Project acronym 3DEpi
Project Transgenerational epigenetic inheritance of chromatin states : the role of Polycomb and 3D chromosome architecture
Researcher (PI) Giacomo CAVALLI
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Advanced Grant (AdG), LS2, ERC-2017-ADG
Summary Epigenetic inheritance entails transmission of phenotypic traits not encoded in the DNA sequence and, in the most extreme case, Transgenerational Epigenetic Inheritance (TEI) involves transmission of memory through multiple generations. Very little is known on the mechanisms governing TEI and this is the subject of the present proposal. By transiently enhancing long-range chromatin interactions, we recently established isogenic Drosophila epilines that carry stable alternative epialleles, defined by differential levels of the Polycomb-dependent H3K27me3 mark. Furthermore, we extended our paradigm to natural phenotypes. These are ideal systems to study the role of Polycomb group (PcG) proteins and other components in regulating nuclear organization and epigenetic inheritance of chromatin states. The present project conjugates genetics, epigenomics, imaging and molecular biology to reach three critical aims.
Aim 1: Analysis of the molecular mechanisms regulating Polycomb-mediated TEI. We will identify the DNA, protein and RNA components that trigger and maintain transgenerational chromatin inheritance as well as their mechanisms of action.
Aim 2: Role of 3D genome organization in the regulation of TEI. We will analyze the developmental dynamics of TEI-inducing long-range chromatin interactions, identify chromatin components mediating 3D chromatin contacts and characterize their function in the TEI process.
Aim 3: Identification of a broader role of TEI during development. TEI might reflect a normal role of PcG components in the transmission of parental chromatin onto the next embryonic generation. We will explore this possibility by establishing other TEI paradigms and by relating TEI to the normal PcG function in these systems and in normal development.
This research program will unravel the biological significance and the molecular underpinnings of TEI and lead the way towards establishing this area of research into a consolidated scientific discipline.
Summary
Epigenetic inheritance entails transmission of phenotypic traits not encoded in the DNA sequence and, in the most extreme case, Transgenerational Epigenetic Inheritance (TEI) involves transmission of memory through multiple generations. Very little is known on the mechanisms governing TEI and this is the subject of the present proposal. By transiently enhancing long-range chromatin interactions, we recently established isogenic Drosophila epilines that carry stable alternative epialleles, defined by differential levels of the Polycomb-dependent H3K27me3 mark. Furthermore, we extended our paradigm to natural phenotypes. These are ideal systems to study the role of Polycomb group (PcG) proteins and other components in regulating nuclear organization and epigenetic inheritance of chromatin states. The present project conjugates genetics, epigenomics, imaging and molecular biology to reach three critical aims.
Aim 1: Analysis of the molecular mechanisms regulating Polycomb-mediated TEI. We will identify the DNA, protein and RNA components that trigger and maintain transgenerational chromatin inheritance as well as their mechanisms of action.
Aim 2: Role of 3D genome organization in the regulation of TEI. We will analyze the developmental dynamics of TEI-inducing long-range chromatin interactions, identify chromatin components mediating 3D chromatin contacts and characterize their function in the TEI process.
Aim 3: Identification of a broader role of TEI during development. TEI might reflect a normal role of PcG components in the transmission of parental chromatin onto the next embryonic generation. We will explore this possibility by establishing other TEI paradigms and by relating TEI to the normal PcG function in these systems and in normal development.
This research program will unravel the biological significance and the molecular underpinnings of TEI and lead the way towards establishing this area of research into a consolidated scientific discipline.
Max ERC Funding
2 500 000 €
Duration
Start date: 2018-11-01, End date: 2023-10-31
Project acronym 4D-GenEx
Project Spatio-temporal Organization and Expression of the Genome
Researcher (PI) Antoine COULON
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), LS2, ERC-2017-STG
Summary This project investigates the two-way relationship between spatio-temporal genome organization and coordinated gene regulation, through an approach at the interface between physics, computer science and biology.
