Project acronym CONFRA
Project Conformal fractals in analysis, dynamics, physics
Researcher (PI) Stanislav Smirnov
Host Institution (HI) UNIVERSITE DE GENEVE
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary The goal of this project is to study conformally invariant fractal structures from the perspectives of analysis, dynamics, probability, geometry and physics, emphasizing interrelations of these fields. In the last two decades such structures emerged in several areas: continuum scaling limits of 2D critical models in statistical physics (percolation, Ising model); extremal configurations for various problems in complex analysis (multifractal harmonic measures, coefficient growth of univalent maps, Brennan's conjecture); chaotic sets for complex dynamical systems (Julia sets, Kleinian groups). Capitalizing on recent successes, I plan to continue my work in these areas, exploiting their interactions and connections to physics. I intend to achieve at least some of the following goals: * To establish that several critical lattice models have conformally invariant scaling limits, by building upon results on percolation and Ising models and finding discrete holomorphic observables. * To study geometric properties of arising fractal curves and random fields by connecting them to Schramm's SLE curves and Gaussian Free Fields. * To investigate massive scaling limits by describing them geometrically with generalizations of SLEs. * To lay mathematical framework behind relevant physical notions, such as Coulomb Gas (by relating height functions to GFFs) and Quantum Gravity (by identifying limits of random planar graphs with Liouville QGs). * To improve known bounds in several old questions in complex analysis by studying multifractal spectra of harmonic measures. * To estimate extremal behavior of such spectra by using holomorphic motions of (quasi) conformal maps and thermodynamic formalism. * To understand nature of extremal multifractals for harmonic measure by studying random and dynamical fractals. The topics involved range from century old to very young ones. Recently connections between them started to emerge, opening exciting possibilities for new developments in some long standing open problems.
Summary
The goal of this project is to study conformally invariant fractal structures from the perspectives of analysis, dynamics, probability, geometry and physics, emphasizing interrelations of these fields. In the last two decades such structures emerged in several areas: continuum scaling limits of 2D critical models in statistical physics (percolation, Ising model); extremal configurations for various problems in complex analysis (multifractal harmonic measures, coefficient growth of univalent maps, Brennan's conjecture); chaotic sets for complex dynamical systems (Julia sets, Kleinian groups). Capitalizing on recent successes, I plan to continue my work in these areas, exploiting their interactions and connections to physics. I intend to achieve at least some of the following goals: * To establish that several critical lattice models have conformally invariant scaling limits, by building upon results on percolation and Ising models and finding discrete holomorphic observables. * To study geometric properties of arising fractal curves and random fields by connecting them to Schramm's SLE curves and Gaussian Free Fields. * To investigate massive scaling limits by describing them geometrically with generalizations of SLEs. * To lay mathematical framework behind relevant physical notions, such as Coulomb Gas (by relating height functions to GFFs) and Quantum Gravity (by identifying limits of random planar graphs with Liouville QGs). * To improve known bounds in several old questions in complex analysis by studying multifractal spectra of harmonic measures. * To estimate extremal behavior of such spectra by using holomorphic motions of (quasi) conformal maps and thermodynamic formalism. * To understand nature of extremal multifractals for harmonic measure by studying random and dynamical fractals. The topics involved range from century old to very young ones. Recently connections between them started to emerge, opening exciting possibilities for new developments in some long standing open problems.
Max ERC Funding
1 278 000 €
Duration
Start date: 2009-01-01, End date: 2013-12-31
Project acronym EQUIARITH
Project Equidistribution in number theory
Researcher (PI) Philippe Michel
Host Institution (HI) ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary The purpose of this proposal is to investigate from various perspectives some equidistribution problems associated with homogeneous spaces of arithmetic type: a typical problem (basically solved) is the distribution of the set of representations of a large integer by an integral quadratic form. Another harder problem is the study of the distribution of special points on Shimura varieties. In a different direction (linked with quantum chaos), the study of the concentration of Laplacian (Maass) eigenforms or of sections of holomorphic bundles is related to similar problems. Given X such a space and G>L the underlying algebraic group and its corresponding lattice L, the above questions boil down to studying the distribution of H-orbits x.H (or more generally H-invariant measures)on the quotient L\G for some subgroups H. This question may be studied different methods: Harmonic Analysis (HA): given a function f on L\G one studies the period integral of f along x.H. This may be done by automorphic methods. In favorable circumstances, the above periods are related to L-functions which one may hope to treat by methods from analytic number theory (the subconvexity problem). Ergodic Theory (ET): one studies the properties of weak*-limits of the measures supported by x.H using rigidity techniques: depending on the nature of H, one might use either rigidity of unipotent actions or the more recent rigidity results for torus actions in rank >1. In fact, HA and ET are intertwined and complementary : the use of ET in this context require a substantial input from number theory and HA, while ET lead to a soft understanding of several features of HA. In addition, the Langlands correspondence principle make it possible to pass from one group G to another. Based on earlier experience, our goal is to develop these interactions systematically and to develop new approaches to outstanding arithmetic problems :eg. the subconvexity problem or the Andre/Oort conjecture.
