Project acronym ADIPODIF
Project Adipocyte Differentiation and Metabolic Functions in Obesity and Type 2 Diabetes
Researcher (PI) Christian Wolfrum
Host Institution (HI) EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Call Details Starting Grant (StG), LS6, ERC-2007-StG
Summary Obesity associated disorders such as T2D, hypertension and CVD, commonly referred to as the “metabolic syndrome”, are prevalent diseases of industrialized societies. Deranged adipose tissue proliferation and differentiation contribute significantly to the development of these metabolic disorders. Comparatively little however is known, about how these processes influence the development of metabolic disorders. Using a multidisciplinary approach, I plan to elucidate molecular mechanisms underlying the altered adipocyte differentiation and maturation in different models of obesity associated metabolic disorders. Special emphasis will be given to the analysis of gene expression, postranslational modifications and lipid molecular species composition. To achieve this goal, I am establishing several novel methods to isolate pure primary preadipocytes including a new animal model that will allow me to monitor preadipocytes, in vivo and track their cellular fate in the context of a complete organism. These systems will allow, for the first time to study preadipocyte biology, in an in vivo setting. By monitoring preadipocyte differentiation in vivo, I will also be able to answer the key questions regarding the development of preadipocytes and examine signals that induce or inhibit their differentiation. Using transplantation techniques, I will elucidate the genetic and environmental contributions to the progression of obesity and its associated metabolic disorders. Furthermore, these studies will integrate a lipidomics approach to systematically analyze lipid molecular species composition in different models of metabolic disorders. My studies will provide new insights into the mechanisms and dynamics underlying adipocyte differentiation and maturation, and relate them to metabolic disorders. Detailed knowledge of these mechanisms will facilitate development of novel therapeutic approaches for the treatment of obesity and associated metabolic disorders.
Summary
Obesity associated disorders such as T2D, hypertension and CVD, commonly referred to as the “metabolic syndrome”, are prevalent diseases of industrialized societies. Deranged adipose tissue proliferation and differentiation contribute significantly to the development of these metabolic disorders. Comparatively little however is known, about how these processes influence the development of metabolic disorders. Using a multidisciplinary approach, I plan to elucidate molecular mechanisms underlying the altered adipocyte differentiation and maturation in different models of obesity associated metabolic disorders. Special emphasis will be given to the analysis of gene expression, postranslational modifications and lipid molecular species composition. To achieve this goal, I am establishing several novel methods to isolate pure primary preadipocytes including a new animal model that will allow me to monitor preadipocytes, in vivo and track their cellular fate in the context of a complete organism. These systems will allow, for the first time to study preadipocyte biology, in an in vivo setting. By monitoring preadipocyte differentiation in vivo, I will also be able to answer the key questions regarding the development of preadipocytes and examine signals that induce or inhibit their differentiation. Using transplantation techniques, I will elucidate the genetic and environmental contributions to the progression of obesity and its associated metabolic disorders. Furthermore, these studies will integrate a lipidomics approach to systematically analyze lipid molecular species composition in different models of metabolic disorders. My studies will provide new insights into the mechanisms and dynamics underlying adipocyte differentiation and maturation, and relate them to metabolic disorders. Detailed knowledge of these mechanisms will facilitate development of novel therapeutic approaches for the treatment of obesity and associated metabolic disorders.
Max ERC Funding
1 607 105 €
Duration
Start date: 2008-07-01, End date: 2013-06-30
Project acronym BIOSTRUCT
Project Multiscale mathematical modelling of dynamics of structure formation in cell systems
Researcher (PI) Anna Marciniak-Czochra
Host Institution (HI) RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG
Call Details Starting Grant (StG), PE1, ERC-2007-StG
Summary The aim of this transdisciplinary project is to develop and analyse multiscale mathematical models of pattern formation in multicellular systems controlled by the dynamics of intracellular signalling pathways and cell-to-cell communication and to develop new mathematical methods for the modelling of such complex processes. This aim will be achieved through a close collaboration with experimental groups and comprehensive analytical investigations of the mathematical problems arising in the modelling of these biological processes. The mathematical methods and techniques to be employed will be the analysis of systems of partial differential equations, asymptotic analysis, as well as methods of dynamical systems. These techniques will be used to formulate the models and to study the spatio-temporal behaviour of solutions, especially stability and dependence on characteristic scales, geometry, initial data and key parameters. Advanced numerical methods will be applied to simulate the models. This comprehensive methodology goes beyond the state-of-the-art, since usually the analyses are limited to a single aspect of model behaviour. Groundbreaking impacts envisioned are threefold: (i) The project will contribute to the understanding of mechanisms of structure formation in the developmental process, in the context of recently discovered signalling pathways. In addition, some of the factors and mechanisms playing a role in developmental processes, such as Wnt signalling, are implicated in carcinogenesis, for instance colon and lung cancer. (ii) Accurate quantitative and predictive mathematical models of cell proliferation and differentiation are important for the control of tumour growth and tissue egeneration; (iii) Qualitative analysis of multiscale mathematical models of biological phenomena generates challenging mathematical problems and, therefore, the project will lead to the development of new mathematical theories and tools.