In the nucleus, preferred positions are observed from chromosomes to single genes, in relation to normal and pathological cellular states. Evidence indicates a complex spatio-temporal coupling between co-regulated genes: e.g. certain genes cluster spatially when responding to similar factors and transcriptional noise patterns suggest domain-wide mechanisms. Yet, no individual experiment allows probing transcriptional coordination in 4 dimensions (FISH, live locus tracking, Hi-C...). Interpreting such data also critically requires theory (stochastic processes, statistical physics…). A lack of appropriate experimental/analytical approaches is impairing our understanding of the 4D genome.
Our proposal combines cutting-edge single-molecule imaging, signal-theory data analysis and physical modeling to study how genes coordinate in space and time in a single nucleus. Our objectives are to understand (a) competition/recycling of shared resources between genes within subnuclear compartments, (b) how enhancers communicate with genes domain-wide, and (c) the role of local conformational dynamics and supercoiling in gene co-regulation. Our organizing hypothesis is that, by acting on their microenvironment, genes shape their co-expression with other genes.
Building upon my expertise, we will use dual-color MS2/PP7 RNA labeling to visualize for the first time transcription and motion of pairs of hormone-responsive genes in real time. With our innovative signal analysis tools, we will extract spatio-temporal signatures of underlying processes, which we will investigate with stochastic modeling and validate through experimental perturbations. We expect to uncover how the functional organization of the linear genome relates to its physical properties and dynamics in 4D.
Summary
This project investigates the two-way relationship between spatio-temporal genome organization and coordinated gene regulation, through an approach at the interface between physics, computer science and biology.
In the nucleus, preferred positions are observed from chromosomes to single genes, in relation to normal and pathological cellular states. Evidence indicates a complex spatio-temporal coupling between co-regulated genes: e.g. certain genes cluster spatially when responding to similar factors and transcriptional noise patterns suggest domain-wide mechanisms. Yet, no individual experiment allows probing transcriptional coordination in 4 dimensions (FISH, live locus tracking, Hi-C...). Interpreting such data also critically requires theory (stochastic processes, statistical physics…). A lack of appropriate experimental/analytical approaches is impairing our understanding of the 4D genome.
Our proposal combines cutting-edge single-molecule imaging, signal-theory data analysis and physical modeling to study how genes coordinate in space and time in a single nucleus. Our objectives are to understand (a) competition/recycling of shared resources between genes within subnuclear compartments, (b) how enhancers communicate with genes domain-wide, and (c) the role of local conformational dynamics and supercoiling in gene co-regulation. Our organizing hypothesis is that, by acting on their microenvironment, genes shape their co-expression with other genes.
Building upon my expertise, we will use dual-color MS2/PP7 RNA labeling to visualize for the first time transcription and motion of pairs of hormone-responsive genes in real time. With our innovative signal analysis tools, we will extract spatio-temporal signatures of underlying processes, which we will investigate with stochastic modeling and validate through experimental perturbations. We expect to uncover how the functional organization of the linear genome relates to its physical properties and dynamics in 4D.
Max ERC Funding
1 499 750 €
Duration
Start date: 2018-04-01, End date: 2023-03-31
Project acronym ANADEL
Project Analysis of Geometrical Effects on Dispersive Equations
Researcher (PI) Danela Oana IVANOVICI
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), PE1, ERC-2017-STG
Summary We are concerned with localization properties of solutions to hyperbolic PDEs, especially problems with a geometric component: how do boundaries and heterogeneous media influence spreading and concentration of solutions. While our first focus is on wave and Schrödinger equations on manifolds with boundary, strong connections exist with phase space localization for (clusters of) eigenfunctions, which are of independent interest. Motivations come from nonlinear dispersive models (in physically relevant settings), properties of eigenfunctions in quantum chaos (related to both physics of optic fiber design as well as number theoretic questions), or harmonic analysis on manifolds.