Summary
The purpose of this proposal is to investigate from various perspectives some equidistribution problems associated with homogeneous spaces of arithmetic type: a typical problem (basically solved) is the distribution of the set of representations of a large integer by an integral quadratic form. Another harder problem is the study of the distribution of special points on Shimura varieties. In a different direction (linked with quantum chaos), the study of the concentration of Laplacian (Maass) eigenforms or of sections of holomorphic bundles is related to similar problems. Given X such a space and G>L the underlying algebraic group and its corresponding lattice L, the above questions boil down to studying the distribution of H-orbits x.H (or more generally H-invariant measures)on the quotient L\G for some subgroups H. This question may be studied different methods: Harmonic Analysis (HA): given a function f on L\G one studies the period integral of f along x.H. This may be done by automorphic methods. In favorable circumstances, the above periods are related to L-functions which one may hope to treat by methods from analytic number theory (the subconvexity problem). Ergodic Theory (ET): one studies the properties of weak*-limits of the measures supported by x.H using rigidity techniques: depending on the nature of H, one might use either rigidity of unipotent actions or the more recent rigidity results for torus actions in rank >1. In fact, HA and ET are intertwined and complementary : the use of ET in this context require a substantial input from number theory and HA, while ET lead to a soft understanding of several features of HA. In addition, the Langlands correspondence principle make it possible to pass from one group G to another. Based on earlier experience, our goal is to develop these interactions systematically and to develop new approaches to outstanding arithmetic problems :eg. the subconvexity problem or the Andre/Oort conjecture.
Max ERC Funding
866 000 €
Duration
Start date: 2008-12-01, End date: 2013-11-30
Project acronym FIRM
Project Mathematical Methods for Financial Risk Management
Researcher (PI) Halil Mete Soner
Host Institution (HI) EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary Since the pioneering works of Black & Scholes, Merton and Markowitch, sophisticated quantitative methods are being used to introduce more complex financial products each year. However, this exciting increase in the complexity forces the industry to engage in proper risk management practices. The recent financial crisis emanating from risky loan practices is a prime example of this acute need. This proposal focuses exactly on this general problem. We will develop mathematical techniques to measure and assess the financial risk of new instruments. In the theoretical direction, we will expand the scope of recent studies on risk measures of Artzner et-al., and the stochastic representation formulae proved by the principal investigator and his collaborators. The core research team consists of mathematicians and the finance faculty. The newly created state-of-the-art finance laboratory at the host institution will have direct access to financial data. Moreover, executive education that is performed in this unit enables the research group to have close contacts with high level executives of the financial industry. The theoretical side of the project focuses on nonlinear partial differential equations (PDE), backward stochastic differential equations (BSDE) and dynamic risk measures. Already a deep connection between BSDEs and dynamic risk measures is developed by Peng, Delbaen and collaborators. Also, the principal investigator and his collaborators developed connections to PDEs. In this project, we further investigate these connections. Chief goals of this project are theoretical results and computational techniques in the general areas of BSDEs, fully nonlinear PDEs, and the development of risk management practices that are acceptable by the industry. The composition of the research team and our expertise in quantitative methods, well position us to effectively formulate and study theoretical problems with financial impact.
Summary
Since the pioneering works of Black & Scholes, Merton and Markowitch, sophisticated quantitative methods are being used to introduce more complex financial products each year. However, this exciting increase in the complexity forces the industry to engage in proper risk management practices. The recent financial crisis emanating from risky loan practices is a prime example of this acute need. This proposal focuses exactly on this general problem. We will develop mathematical techniques to measure and assess the financial risk of new instruments. In the theoretical direction, we will expand the scope of recent studies on risk measures of Artzner et-al., and the stochastic representation formulae proved by the principal investigator and his collaborators. The core research team consists of mathematicians and the finance faculty. The newly created state-of-the-art finance laboratory at the host institution will have direct access to financial data. Moreover, executive education that is performed in this unit enables the research group to have close contacts with high level executives of the financial industry. The theoretical side of the project focuses on nonlinear partial differential equations (PDE), backward stochastic differential equations (BSDE) and dynamic risk measures. Already a deep connection between BSDEs and dynamic risk measures is developed by Peng, Delbaen and collaborators. Also, the principal investigator and his collaborators developed connections to PDEs. In this project, we further investigate these connections. Chief goals of this project are theoretical results and computational techniques in the general areas of BSDEs, fully nonlinear PDEs, and the development of risk management practices that are acceptable by the industry. The composition of the research team and our expertise in quantitative methods, well position us to effectively formulate and study theoretical problems with financial impact.
