the basis of two distinctive features of this period—the creation and maintenance of the first Tibetan standing army and the limited number of the troops compared to former times—the project will explore the enduring ambivalence of the Dalai Lamas’ government towards having its own army, as well as its reasons, consequences and expressions in discourse and practice.
The methodology follows a multifaceted approach towards the military in Tibet, by taking into considerations its social, economic, political, legal, religious and cultural aspects, and focussing on the multicultural and connected historical context of the Tibetan army’s evolution (foreign Mongol and Manchu armies stationed in Tibet, and the later adoption of British and Japanese military models). The research project, based on written and oral multilingual sources, is structured along 5 thematic axes:
1. A history of the army institution (17th-20th c.): social, economic and political aspects; 2. Interactions with the Sino-Manchu troops and other foreign influences on the Tibetan army; 3. Cultural and discursive aspects: integration of the army within the Buddhist frame; 4. Material culture and photographs: a visual history of the Army (with photograph exhibition); 5. A lexicon of military terminology.
By focussing on the links between Buddhism and the military in Tibet, TibArmy will achieve a clearer understanding of the links between State construction, religion and army, and will also shed light on the past and current geo-political situation in Asia.
Summary
TibArmy proposes to undertake a study of a previously unresearched subject: the Tibetan army during the period of the Buddhist government of the Dalai Lamas, known as the Ganden Phodrang, from 1642 to 1959. This government was the heir to a robust military culture with long experience in the defence of Buddhism since the Tibetan Imperial Period (7th-9th centuries); however, from its inception it decided to rely on foreign armies for its protection. On the basis of two distinctive features of this period—the creation and maintenance of the first Tibetan standing army and the limited number of the troops compared to former times—the project will explore the enduring ambivalence of the Dalai Lamas’ government towards having its own army, as well as its reasons, consequences and expressions in discourse and practice.
The methodology follows a multifaceted approach towards the military in Tibet, by taking into considerations its social, economic, political, legal, religious and cultural aspects, and focussing on the multicultural and connected historical context of the Tibetan army’s evolution (foreign Mongol and Manchu armies stationed in Tibet, and the later adoption of British and Japanese military models). The research project, based on written and oral multilingual sources, is structured along 5 thematic axes:
1. A history of the army institution (17th-20th c.): social, economic and political aspects; 2. Interactions with the Sino-Manchu troops and other foreign influences on the Tibetan army; 3. Cultural and discursive aspects: integration of the army within the Buddhist frame; 4. Material culture and photographs: a visual history of the Army (with photograph exhibition); 5. A lexicon of military terminology.
By focussing on the links between Buddhism and the military in Tibet, TibArmy will achieve a clearer understanding of the links between State construction, religion and army, and will also shed light on the past and current geo-political situation in Asia.
Max ERC Funding
1 499 875 €
Duration
Start date: 2016-10-01, End date: 2021-09-30
Project acronym urban-rev politics
Project The Urban Revolution and the Political
Researcher (PI) Ozan Karaman
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), SH2, ERC-2015-STG
Summary This project is a transnational and comparative study of the political implications of the contemporary ‘urban revolution,’ namely the sweeping socio-cultural, economic, and territorial transformations through which the urban becomes the predominant mode of existence of societies across the world. Across the social sciences and as well as journalistic literatures, there has been a remarkable proliferation of debates around the social and ecological implications of contemporary urbanization.
What is largely missing in these timely debates, however, is any systematic and in-depth engagement with the political significance of the ongoing ‘urban revolution.’ This is due to a lack of systematic research and theoretical engagement regarding the unprecedented prominence of accumulation regimes based on the speculative production, trade and consumption of space. Similarly, extant theoretical tools of urban political analysis fall short of conceptualizing the increasingly planetary nature of privatization and exploitation of the urban and their intricate links to global finance. In addressing these gaps the project advances two overarching goals: 1. to develop conceptual tools for and comparative insights into the increasingly dominant urban-based accumulation regimes, and 2. to advance the politicization of academic and public discourses on the planetary urban condition.
I propose three relational levels (extended moments) of analysis, which respectively focus on the finance/real-estate/state nexus, the exploitation of the urban, and the emerging spaces of the political. These correspond to three subprojects that focus on transnational, everyday, and political dimensions of the urban revolution. The methodological approach will be multi-sited global ethnography, which will combine ethnographies of place-based relations and transnational networks. Filmmaking will be used not only as a research method but also as a storytelling medium.
Summary
This project is a transnational and comparative study of the political implications of the contemporary ‘urban revolution,’ namely the sweeping socio-cultural, economic, and territorial transformations through which the urban becomes the predominant mode of existence of societies across the world. Across the social sciences and as well as journalistic literatures, there has been a remarkable proliferation of debates around the social and ecological implications of contemporary urbanization.
What is largely missing in these timely debates, however, is any systematic and in-depth engagement with the political significance of the ongoing ‘urban revolution.’ This is due to a lack of systematic research and theoretical engagement regarding the unprecedented prominence of accumulation regimes based on the speculative production, trade and consumption of space. Similarly, extant theoretical tools of urban political analysis fall short of conceptualizing the increasingly planetary nature of privatization and exploitation of the urban and their intricate links to global finance. In addressing these gaps the project advances two overarching goals: 1. to develop conceptual tools for and comparative insights into the increasingly dominant urban-based accumulation regimes, and 2. to advance the politicization of academic and public discourses on the planetary urban condition.
I propose three relational levels (extended moments) of analysis, which respectively focus on the finance/real-estate/state nexus, the exploitation of the urban, and the emerging spaces of the political. These correspond to three subprojects that focus on transnational, everyday, and political dimensions of the urban revolution. The methodological approach will be multi-sited global ethnography, which will combine ethnographies of place-based relations and transnational networks. Filmmaking will be used not only as a research method but also as a storytelling medium.
Max ERC Funding
1 499 940 €
Duration
Start date: 2016-11-01, End date: 2021-10-31