Waves propagation in real life physics occur in media which are neither homogeneous or spatially infinity. The birth of radar/sonar technologies (and the raise of computed tomography) greatly motivated numerous developments in microlocal analysis and the linear theory. Only recently toy nonlinear models have been studied on a curved background, sometimes compact or rough. Understanding how to extend such tools, dealing with wave dispersion or focusing, will allow us to significantly progress in our mathematical understanding of physically relevant models. There, boundaries appear naturally and most earlier developments related to propagation of singularities in this context have limited scope with respect to crucial dispersive effects. Despite great progress over the last decade, driven by the study of quasilinear equations, our knowledge is still very limited. Going beyond this recent activity requires new tools whose development is at the heart of this proposal, including good approximate solutions (parametrices) going over arbitrarily large numbers of caustics, sharp pointwise bounds on Green functions, development of efficient wave packets methods, quantitative refinements of propagation of singularities (with direct applications in control theory), only to name a few important ones.
Summary
We are concerned with localization properties of solutions to hyperbolic PDEs, especially problems with a geometric component: how do boundaries and heterogeneous media influence spreading and concentration of solutions. While our first focus is on wave and Schrödinger equations on manifolds with boundary, strong connections exist with phase space localization for (clusters of) eigenfunctions, which are of independent interest. Motivations come from nonlinear dispersive models (in physically relevant settings), properties of eigenfunctions in quantum chaos (related to both physics of optic fiber design as well as number theoretic questions), or harmonic analysis on manifolds.
Waves propagation in real life physics occur in media which are neither homogeneous or spatially infinity. The birth of radar/sonar technologies (and the raise of computed tomography) greatly motivated numerous developments in microlocal analysis and the linear theory. Only recently toy nonlinear models have been studied on a curved background, sometimes compact or rough. Understanding how to extend such tools, dealing with wave dispersion or focusing, will allow us to significantly progress in our mathematical understanding of physically relevant models. There, boundaries appear naturally and most earlier developments related to propagation of singularities in this context have limited scope with respect to crucial dispersive effects. Despite great progress over the last decade, driven by the study of quasilinear equations, our knowledge is still very limited. Going beyond this recent activity requires new tools whose development is at the heart of this proposal, including good approximate solutions (parametrices) going over arbitrarily large numbers of caustics, sharp pointwise bounds on Green functions, development of efficient wave packets methods, quantitative refinements of propagation of singularities (with direct applications in control theory), only to name a few important ones.
Max ERC Funding
1 293 763 €
Duration
Start date: 2018-02-01, End date: 2023-01-31
Project acronym BactRNA
Project Bacterial small RNAs networks unravelling novel features of transcription and translation
Researcher (PI) Maude Audrey Guillier
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Consolidator Grant (CoG), LS2, ERC-2018-COG
Summary Regulation of gene expression plays a key role in the ability of bacteria to rapidly adapt to changing environments and to colonize extremely diverse habitats. The relatively recent discovery of a plethora of small regulatory RNAs and the beginning of their characterization has unravelled new aspects of bacterial gene expression. First, the expression of many bacterial genes responds to a complex network of both transcriptional and post-transcriptional regulators. However, the properties of the resulting regulatory circuits on the dynamics of gene expression and in the bacterial adaptive response have been poorly addressed so far. In a first part of this project, we will tackle this question by characterizing the circuits that are formed between two widespread classes of bacterial regulators, the sRNAs and the two-component systems, which act at the post-transcriptional and the transcriptional level, respectively. The study of sRNAs also led to major breakthroughs regarding the basic mechanisms of gene expression. In particular, we recently showed that repressor sRNAs can target activating stem-loop structures located within the coding region of mRNAs that promote translation initiation, in striking contrast with the previously recognized inhibitory role of mRNA structures in translation. The second objective of this project is thus to draw an unprecedented map of non-canonical translation initiation events and their regulation by sRNAs.
Overall, this project will greatly improve our understanding of how bacteria can so rapidly and successfully adapt to many different environments, and in the long term, provide clues towards the development of anti-bacterial strategies.