Summary
The aim of this transdisciplinary project is to develop and analyse multiscale mathematical models of pattern formation in multicellular systems controlled by the dynamics of intracellular signalling pathways and cell-to-cell communication and to develop new mathematical methods for the modelling of such complex processes. This aim will be achieved through a close collaboration with experimental groups and comprehensive analytical investigations of the mathematical problems arising in the modelling of these biological processes. The mathematical methods and techniques to be employed will be the analysis of systems of partial differential equations, asymptotic analysis, as well as methods of dynamical systems. These techniques will be used to formulate the models and to study the spatio-temporal behaviour of solutions, especially stability and dependence on characteristic scales, geometry, initial data and key parameters. Advanced numerical methods will be applied to simulate the models. This comprehensive methodology goes beyond the state-of-the-art, since usually the analyses are limited to a single aspect of model behaviour. Groundbreaking impacts envisioned are threefold: (i) The project will contribute to the understanding of mechanisms of structure formation in the developmental process, in the context of recently discovered signalling pathways. In addition, some of the factors and mechanisms playing a role in developmental processes, such as Wnt signalling, are implicated in carcinogenesis, for instance colon and lung cancer. (ii) Accurate quantitative and predictive mathematical models of cell proliferation and differentiation are important for the control of tumour growth and tissue egeneration; (iii) Qualitative analysis of multiscale mathematical models of biological phenomena generates challenging mathematical problems and, therefore, the project will lead to the development of new mathematical theories and tools.
Max ERC Funding
750 000 €
Duration
Start date: 2008-09-01, End date: 2013-08-31
Project acronym DC-LYMPH
Project The Role of Lymphatic Vessels in Dendritic Cell Homing and Maturation
Researcher (PI) Melody A. Swartz
Host Institution (HI) ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Call Details Starting Grant (StG), LS3, ERC-2007-StG
Summary Dendritic cell (DC) activation and homing from the periphery to lymph nodes is a critical first event in the immune response. It involves upregulation of the chemokine receptor CCR7 and chemoinvasion towards lymphatic vessels. Despite its critical importance in adaptive immunity, the mechanisms of DC migration towards and entry into lymphatics are still poorly understood; this severely limits new therapeutic strategies for immunomodulation and even strategies for treating lymphedema, which is exacerbated by poor immune functioning. We propose a battery of physiological, cell-biological, molecular, and computational studies to determine both the mechanisms of DC homing to lymphatic vessels and how DCs modulate lymphatic function. We approach this from the perspectives of both the DC and the lymphatic vessel. Regarding the DC, we will examine computationally and experimentally how draining flows toward the lymphatic alter their migration tactics and test our hypothesis that DCs possess a biomolecular flow-detector network (which we refer to as autologous chemotaxis) and are thus able to sense the direction of the subtle flow of fluid toward the lymphatics. Regarding the lymphatic vessel, we will elucidate how biochemical and biophysical inflammatory signals regulate their drainage function, alter cell-cell adhesions and overall permeability, and alter adhesion receptors to facilitate DC homing and entry. Finally, we will examine DC migration in mice with dysfunctional lymphatics and explore strategies to improve immune response. These will be carried out in 4 main projects, and will complement our recent work in lymphatic functional biology as well as our more therapeutic investigations in DC targeting and activation (Reddy et al., Nature Biotechnol., 2007). This deeper knowledge of mechanisms of DC-lymphatic cross-talk in a relevant biophysical context will enable our long-term goal of rational design for therapeutic immunomodulation and lymphedema.
