Project acronym ARIPHYHIMO
Project Arithmetic and physics of Higgs moduli spaces
Researcher (PI) Tamas Hausel
Host Institution (HI) INSTITUTE OF SCIENCE AND TECHNOLOGYAUSTRIA
Call Details Advanced Grant (AdG), PE1, ERC-2012-ADG_20120216
Summary The proposal studies problems concerning the geometry and topology of moduli spaces of Higgs bundles on a Riemann surface motivated by parallel considerations in number theory and mathematical physics. In this way the proposal bridges various duality theories in string theory with the Langlands program in number theory.
The heart of the proposal is a circle of precise conjectures relating to the topology of the moduli space of Higgs bundles. The formulation and motivations of the conjectures make direct contact with the Langlands program in number theory, various duality conjectures in string theory, algebraic combinatorics, knot theory and low dimensional topology and representation theory of quivers, finite groups and algebras of Lie type and Cherednik algebras.
Summary
The proposal studies problems concerning the geometry and topology of moduli spaces of Higgs bundles on a Riemann surface motivated by parallel considerations in number theory and mathematical physics. In this way the proposal bridges various duality theories in string theory with the Langlands program in number theory.
The heart of the proposal is a circle of precise conjectures relating to the topology of the moduli space of Higgs bundles. The formulation and motivations of the conjectures make direct contact with the Langlands program in number theory, various duality conjectures in string theory, algebraic combinatorics, knot theory and low dimensional topology and representation theory of quivers, finite groups and algebras of Lie type and Cherednik algebras.
Max ERC Funding
1 304 945 €
Duration
Start date: 2013-04-01, End date: 2018-08-31
Project acronym EMOTIONCIRCUITS
Project Circuit mechanics of emotions in the limbic system
Researcher (PI) Wulf Eckhard Haubensak
Host Institution (HI) FORSCHUNGSINSTITUT FUR MOLEKULARE PATHOLOGIE GESELLSCHAFT MBH
Call Details Starting Grant (StG), LS5, ERC-2012-StG_20111109
Summary Numerous studies established the role of the limbic system in fear and reward: it integrates sensory information, encodes emotional states and instructs other brain centers to regulate physiology and behavior. The limbic system, however, consists of many distinct and highly interconnected neuronal populations. Resolving how emotions are processed in this network at the level of single neural circuits remains a major challenge.
As entry point into the complexity of emotion circuitry, we propose to study, in exemplary fashion, how fear, as the most basic paradigm for emotions, is processed in key limbic hubs. Genetic manipulation of brain circuitry with electrophysiological methods and Pavlovian conditioning in mice, are powerful tools to explore which and how individual circuits in these hubs control emotional states, and, in turn, how genes and psychoactive drugs modulate circuit activity, emotional states and behavior.
We envision this ERC funded research to uncover general principles of the network organization of both emotions and behaviors. It is our hope that we contribute useful tools and methodological framework for investigating other brain functions in a similar manner.
Summary
Numerous studies established the role of the limbic system in fear and reward: it integrates sensory information, encodes emotional states and instructs other brain centers to regulate physiology and behavior. The limbic system, however, consists of many distinct and highly interconnected neuronal populations. Resolving how emotions are processed in this network at the level of single neural circuits remains a major challenge.
As entry point into the complexity of emotion circuitry, we propose to study, in exemplary fashion, how fear, as the most basic paradigm for emotions, is processed in key limbic hubs. Genetic manipulation of brain circuitry with electrophysiological methods and Pavlovian conditioning in mice, are powerful tools to explore which and how individual circuits in these hubs control emotional states, and, in turn, how genes and psychoactive drugs modulate circuit activity, emotional states and behavior.
We envision this ERC funded research to uncover general principles of the network organization of both emotions and behaviors. It is our hope that we contribute useful tools and methodological framework for investigating other brain functions in a similar manner.
Max ERC Funding
1 499 922 €
Duration
Start date: 2013-01-01, End date: 2018-06-30
Project acronym FRU CIRCUIT
Project Neural basis of Drosophila mating behaviours
Researcher (PI) Barry Dickson
Host Institution (HI) FORSCHUNGSINSTITUT FUR MOLEKULARE PATHOLOGIE GESELLSCHAFT MBH
Call Details Advanced Grant (AdG), LS5, ERC-2008-AdG
Summary How does information processing in neural circuits generate behaviour? Answering this question requires identifying each of the distinct neuronal types that contributes to a behaviour, defining their anatomy and connectivity, and establishing causal relationships between their activity, the activity of other neurons in the circuit, and the behaviour. Here, I propose such an analysis of the neural circuits that guide Drosophila mating behaviours. The distinct mating behaviours of males and females are genetically pre-programmed, yet can also be modified by experience. The set of ~2000 neurons that express the fru gene have been intimately linked to both male and female mating behaviours. This set of neurons includes specific sensory, central, and motor neurons, at least some of which are directly connected. Male-specific fruM isoforms configure this circuit developmentally for male rather than female behaviour. In females, mating triggers a biochemical cascade that reconfigures the circuit for post-mating rather than virgin female behaviour. We estimate that there are ~100 distinct classes of fru neuron. Using genetic and optical tools, we aim to identify each distinct class of fru neuron and to define its anatomy and connectivity. By silencing or activating specific neurons, or changing their genetic sex, we will assess their contributions to male and female behaviours, and how these perturbations impinge on activity patterns in other fru neurons. We also aim to define how a specific experience can modify the physiological properties of these circuits, and how these changes in turn modulate mating behaviour. These studies will define the operating principles of these neural circuits, contributing to a molecules-to-systems explanation of Drosophila s mating behaviours.