Summary
Regulation of gene expression plays a key role in the ability of bacteria to rapidly adapt to changing environments and to colonize extremely diverse habitats. The relatively recent discovery of a plethora of small regulatory RNAs and the beginning of their characterization has unravelled new aspects of bacterial gene expression. First, the expression of many bacterial genes responds to a complex network of both transcriptional and post-transcriptional regulators. However, the properties of the resulting regulatory circuits on the dynamics of gene expression and in the bacterial adaptive response have been poorly addressed so far. In a first part of this project, we will tackle this question by characterizing the circuits that are formed between two widespread classes of bacterial regulators, the sRNAs and the two-component systems, which act at the post-transcriptional and the transcriptional level, respectively. The study of sRNAs also led to major breakthroughs regarding the basic mechanisms of gene expression. In particular, we recently showed that repressor sRNAs can target activating stem-loop structures located within the coding region of mRNAs that promote translation initiation, in striking contrast with the previously recognized inhibitory role of mRNA structures in translation. The second objective of this project is thus to draw an unprecedented map of non-canonical translation initiation events and their regulation by sRNAs.
Overall, this project will greatly improve our understanding of how bacteria can so rapidly and successfully adapt to many different environments, and in the long term, provide clues towards the development of anti-bacterial strategies.
Max ERC Funding
1 999 754 €
Duration
Start date: 2019-09-01, End date: 2024-08-31
Project acronym BITCRUMBS
Project Towards a Reliable and Automated Analysis of Compromised Systems
Researcher (PI) Davide BALZAROTTI
Host Institution (HI) EURECOM
Call Details Consolidator Grant (CoG), PE6, ERC-2017-COG
Summary "The vast majority of research in computer security is dedicated to the design of detection, protection, and prevention solutions. While these techniques play a critical role to increase the security and privacy of our digital infrastructure, it is enough to look at the news to understand that it is not a matter of ""if"" a computer system will be compromised, but only a matter of ""when"". It is a well known fact that there is no 100% secure system, and that there is no practical way to prevent attackers with enough resources from breaking into sensitive targets. Therefore, it is extremely important to develop automated techniques to timely and precisely analyze computer security incidents and compromised systems. Unfortunately, the area of incident response received very little research attention, and it is still largely considered an art more than a science because of its lack of a proper theoretical and scientific background.
The objective of BITCRUMBS is to rethink the Incident Response (IR) field from its foundations by proposing a more scientific and comprehensive approach to the analysis of compromised systems. BITCRUMBS will achieve this goal in three steps: (1) by introducing a new systematic approach to precisely measure the effectiveness and accuracy of IR techniques and their resilience to evasion and forgery; (2) by designing and implementing new automated techniques to cope with advanced threats and the analysis of IoT devices; and (3) by proposing a novel forensics-by-design development methodology and a set of guidelines for the design of future systems and software.
To provide the right context for these new techniques and show the impact of the project in different fields and scenarios, BITCRUMBS plans to address its objectives using real case studies borrowed from two different
domains: traditional computer software, and embedded systems.
"
Summary
"The vast majority of research in computer security is dedicated to the design of detection, protection, and prevention solutions. While these techniques play a critical role to increase the security and privacy of our digital infrastructure, it is enough to look at the news to understand that it is not a matter of ""if"" a computer system will be compromised, but only a matter of ""when"". It is a well known fact that there is no 100% secure system, and that there is no practical way to prevent attackers with enough resources from breaking into sensitive targets. Therefore, it is extremely important to develop automated techniques to timely and precisely analyze computer security incidents and compromised systems. Unfortunately, the area of incident response received very little research attention, and it is still largely considered an art more than a science because of its lack of a proper theoretical and scientific background.
The objective of BITCRUMBS is to rethink the Incident Response (IR) field from its foundations by proposing a more scientific and comprehensive approach to the analysis of compromised systems. BITCRUMBS will achieve this goal in three steps: (1) by introducing a new systematic approach to precisely measure the effectiveness and accuracy of IR techniques and their resilience to evasion and forgery; (2) by designing and implementing new automated techniques to cope with advanced threats and the analysis of IoT devices; and (3) by proposing a novel forensics-by-design development methodology and a set of guidelines for the design of future systems and software.