Summary
Dendritic cell (DC) activation and homing from the periphery to lymph nodes is a critical first event in the immune response. It involves upregulation of the chemokine receptor CCR7 and chemoinvasion towards lymphatic vessels. Despite its critical importance in adaptive immunity, the mechanisms of DC migration towards and entry into lymphatics are still poorly understood; this severely limits new therapeutic strategies for immunomodulation and even strategies for treating lymphedema, which is exacerbated by poor immune functioning. We propose a battery of physiological, cell-biological, molecular, and computational studies to determine both the mechanisms of DC homing to lymphatic vessels and how DCs modulate lymphatic function. We approach this from the perspectives of both the DC and the lymphatic vessel. Regarding the DC, we will examine computationally and experimentally how draining flows toward the lymphatic alter their migration tactics and test our hypothesis that DCs possess a biomolecular flow-detector network (which we refer to as autologous chemotaxis) and are thus able to sense the direction of the subtle flow of fluid toward the lymphatics. Regarding the lymphatic vessel, we will elucidate how biochemical and biophysical inflammatory signals regulate their drainage function, alter cell-cell adhesions and overall permeability, and alter adhesion receptors to facilitate DC homing and entry. Finally, we will examine DC migration in mice with dysfunctional lymphatics and explore strategies to improve immune response. These will be carried out in 4 main projects, and will complement our recent work in lymphatic functional biology as well as our more therapeutic investigations in DC targeting and activation (Reddy et al., Nature Biotechnol., 2007). This deeper knowledge of mechanisms of DC-lymphatic cross-talk in a relevant biophysical context will enable our long-term goal of rational design for therapeutic immunomodulation and lymphedema.
Max ERC Funding
1 730 966 €
Duration
Start date: 2008-05-01, End date: 2013-04-30
Project acronym HA-NFKB-VILI
Project Hypercapnic Acidosis and NF-kB in Ventilator Induced Lung Injury: Developing strategies to minimize lung injury and facilitate repair
Researcher (PI) John Laffey
Host Institution (HI) NATIONAL UNIVERSITY OF IRELAND GALWAY
Call Details Starting Grant (StG), LS6, ERC-2007-StG
Summary Acute Respiratory Distress Syndrome and Acute Lung Injury [ALI/ARDS] are devastating diseases, causing over 20,000 deaths annually in the US. Mechanical ventilation may worsen ALI/ARDS, a process termed Ventilator Induced Lung Injury [VILI]. Hypercapnic acidosis (HA) is a central component of lung ventilatory strategies to minimize VILI, and is a potent biologic agent, exerting a myriad of effects on diverse biologic pathways. Deliberately induced HA is protective in multiple lung injury models. However, HA may inhibit the host response to bacterial sepsis. Furthermore, HA may retard the repair process and slow recovery following ALI/ARDS. Hence, the diverse biologic actions of HA may result in net beneficial – or deleterious – effects depending on the specific context. An alternative approach is to manipulate a single key effector pathway, central to the protective effects of HA, which would also be effective in patients in whom hypercapnia is contra-indicated. Hypercapnia attenuates NF-kB activation, and may exert its effects – both beneficial and deleterious – via this mechanism. NF-kB is a pivotal regulator of the pro-inflammatory response, but is also a key epithelial cytoprotectant. Selective modulation of the NF-kB pathway, at the pulmonary epithelial surface, may accentuate the beneficial effects of HA on injury but minimize the potential for delayed tissue repair. We will investigate the contribution of NF-kB to the effects of HA, and characterize the direct effects modulation of NF-kB, in both in vitro and preclinical models of lung injury and repair. We will utilize pulmonary gene therapy, which facilitates delivery of high quantities of the therapeutic agent directly to the injury site, to maximize the potential for therapeutic benefit. These studies will provide novel insights into: key pathways contributing to lung injury and to repair; the role of HA and NF-kB in these processes; and the potential of pulmonary gene therapy in ALI/ARDS.