Max ERC Funding
880 560 €
Duration
Start date: 2008-12-01, End date: 2013-11-30
Project acronym GUTDROSO
Project Gut immunity and homeostasis in Drosophila
Researcher (PI) Bruno Lemaitre
Host Institution (HI) ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Call Details Advanced Grant (AdG), LS6, ERC-2008-AdG
Summary The gut is the major interface between microbes and their animal hosts and constitutes the main entry route for pathogens. As a consequence gut cells must be armed with efficient immune defenses to combat invasion and colonisation by pathogens. However, the gut also harbors a flora of commensal bacteria, with potentially beneficial effects for the host, which must be tolerated without a chronic, and harmful, immune response. In recent years Drosophila has emerged as a powerful model to dissect host-pathogen interactions, leading to the paradigm of antimicrobial peptide regulation by the Toll and Imd signaling pathways. The strength of this model derives from the availability of powerful and cost effective genetic and genomic tools as well as the high degree of similarities to vertebrate innate immunity. However, in spite of growing interest in gut mucosal immunity generally, very little is known about the immune response of the Drosophila gut. Using powerful new tools and those developed in the study of the systemic response, we propose to raise our understanding of Drosophila gut immunity to the same level as that of systemic immunity within the next five years. This project will involve integrated approaches to dissect not only the gut immune response but also gut homeostasis in the presence of commensal microbiota, as well as strategies used by entomopathogens to circumvent these defenses. We believe that the fundamental knowledge generated on Drosophila gut immunity will serve as a paradigm of epithelial immune reactivity and have a wider impact on our comprehension of animal defense mechanisms.
Summary
The gut is the major interface between microbes and their animal hosts and constitutes the main entry route for pathogens. As a consequence gut cells must be armed with efficient immune defenses to combat invasion and colonisation by pathogens. However, the gut also harbors a flora of commensal bacteria, with potentially beneficial effects for the host, which must be tolerated without a chronic, and harmful, immune response. In recent years Drosophila has emerged as a powerful model to dissect host-pathogen interactions, leading to the paradigm of antimicrobial peptide regulation by the Toll and Imd signaling pathways. The strength of this model derives from the availability of powerful and cost effective genetic and genomic tools as well as the high degree of similarities to vertebrate innate immunity. However, in spite of growing interest in gut mucosal immunity generally, very little is known about the immune response of the Drosophila gut. Using powerful new tools and those developed in the study of the systemic response, we propose to raise our understanding of Drosophila gut immunity to the same level as that of systemic immunity within the next five years. This project will involve integrated approaches to dissect not only the gut immune response but also gut homeostasis in the presence of commensal microbiota, as well as strategies used by entomopathogens to circumvent these defenses. We believe that the fundamental knowledge generated on Drosophila gut immunity will serve as a paradigm of epithelial immune reactivity and have a wider impact on our comprehension of animal defense mechanisms.
Max ERC Funding
1 485 627 €
Duration
Start date: 2009-04-01, End date: 2014-03-31
Project acronym MATHCARD
Project Mathematical Modelling and Simulation of the Cardiovascular System
Researcher (PI) Alfio Quarteroni
Host Institution (HI) ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary This research project aims at the development, analysis and computer implementation of mathematical models of the cardiovascular system. Our goal is to describe and simulate the anatomic structure and the physiological response of the human cardiovascular system in healthy or diseased states. This demands to address many fundamental issues. Blood flow interacts both mechanically and chemically with the vessel walls and tissue, giving rise to complex fluid-structure interaction problems. The mathematical analysis of these problems is complicated and the related numerical analysis difficult. We propose to extend the recently achieved results on blood flow simulations by directing our analysis in several new directions. Our goal is to encompass aspects of metabolic regulation, micro-circulation, the electrical and mechanical activity of the heart, and their interactions. Modelling and optimisation of drugs delivery in clinical diseases will be addressed as well. This requires the understanding of transport, diffusion and reaction processes within the blood and organs of the body. The emphasis of this project will be put on mathematical modelling, numerical analysis, algorithm implementation, computational efficiency, validation and verification. Our purpose is to set up a mathematical simulation platform eventually leading to the improvement of vascular diseases diagnosis, setting up of surgical planning, and cure of inflammatory processes in the circulatory system. This platform might also help physicians to construct and evaluate combined anatomic/physiological models to predict the outcome of alternative treatment plans for individual patients.