To provide the right context for these new techniques and show the impact of the project in different fields and scenarios, BITCRUMBS plans to address its objectives using real case studies borrowed from two different
domains: traditional computer software, and embedded systems.
"
Max ERC Funding
1 991 504 €
Duration
Start date: 2018-04-01, End date: 2023-03-31
Project acronym CENEVO
Project A new paradigm for centromere biology:Evolution and mechanism of CenH3-independent chromosome segregation in holocentric insects
Researcher (PI) Ines DRINNENBERG
Host Institution (HI) INSTITUT CURIE
Call Details Starting Grant (StG), LS2, ERC-2017-STG
Summary Faithful chromosome segregation in all eukaryotes relies on centromeres, the chromosomal sites that recruit kinetochore proteins and mediate spindle attachment during cell division. Fundamental to centromere function is a histone H3 variant, CenH3, that initiates kinetochore assembly on centromeric DNA. CenH3 is conserved throughout most eukaryotes; its deletion is lethal in all organisms tested. These findings established the paradigm that CenH3 is an absolute requirement for centromere function. My recent findings undermined this paradigm of CenH3 essentiality. I showed that CenH3 was lost independently in four lineages of insects. These losses are concomitant with dramatic changes in their centromeric architecture, in which each lineage independently transitioned from monocentromeres (where microtubules attach to a single chromosomal region) to holocentromeres (where microtubules attach along the entire length of the chromosome). Here, I aim to characterize this unique CenH3-deficient chromosome segregation pathway. Using proteomic and genomic approaches in lepidopteran cell lines, I will determine the mechanism of CenH3-independent kinetochore assembly that led to the establishment of their holocentric architecture. Using comparative genomic approaches, I will determine whether this kinetochore assembly pathway has recurrently evolved over the course of 400 million years of evolution and its impact on the chromosome segregation machinery.
My discovery of CenH3 loss in holocentric insects establishes a new class of centromeres. My research will reveal how CenH3 that is essential in most other eukaryotes, could have become dispensable in holocentric insects. Since the evolution of this CenH3-independent chromosome segregation pathway is associated with the independent rises of holocentric architectures, my research will also provide the first insights into the transition from a monocentromere to a holocentromere.
Summary
Faithful chromosome segregation in all eukaryotes relies on centromeres, the chromosomal sites that recruit kinetochore proteins and mediate spindle attachment during cell division. Fundamental to centromere function is a histone H3 variant, CenH3, that initiates kinetochore assembly on centromeric DNA. CenH3 is conserved throughout most eukaryotes; its deletion is lethal in all organisms tested. These findings established the paradigm that CenH3 is an absolute requirement for centromere function. My recent findings undermined this paradigm of CenH3 essentiality. I showed that CenH3 was lost independently in four lineages of insects. These losses are concomitant with dramatic changes in their centromeric architecture, in which each lineage independently transitioned from monocentromeres (where microtubules attach to a single chromosomal region) to holocentromeres (where microtubules attach along the entire length of the chromosome). Here, I aim to characterize this unique CenH3-deficient chromosome segregation pathway. Using proteomic and genomic approaches in lepidopteran cell lines, I will determine the mechanism of CenH3-independent kinetochore assembly that led to the establishment of their holocentric architecture. Using comparative genomic approaches, I will determine whether this kinetochore assembly pathway has recurrently evolved over the course of 400 million years of evolution and its impact on the chromosome segregation machinery.
My discovery of CenH3 loss in holocentric insects establishes a new class of centromeres. My research will reveal how CenH3 that is essential in most other eukaryotes, could have become dispensable in holocentric insects. Since the evolution of this CenH3-independent chromosome segregation pathway is associated with the independent rises of holocentric architectures, my research will also provide the first insights into the transition from a monocentromere to a holocentromere.