Summary
Acute Respiratory Distress Syndrome and Acute Lung Injury [ALI/ARDS] are devastating diseases, causing over 20,000 deaths annually in the US. Mechanical ventilation may worsen ALI/ARDS, a process termed Ventilator Induced Lung Injury [VILI]. Hypercapnic acidosis (HA) is a central component of lung ventilatory strategies to minimize VILI, and is a potent biologic agent, exerting a myriad of effects on diverse biologic pathways. Deliberately induced HA is protective in multiple lung injury models. However, HA may inhibit the host response to bacterial sepsis. Furthermore, HA may retard the repair process and slow recovery following ALI/ARDS. Hence, the diverse biologic actions of HA may result in net beneficial – or deleterious – effects depending on the specific context. An alternative approach is to manipulate a single key effector pathway, central to the protective effects of HA, which would also be effective in patients in whom hypercapnia is contra-indicated. Hypercapnia attenuates NF-kB activation, and may exert its effects – both beneficial and deleterious – via this mechanism. NF-kB is a pivotal regulator of the pro-inflammatory response, but is also a key epithelial cytoprotectant. Selective modulation of the NF-kB pathway, at the pulmonary epithelial surface, may accentuate the beneficial effects of HA on injury but minimize the potential for delayed tissue repair. We will investigate the contribution of NF-kB to the effects of HA, and characterize the direct effects modulation of NF-kB, in both in vitro and preclinical models of lung injury and repair. We will utilize pulmonary gene therapy, which facilitates delivery of high quantities of the therapeutic agent directly to the injury site, to maximize the potential for therapeutic benefit. These studies will provide novel insights into: key pathways contributing to lung injury and to repair; the role of HA and NF-kB in these processes; and the potential of pulmonary gene therapy in ALI/ARDS.
Max ERC Funding
1 052 556 €
Duration
Start date: 2009-01-01, End date: 2013-12-31
Project acronym IWASAWA
Project Iwasawa theory of p-adic Lie extensions
Researcher (PI) Otmar Venjakob
Host Institution (HI) RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG
Call Details Starting Grant (StG), PE1, ERC-2007-StG
Summary One of the most challenging topics in modern number theory is the mysterious relation between special values of L-functions and Galois cohomology: they are the “shadows” in the two completely different worlds of complex and p-adic analysis of one and the same geometric object, viz the space of solutions for a given diophantine equation over the integral numbers, or more generally a motive M. The main idea of Iwasawa theory is to study manifestations of this principle such as the class number formula or the Birch and Swinnerton Dyer Conjecture simultaneously for whole p-adic families of such motives, which arise e.g. by considering towers of number fields or by (Hida) families of modular forms. The aim of this project is to supply further evidence for I. the existence of p-adic L-functions and for main conjectures in (non-commutative) Iwasawa theory, II. the (equivariant) epsilon-conjecture of Fukaya and Kato as well as III. the 2-variable main conjecture of Hida families. In particular, we hope to construct the first genuine “non-commutative” p-adic L-function as well as to find (non-commutative) examples fulfilling the expectation that the epsilon-constants, which are determined by the functional equations of the corresponding L-functions, build p-adic families themselves. In the third item a systematic study of Lie groups over pro-p-rings and Big Galois representations is planned with applications to the arithmetic of Hida families.
Summary
One of the most challenging topics in modern number theory is the mysterious relation between special values of L-functions and Galois cohomology: they are the “shadows” in the two completely different worlds of complex and p-adic analysis of one and the same geometric object, viz the space of solutions for a given diophantine equation over the integral numbers, or more generally a motive M. The main idea of Iwasawa theory is to study manifestations of this principle such as the class number formula or the Birch and Swinnerton Dyer Conjecture simultaneously for whole p-adic families of such motives, which arise e.g. by considering towers of number fields or by (Hida) families of modular forms. The aim of this project is to supply further evidence for I. the existence of p-adic L-functions and for main conjectures in (non-commutative) Iwasawa theory, II. the (equivariant) epsilon-conjecture of Fukaya and Kato as well as III. the 2-variable main conjecture of Hida families. In particular, we hope to construct the first genuine “non-commutative” p-adic L-function as well as to find (non-commutative) examples fulfilling the expectation that the epsilon-constants, which are determined by the functional equations of the corresponding L-functions, build p-adic families themselves. In the third item a systematic study of Lie groups over pro-p-rings and Big Galois representations is planned with applications to the arithmetic of Hida families.