Summary
This research project aims at the development, analysis and computer implementation of mathematical models of the cardiovascular system. Our goal is to describe and simulate the anatomic structure and the physiological response of the human cardiovascular system in healthy or diseased states. This demands to address many fundamental issues. Blood flow interacts both mechanically and chemically with the vessel walls and tissue, giving rise to complex fluid-structure interaction problems. The mathematical analysis of these problems is complicated and the related numerical analysis difficult. We propose to extend the recently achieved results on blood flow simulations by directing our analysis in several new directions. Our goal is to encompass aspects of metabolic regulation, micro-circulation, the electrical and mechanical activity of the heart, and their interactions. Modelling and optimisation of drugs delivery in clinical diseases will be addressed as well. This requires the understanding of transport, diffusion and reaction processes within the blood and organs of the body. The emphasis of this project will be put on mathematical modelling, numerical analysis, algorithm implementation, computational efficiency, validation and verification. Our purpose is to set up a mathematical simulation platform eventually leading to the improvement of vascular diseases diagnosis, setting up of surgical planning, and cure of inflammatory processes in the circulatory system. This platform might also help physicians to construct and evaluate combined anatomic/physiological models to predict the outcome of alternative treatment plans for individual patients.
Max ERC Funding
1 810 992 €
Duration
Start date: 2009-01-01, End date: 2014-06-30
Project acronym NANOIMMUNE
Project Nanoparticle Vaccines: At the interface of bionanotechnology and adaptive immunity
Researcher (PI) Jeffrey Hubbell
Host Institution (HI) ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Call Details Advanced Grant (AdG), LS6, ERC-2008-AdG
Summary We have recently developed a bionanotechnology approach to vaccination (Reddy et al., Nature Biotechnology, 25, 1159-1164, 2007): degradable polymeric nanoparticles are designed that: (i) are so small that they can enter the lymphatic circulation by biophysical means; (ii) are efficiently taken up by a large fraction of dendritic cells (DCs) that are resident in the lymph node that drains the injection site; (iii) activate the complement cascade and provide a potent, yet safe, activation signal to those DCs; and (iv) thereby induce a potent, Th1 adaptive immune response to antigen bound to the nanoparticles, with the generation of both antibodies and cytotoxic T lymphocytes. In the present project, we focus on next-generation bionanotechnology vaccine platforms for vaccination. We propose three technological advances, and we propose to demonstrate those three advances in definitive models in the mouse. Specifically, we propose to (Specific Aim 1) evaluate the current approach of complement-mediated DC activation in breaking tolerance to a chronic viral infection (hepatitis B virus, HBV, targeting hepatitis B virus surface antigen, HBsAg) and to combine complement as a danger signal with other nanoparticle-borne danger signals to develop an effective bionanotechnological platform for therapeutic antiviral vaccination; (Specific Aim 2) to develop a new, ultrasmall nanoparticle implementation suitable for delivery of DNA to lymph node-resident DCs, also activating them, to enable more efficient DNA vaccination; and (Specific Aim 3) to develop an ultrasmall nanoparticle implementation suitable for delivery of DNA to DCs resident within the sublingual mucosa, also activating them, to enable efficient DNA mucosal vaccination. The Specific Aim addressing the oral mucosa will begin with HBsAg, to allow comparison to other routes of administration, and will then proceed to antigens from influenza A.