Max ERC Funding
1 497 500 €
Duration
Start date: 2018-04-01, End date: 2023-03-31
Project acronym COMBINEPIC
Project Elliptic Combinatorics: Solving famous models from combinatorics, probability and statistical mechanics, via a transversal approach of special functions
Researcher (PI) Kilian RASCHEL
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), PE1, ERC-2017-STG
Summary I am willing to solve several well-known models from combinatorics, probability theory and statistical mechanics: the Ising model on isoradial graphs, dimer models, spanning forests, random walks in cones, occupation time problems. Although completely unrelated a priori, these models have the common feature of being presumed “exactly solvable” models, for which surprising and spectacular formulas should exist for quantities of interest. This is captured by the title “Elliptic Combinatorics”, the wording elliptic referring to the use of special functions, in a broad sense: algebraic/differentially finite (or holonomic)/diagonals/(hyper)elliptic/ hypergeometric/etc.
Besides the exciting nature of the models which we aim at solving, one main strength of our project lies in the variety of modern methods and fields that we cover: combinatorics, probability, algebra (representation theory), computer algebra, algebraic geometry, with a spectrum going from applied to pure mathematics.
We propose in addition two major applications, in finance (Markovian order books) and in population biology (evolution of multitype populations). We plan to work in close collaborations with researchers from these fields, to eventually apply our results (study of extinction probabilities for self-incompatible flower populations, for instance).
Summary
I am willing to solve several well-known models from combinatorics, probability theory and statistical mechanics: the Ising model on isoradial graphs, dimer models, spanning forests, random walks in cones, occupation time problems. Although completely unrelated a priori, these models have the common feature of being presumed “exactly solvable” models, for which surprising and spectacular formulas should exist for quantities of interest. This is captured by the title “Elliptic Combinatorics”, the wording elliptic referring to the use of special functions, in a broad sense: algebraic/differentially finite (or holonomic)/diagonals/(hyper)elliptic/ hypergeometric/etc.
Besides the exciting nature of the models which we aim at solving, one main strength of our project lies in the variety of modern methods and fields that we cover: combinatorics, probability, algebra (representation theory), computer algebra, algebraic geometry, with a spectrum going from applied to pure mathematics.
We propose in addition two major applications, in finance (Markovian order books) and in population biology (evolution of multitype populations). We plan to work in close collaborations with researchers from these fields, to eventually apply our results (study of extinction probabilities for self-incompatible flower populations, for instance).
Max ERC Funding
1 242 400 €
Duration
Start date: 2018-02-01, End date: 2023-01-31
Project acronym CORFRONMAT
Project Correlated frontiers of many-body quantum mathematics and condensed matter physics
Researcher (PI) Nicolas ROUGERIE
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), PE1, ERC-2017-STG
Summary One of the main challenges in condensed matter physics is to understand strongly correlated quantum systems. Our purpose is to approach this issue from the point of view of rigorous mathematical analysis. The goals are twofold: develop a mathematical framework applicable to physically relevant scenarii, take inspiration from the physics to introduce new topics in mathematics. The scope of the proposal thus goes from physically oriented questions (theoretical description and modelization of physical systems) to analytical ones (rigorous derivation and analysis of reduced models) in several cases where strong correlations play the key role.
In a first part, we aim at developing mathematical methods of general applicability to go beyond mean-field theory in different contexts. Our long-term goal is to forge new tools to attack important open problems in the field. Particular emphasis will be put on the structural properties of large quantum states as a general tool.
A second part is concerned with so-called fractional quantum Hall states, host of the fractional quantum Hall effect. Despite the appealing structure of their built-in correlations, their mathematical study is in its infancy. They however constitute an excellent testing ground to develop ideas of possible wider applicability. In particular, we introduce and study a new class of many-body variational problems.
In the third part we discuss so-called anyons, exotic quasi-particles thought to emerge as excitations of highly-correlated quantum systems. Their modelization gives rise to rather unusual, strongly interacting, many-body Hamiltonians with a topological content. Mathematical analysis will help us shed light on those, clarifying the characteristic properties that could ultimately be experimentally tested.