Max ERC Funding
500 000 €
Duration
Start date: 2008-07-01, End date: 2013-06-30
Project acronym LUEDDE-MED3-AACHEN
Project The Function of inflammatory signalling pathways in acute and chronic liver disease and liver cancer
Researcher (PI) Tom Luedde
Host Institution (HI) UNIVERSITAETSKLINIKUM AACHEN
Call Details Starting Grant (StG), LS6, ERC-2007-StG
Summary The aim of this proposal is to examine the role of inflammatory signalling pathways in murine models of liver and biliary disease by application of conditional gene targeting using cre/loxP technology. Previous studies have provided evidence that the NF-kB pathway and its activating kinase complex – consisting of three subunits: IKK1, IKK2 and NEMO – are crucial regulators of liver physiology and pathology, but their differential, cell specific functions in the liver are currently only poorly understood. The first part of this proposal will focus on the evaluation of molecular mechanisms underlying the development of hepatocellular carcinoma in a setting of chronic hepatitis. By using a novel mouse model of spontaneous liver cancer based on conditional deletion of NEMO in hepatocytes, the functions of cytokines, specific intracellular signalling pathways, the innate and adaptive immune system and the role of hepatic stem cells in hepatitis and carcinogenesis will be examined. In the second part of this proposal, we will extend these studies by evaluating the function of NEMO/NF-kB in other hepatic cell compartments, specifically the function of NEMO in hepatic stellate cells and liver fibrosis, the endothelial function of NEMO/NF-kB in an in vivo model of hepatic ischemia-reperfusion injury and the role of the NF-kB pathway in biliary epithelial cells and inflammatory biliary diseases. Finally, in the third part of this proposal we will analyse the unknown intrahepatic role of non-canonical, IKK1-dependent signalling pathways and the function of TAK1 – a molecule at the interface between inflammatory and developmental pathways – in liver injury, fatty-liver-disease and insulin-resistance. Knowledge gained by these studies and the further understanding of the cell specific hepatic function of NF-kB and related pathways might build the basis for the development of novel pharmacological approaches for the future treatment of liver diseases and cancer in humans.
Summary
The aim of this proposal is to examine the role of inflammatory signalling pathways in murine models of liver and biliary disease by application of conditional gene targeting using cre/loxP technology. Previous studies have provided evidence that the NF-kB pathway and its activating kinase complex – consisting of three subunits: IKK1, IKK2 and NEMO – are crucial regulators of liver physiology and pathology, but their differential, cell specific functions in the liver are currently only poorly understood. The first part of this proposal will focus on the evaluation of molecular mechanisms underlying the development of hepatocellular carcinoma in a setting of chronic hepatitis. By using a novel mouse model of spontaneous liver cancer based on conditional deletion of NEMO in hepatocytes, the functions of cytokines, specific intracellular signalling pathways, the innate and adaptive immune system and the role of hepatic stem cells in hepatitis and carcinogenesis will be examined. In the second part of this proposal, we will extend these studies by evaluating the function of NEMO/NF-kB in other hepatic cell compartments, specifically the function of NEMO in hepatic stellate cells and liver fibrosis, the endothelial function of NEMO/NF-kB in an in vivo model of hepatic ischemia-reperfusion injury and the role of the NF-kB pathway in biliary epithelial cells and inflammatory biliary diseases. Finally, in the third part of this proposal we will analyse the unknown intrahepatic role of non-canonical, IKK1-dependent signalling pathways and the function of TAK1 – a molecule at the interface between inflammatory and developmental pathways – in liver injury, fatty-liver-disease and insulin-resistance. Knowledge gained by these studies and the further understanding of the cell specific hepatic function of NF-kB and related pathways might build the basis for the development of novel pharmacological approaches for the future treatment of liver diseases and cancer in humans.