Summary
We have recently developed a bionanotechnology approach to vaccination (Reddy et al., Nature Biotechnology, 25, 1159-1164, 2007): degradable polymeric nanoparticles are designed that: (i) are so small that they can enter the lymphatic circulation by biophysical means; (ii) are efficiently taken up by a large fraction of dendritic cells (DCs) that are resident in the lymph node that drains the injection site; (iii) activate the complement cascade and provide a potent, yet safe, activation signal to those DCs; and (iv) thereby induce a potent, Th1 adaptive immune response to antigen bound to the nanoparticles, with the generation of both antibodies and cytotoxic T lymphocytes. In the present project, we focus on next-generation bionanotechnology vaccine platforms for vaccination. We propose three technological advances, and we propose to demonstrate those three advances in definitive models in the mouse. Specifically, we propose to (Specific Aim 1) evaluate the current approach of complement-mediated DC activation in breaking tolerance to a chronic viral infection (hepatitis B virus, HBV, targeting hepatitis B virus surface antigen, HBsAg) and to combine complement as a danger signal with other nanoparticle-borne danger signals to develop an effective bionanotechnological platform for therapeutic antiviral vaccination; (Specific Aim 2) to develop a new, ultrasmall nanoparticle implementation suitable for delivery of DNA to lymph node-resident DCs, also activating them, to enable more efficient DNA vaccination; and (Specific Aim 3) to develop an ultrasmall nanoparticle implementation suitable for delivery of DNA to DCs resident within the sublingual mucosa, also activating them, to enable efficient DNA mucosal vaccination. The Specific Aim addressing the oral mucosa will begin with HBsAg, to allow comparison to other routes of administration, and will then proceed to antigens from influenza A.
Max ERC Funding
2 499 425 €
Duration
Start date: 2009-05-01, End date: 2014-04-30
Project acronym VIRNA
Project Cellular biology of virus infection
Researcher (PI) Ari Helenius
Host Institution (HI) EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Call Details Advanced Grant (AdG), LS6, ERC-2008-AdG
Summary Viruses are simple, obligatory, intracellular parasites that depend on the host cell for most of the steps in the replication cycle. Not only do they rely on the cells biosynthetic machinery, they exploit cellular processes for signaling, membrane trafficking, intra-cellular transport, nuclear import and export, molecular sorting, transcriptional regulation, etc. To access the full spectrum of host cell functions in the infection of three different viruses in an unbiased and systematic fashion, we will identify the critical host cell proteins needed by monitoring infection in human tissue culture cells after silencing individual genes using genome-wide siRNA libraries and large sub-libraries based on the human genome. The three viruses are vaccinia virus (a poxvirus), human papilloma virus 16, and Uukuniemi virus (a bunyavirus). They are members of important but poorly analyzed pathogen families representing enveloped and nonenveloped viruses, RNA and DNA viruses, viruses that replicate in the nucleus and in the cytosol. The infection assays to be used are fully automated, and make use of high-content microscopic read-outs for infection and virus production. Identification of the viral infectomes , in this way, offers a valuable, new perspective into the complexities of the infection process, and opens wide new areas of basic and applied research. After validation of hits , extensive biochemical and cell biological analysis will be performed on a selected set of host proteins and pathways identified through the infectome analysis. We will determine which steps in the replication cycle are affected, which mechanisms are involved, and which cellular pathways play a role. For detailed analysis, we will focus on mechanisms in entry, uncoating, and early intracellular events. A large spectrum of techniques including live cell imaging and single particle tracking will be used to follow up the screening results with functional and mechanistic studies.
Summary
Viruses are simple, obligatory, intracellular parasites that depend on the host cell for most of the steps in the replication cycle. Not only do they rely on the cells biosynthetic machinery, they exploit cellular processes for signaling, membrane trafficking, intra-cellular transport, nuclear import and export, molecular sorting, transcriptional regulation, etc. To access the full spectrum of host cell functions in the infection of three different viruses in an unbiased and systematic fashion, we will identify the critical host cell proteins needed by monitoring infection in human tissue culture cells after silencing individual genes using genome-wide siRNA libraries and large sub-libraries based on the human genome. The three viruses are vaccinia virus (a poxvirus), human papilloma virus 16, and Uukuniemi virus (a bunyavirus). They are members of important but poorly analyzed pathogen families representing enveloped and nonenveloped viruses, RNA and DNA viruses, viruses that replicate in the nucleus and in the cytosol. The infection assays to be used are fully automated, and make use of high-content microscopic read-outs for infection and virus production. Identification of the viral infectomes , in this way, offers a valuable, new perspective into the complexities of the infection process, and opens wide new areas of basic and applied research. After validation of hits , extensive biochemical and cell biological analysis will be performed on a selected set of host proteins and pathways identified through the infectome analysis. We will determine which steps in the replication cycle are affected, which mechanisms are involved, and which cellular pathways play a role. For detailed analysis, we will focus on mechanisms in entry, uncoating, and early intracellular events. A large spectrum of techniques including live cell imaging and single particle tracking will be used to follow up the screening results with functional and mechanistic studies.
Max ERC Funding
2 498 400 €
Duration
Start date: 2009-02-01, End date: 2014-01-31