Summary
One of the main challenges in condensed matter physics is to understand strongly correlated quantum systems. Our purpose is to approach this issue from the point of view of rigorous mathematical analysis. The goals are twofold: develop a mathematical framework applicable to physically relevant scenarii, take inspiration from the physics to introduce new topics in mathematics. The scope of the proposal thus goes from physically oriented questions (theoretical description and modelization of physical systems) to analytical ones (rigorous derivation and analysis of reduced models) in several cases where strong correlations play the key role.
In a first part, we aim at developing mathematical methods of general applicability to go beyond mean-field theory in different contexts. Our long-term goal is to forge new tools to attack important open problems in the field. Particular emphasis will be put on the structural properties of large quantum states as a general tool.
A second part is concerned with so-called fractional quantum Hall states, host of the fractional quantum Hall effect. Despite the appealing structure of their built-in correlations, their mathematical study is in its infancy. They however constitute an excellent testing ground to develop ideas of possible wider applicability. In particular, we introduce and study a new class of many-body variational problems.
In the third part we discuss so-called anyons, exotic quasi-particles thought to emerge as excitations of highly-correlated quantum systems. Their modelization gives rise to rather unusual, strongly interacting, many-body Hamiltonians with a topological content. Mathematical analysis will help us shed light on those, clarifying the characteristic properties that could ultimately be experimentally tested.
Max ERC Funding
1 056 664 €
Duration
Start date: 2018-01-01, End date: 2022-12-31
Project acronym CriBLaM
Project Critical behavior of lattice models
Researcher (PI) Hugo DUMINIL-COPIN
Host Institution (HI) INSTITUT DES HAUTES ETUDES SCIENTIFIQUES
Call Details Starting Grant (StG), PE1, ERC-2017-STG
Summary Statistical physics is a theory allowing the derivation of the statistical behavior of macroscopic systems from the description of the interactions of their microscopic constituents. For more than a century, lattice models (i.e. random systems defined on lattices) have been introduced as discrete models describing the phase transition for a large variety of phenomena, ranging from ferroelectrics to lattice gas.
In the last decades, our understanding of percolation and the Ising model, two classical exam- ples of lattice models, progressed greatly. Nonetheless, major questions remain open on these two models.
The goal of this project is to break new grounds in the understanding of phase transition in statistical physics by using and aggregating in a pioneering way multiple techniques from proba- bility, combinatorics, analysis and integrable systems. In this project, we will focus on three main goals:
Objective A Provide a solid mathematical framework for the study of universality for Bernoulli percolation and the Ising model in two dimensions.
Objective B Advance in the understanding of the critical behavior of Bernoulli percolation and the Ising model in dimensions larger or equal to 3.
Objective C Greatly improve the understanding of planar lattice models obtained by general- izations of percolation and the Ising model, through the design of an innovative mathematical theory of phase transition dedicated to graphical representations of classical lattice models, such as Fortuin-Kasteleyn percolation, Ashkin-Teller models and Loop models.
Most of the questions that we propose to tackle are notoriously difficult open problems. We believe that breakthroughs in these fundamental questions would reshape significantly our math- ematical understanding of phase transition.
Summary
Statistical physics is a theory allowing the derivation of the statistical behavior of macroscopic systems from the description of the interactions of their microscopic constituents. For more than a century, lattice models (i.e. random systems defined on lattices) have been introduced as discrete models describing the phase transition for a large variety of phenomena, ranging from ferroelectrics to lattice gas.
In the last decades, our understanding of percolation and the Ising model, two classical exam- ples of lattice models, progressed greatly. Nonetheless, major questions remain open on these two models.
The goal of this project is to break new grounds in the understanding of phase transition in statistical physics by using and aggregating in a pioneering way multiple techniques from proba- bility, combinatorics, analysis and integrable systems. In this project, we will focus on three main goals:
Objective A Provide a solid mathematical framework for the study of universality for Bernoulli percolation and the Ising model in two dimensions.