Max ERC Funding
1 600 356 €
Duration
Start date: 2008-09-01, End date: 2014-08-31
Project acronym MICROFLEX
Project Microbiology of Dehalococcoides-like Chloroflexi
Researcher (PI) Lorenz Adrian
Host Institution (HI) HELMHOLTZ-ZENTRUM FUR UMWELTFORSCHUNG GMBH - UFZ
Call Details Starting Grant (StG), LS3, ERC-2007-StG
Summary I propose to initiate research on a specific group of bacteria, here denominated as the “Dehalococcoides-like Chloroflexi”. This group of bacteria is formed by several cultivated strains of the genus Dehalococcoides and many sequences of uncultivated organisms mostly from marine sediment or subsurface locations. All together form one subphylum of the Chloroflexi. Bacteria of the Dehalococcoides-like Chloroflexi are of particular importance for two independent reasons: first, the subphylum contains all bacteria known to transform under anaerobic conditions toxic and persistent halogenated compounds such as chlorinated dioxins, benzenes, biphenyls, vinyl chloride or brominated biphenylethers; secondly, massive amounts of Dehalococcoides-like Chloroflexi have recently been detected in marine organic-rich deep sediments dominating the populations with up to 80% of the total cell counts. However, many aspects of the physiology of Dehalococcoides species are unclear and almost nothing is known about Chloroflexi in deep sediments. I have worked for many years on the microbiology, biochemistry and genomics of Dehalococcoides species. With the proposed group I plan to focus on the physiological links between Chloroflexi in contaminated aquifers and those in marine sediments. Initially, cultures of marine sediment-Chloroflexi will be established in our lab and compared with pure Dehalococcoides strains. Objectives of our research towards marine Chloroflexi will be the description of the physiology, of the biochemistry of energy conservation and of key genes encoded in the genomes. It is anticipated that the research leads to a substantiated hypothesis on the mode of energy fixation in marine deep-sediments and an initial description of the role of Dehalococcoides-like Chloroflexi in biogeochemical cycles. We also expect to find insights into Chloroflexi evolution and their role in earth history by comparing genomes between Dehalococcoides species and marine Chloroflexi.
Summary
I propose to initiate research on a specific group of bacteria, here denominated as the “Dehalococcoides-like Chloroflexi”. This group of bacteria is formed by several cultivated strains of the genus Dehalococcoides and many sequences of uncultivated organisms mostly from marine sediment or subsurface locations. All together form one subphylum of the Chloroflexi. Bacteria of the Dehalococcoides-like Chloroflexi are of particular importance for two independent reasons: first, the subphylum contains all bacteria known to transform under anaerobic conditions toxic and persistent halogenated compounds such as chlorinated dioxins, benzenes, biphenyls, vinyl chloride or brominated biphenylethers; secondly, massive amounts of Dehalococcoides-like Chloroflexi have recently been detected in marine organic-rich deep sediments dominating the populations with up to 80% of the total cell counts. However, many aspects of the physiology of Dehalococcoides species are unclear and almost nothing is known about Chloroflexi in deep sediments. I have worked for many years on the microbiology, biochemistry and genomics of Dehalococcoides species. With the proposed group I plan to focus on the physiological links between Chloroflexi in contaminated aquifers and those in marine sediments. Initially, cultures of marine sediment-Chloroflexi will be established in our lab and compared with pure Dehalococcoides strains. Objectives of our research towards marine Chloroflexi will be the description of the physiology, of the biochemistry of energy conservation and of key genes encoded in the genomes. It is anticipated that the research leads to a substantiated hypothesis on the mode of energy fixation in marine deep-sediments and an initial description of the role of Dehalococcoides-like Chloroflexi in biogeochemical cycles. We also expect to find insights into Chloroflexi evolution and their role in earth history by comparing genomes between Dehalococcoides species and marine Chloroflexi.
Max ERC Funding
1 287 258 €
Duration
Start date: 2008-06-01, End date: 2013-12-31
Project acronym NCIRW
Project Non-classical interacting random walks
Researcher (PI) Martin Paul Wilhelm Zerner
Host Institution (HI) EBERHARD KARLS UNIVERSITAET TUEBINGEN
Call Details Starting Grant (StG), PE1, ERC-2007-StG
Summary The proposed project deals with various topics in the area of random walks (RWs) which interact with their own history and/or a possibly non-homogeneous, random environment. Such models arise from physics and other natural sciences as simplified models of complex phenomena and have recently attracted a lot of attention. They include: (a) Self-interacting RWs, i.e. RWs with memory, for example excited RWs, self-avoiding RWs, and RWs arising from two dimensional statistical mechanics models like Lorentz lattice gas models. (b) RWs in random media, for example RWs in random environments (RWRE), RWs on percolation clusters, and RWs in random potentials. Some of the problems to be considered concern recurrence and transience properties, laws of large numbers, ballistic versus sub-ballistic behavior, zero-one laws, scaling properties, other asymptotic properties, the relation between quenched and annealed behavior and monotonicity properties.