Objective B Advance in the understanding of the critical behavior of Bernoulli percolation and the Ising model in dimensions larger or equal to 3.
Objective C Greatly improve the understanding of planar lattice models obtained by general- izations of percolation and the Ising model, through the design of an innovative mathematical theory of phase transition dedicated to graphical representations of classical lattice models, such as Fortuin-Kasteleyn percolation, Ashkin-Teller models and Loop models.
Most of the questions that we propose to tackle are notoriously difficult open problems. We believe that breakthroughs in these fundamental questions would reshape significantly our math- ematical understanding of phase transition.
Max ERC Funding
1 499 912 €
Duration
Start date: 2018-09-01, End date: 2023-08-31
Project acronym DEBATE
Project Debate: Innovation as Performance in Late-Medieval Universities
Researcher (PI) Monica BRINZEI
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Consolidator Grant (CoG), SH6, ERC-2017-COG
Summary The switch from parchment to paper had a fundamental impact on later medieval universities, equivalent to the shift to Open Access today, hindering some intellectual practices while encouraging others. The DEBATE project identifies a neglected genre of latin texts that flourished on paper, the Principia, which record the public confrontations between candidates (socii) for the title of doctor. These debates, imposed by university statutes throughout Europe as annual exercises linked to lectures on the Sentences (the medieval parallel to our PhD thesis), forced the candidate to reveal his innovative theories (sheets of papers were exchanged among the socii beforehand), display his erudition and prove his intellectual prowess before a large audience. The futuristic discussion usually exceeded the confines of one discipline and allowed the bachelor to indulge his interdisciplinary interests, employing science, theology, mathematics, politics, literature, and rhetoric in his polemics against his colleagues. Principia thus reveal the cutting edge method of fostering science in later medieval universities. The DEBATE team intends to identify new manuscripts, edit the texts, establish authorship for anonymous fragments and propose an interpretation that will help explain how innovation was a primordial target in medieval academia. Putting together all the surviving texts of Principia produced in various cultural contexts, this project will provide a wealth of material that will bring about a basic change in our understanding of the mechanism of the production of academic knowledge in the early universities all around Europe.The project is designed to promote erudition by combining a palaeographical, codicological, editorial and hermeneutical approach, aiming to open an advanced area of inquiry focusing on an intellectual practice that bound together medieval universities from different geographical and cultural regions: Paris, Bologna, Vienna, Prague, Krakow and Cologne.
Summary
The switch from parchment to paper had a fundamental impact on later medieval universities, equivalent to the shift to Open Access today, hindering some intellectual practices while encouraging others. The DEBATE project identifies a neglected genre of latin texts that flourished on paper, the Principia, which record the public confrontations between candidates (socii) for the title of doctor. These debates, imposed by university statutes throughout Europe as annual exercises linked to lectures on the Sentences (the medieval parallel to our PhD thesis), forced the candidate to reveal his innovative theories (sheets of papers were exchanged among the socii beforehand), display his erudition and prove his intellectual prowess before a large audience. The futuristic discussion usually exceeded the confines of one discipline and allowed the bachelor to indulge his interdisciplinary interests, employing science, theology, mathematics, politics, literature, and rhetoric in his polemics against his colleagues. Principia thus reveal the cutting edge method of fostering science in later medieval universities. The DEBATE team intends to identify new manuscripts, edit the texts, establish authorship for anonymous fragments and propose an interpretation that will help explain how innovation was a primordial target in medieval academia. Putting together all the surviving texts of Principia produced in various cultural contexts, this project will provide a wealth of material that will bring about a basic change in our understanding of the mechanism of the production of academic knowledge in the early universities all around Europe.The project is designed to promote erudition by combining a palaeographical, codicological, editorial and hermeneutical approach, aiming to open an advanced area of inquiry focusing on an intellectual practice that bound together medieval universities from different geographical and cultural regions: Paris, Bologna, Vienna, Prague, Krakow and Cologne.
Max ERC Funding
1 997 976 €
Duration
Start date: 2018-08-01, End date: 2023-07-31