Summary
The proposed project deals with various topics in the area of random walks (RWs) which interact with their own history and/or a possibly non-homogeneous, random environment. Such models arise from physics and other natural sciences as simplified models of complex phenomena and have recently attracted a lot of attention. They include: (a) Self-interacting RWs, i.e. RWs with memory, for example excited RWs, self-avoiding RWs, and RWs arising from two dimensional statistical mechanics models like Lorentz lattice gas models. (b) RWs in random media, for example RWs in random environments (RWRE), RWs on percolation clusters, and RWs in random potentials. Some of the problems to be considered concern recurrence and transience properties, laws of large numbers, ballistic versus sub-ballistic behavior, zero-one laws, scaling properties, other asymptotic properties, the relation between quenched and annealed behavior and monotonicity properties.
Max ERC Funding
500 000 €
Duration
Start date: 2008-10-01, End date: 2014-09-30
Project acronym TQFT
Project The geometry of topological quantum field theories
Researcher (PI) Katrin Wendland
Host Institution (HI) ALBERT-LUDWIGS-UNIVERSITAET FREIBURG
Call Details Starting Grant (StG), PE1, ERC-2007-StG
Summary The predictive power of quantum field theory (QFT) is a perpetual driving force in geometry. Examples include the invention of Frobenius manifolds, mixed twistor structures, primitive forms, and harmonic bundles, up to the discovery of the McKay correspondence, mirror symmetry, and Gromov-Witten invariants. Still seemingly disparate, in fact these all are related to topological (T) QFT and thereby to the work by Cecotti, Vafa et al of more than 20 years ago. The broad aim of the proposed research is to pull the strands together which have evolved from TQFT, by implementing insights from mathematics and physics. The goal is a unified, conclusive picture of the geometry of TQFTs. Solving the fundamental questions on the underlying common structure will open new horizons for all disciplines built on TQFT. Hertling’s “TERP” structures, formally unifying the geometric ingredients, will be key. The work plan is textured into four independent strands which gain full power from their intricate interrelations. (1) To implement TQFT, a construction by Hitchin will be generalised to perform geometric quantisation for spaces with TERP structure. Quasi-classical limits and conformal blocks will be studied as well as TERP structures in the Barannikov-Kontsevich construction of Frobenius manifolds. (2) Relating to singularity theory, a complete picture is aspired, including matrix factorisation and allowing singularities of functions on complete intersections. A main new ingredient are QFT results by Martinec and Moore. (3) Incorporating D-branes, spaces of stability conditions in triangulated categories will be equipped with TERP structures. To use geometric quantisation is a novel approach which should solve the expected convergence issues. (4) For Borcherds automorphic forms and GKM algebras their as yet cryptic relation to “generalised indices” shall be demystified: In a geometric quantisation of TERP structures, generalised theta functions should appear naturally.
Summary
The predictive power of quantum field theory (QFT) is a perpetual driving force in geometry. Examples include the invention of Frobenius manifolds, mixed twistor structures, primitive forms, and harmonic bundles, up to the discovery of the McKay correspondence, mirror symmetry, and Gromov-Witten invariants. Still seemingly disparate, in fact these all are related to topological (T) QFT and thereby to the work by Cecotti, Vafa et al of more than 20 years ago. The broad aim of the proposed research is to pull the strands together which have evolved from TQFT, by implementing insights from mathematics and physics. The goal is a unified, conclusive picture of the geometry of TQFTs. Solving the fundamental questions on the underlying common structure will open new horizons for all disciplines built on TQFT. Hertling’s “TERP” structures, formally unifying the geometric ingredients, will be key. The work plan is textured into four independent strands which gain full power from their intricate interrelations. (1) To implement TQFT, a construction by Hitchin will be generalised to perform geometric quantisation for spaces with TERP structure. Quasi-classical limits and conformal blocks will be studied as well as TERP structures in the Barannikov-Kontsevich construction of Frobenius manifolds. (2) Relating to singularity theory, a complete picture is aspired, including matrix factorisation and allowing singularities of functions on complete intersections. A main new ingredient are QFT results by Martinec and Moore. (3) Incorporating D-branes, spaces of stability conditions in triangulated categories will be equipped with TERP structures. To use geometric quantisation is a novel approach which should solve the expected convergence issues. (4) For Borcherds automorphic forms and GKM algebras their as yet cryptic relation to “generalised indices” shall be demystified: In a geometric quantisation of TERP structures, generalised theta functions should appear naturally.
Max ERC Funding
750 000 €
Duration
Start date: 2009-01-01, End date: 2014-06-30