Summary
How does information processing in neural circuits generate behaviour? Answering this question requires identifying each of the distinct neuronal types that contributes to a behaviour, defining their anatomy and connectivity, and establishing causal relationships between their activity, the activity of other neurons in the circuit, and the behaviour. Here, I propose such an analysis of the neural circuits that guide Drosophila mating behaviours. The distinct mating behaviours of males and females are genetically pre-programmed, yet can also be modified by experience. The set of ~2000 neurons that express the fru gene have been intimately linked to both male and female mating behaviours. This set of neurons includes specific sensory, central, and motor neurons, at least some of which are directly connected. Male-specific fruM isoforms configure this circuit developmentally for male rather than female behaviour. In females, mating triggers a biochemical cascade that reconfigures the circuit for post-mating rather than virgin female behaviour. We estimate that there are ~100 distinct classes of fru neuron. Using genetic and optical tools, we aim to identify each distinct class of fru neuron and to define its anatomy and connectivity. By silencing or activating specific neurons, or changing their genetic sex, we will assess their contributions to male and female behaviours, and how these perturbations impinge on activity patterns in other fru neurons. We also aim to define how a specific experience can modify the physiological properties of these circuits, and how these changes in turn modulate mating behaviour. These studies will define the operating principles of these neural circuits, contributing to a molecules-to-systems explanation of Drosophila s mating behaviours.
Max ERC Funding
2 492 164 €
Duration
Start date: 2009-07-01, End date: 2013-09-30
Project acronym GEMIS
Project Generalized Homological Mirror Symmetry and Applications
Researcher (PI) Ludmil Katzarkov
Host Institution (HI) UNIVERSITAT WIEN
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary Mirror symmetry arose originally in physics, as a duality between $N = 2$ superconformal field theories. Witten formulated a more mathematically accessible version, in terms of topological field theories. Both conformal and topological field theories can be defined axiomatically, but more interestingly, there are several geometric ways of constructing them. A priori, the mirror correspondence is not unique, and it does not necessarily remain within a single class of geometric models. The classical case relates $\sigma$-models, but in a more modern formulation, one has mirror dualities between different Landau-Ginzburg models, as well as between such models and $\sigma$-models; orbifolds should also be included in this. The simplest example would be the function $W: \C \rightarrow \C$, $W(x) = x^{n+1}$, which is self-mirror (up to dividing by the $\bZ/n+1$ symmetry group, in an orbifold sense). While the mathematics of the $\sigma$-model mirror correspondence is familiar by now, generalizations to Landau-Ginzburg theories are only beginning to be understood. Today it is clear that Homologcal Mirror Symmetry (HMS) as a categorical correspondence works and it is time for developing direct geometric applications to classical problems - rationality of algebraic varieties and Hodge conjecture. This the main goal of the proposal. But in order to attack the above problems we need to generalize HMS and explore its connection to new developments in modern Hodge theory. In order to carry the above program we plan to further already working team Vienna, Paris, Moscow, MIT.
Summary
Mirror symmetry arose originally in physics, as a duality between $N = 2$ superconformal field theories. Witten formulated a more mathematically accessible version, in terms of topological field theories. Both conformal and topological field theories can be defined axiomatically, but more interestingly, there are several geometric ways of constructing them. A priori, the mirror correspondence is not unique, and it does not necessarily remain within a single class of geometric models. The classical case relates $\sigma$-models, but in a more modern formulation, one has mirror dualities between different Landau-Ginzburg models, as well as between such models and $\sigma$-models; orbifolds should also be included in this. The simplest example would be the function $W: \C \rightarrow \C$, $W(x) = x^{n+1}$, which is self-mirror (up to dividing by the $\bZ/n+1$ symmetry group, in an orbifold sense). While the mathematics of the $\sigma$-model mirror correspondence is familiar by now, generalizations to Landau-Ginzburg theories are only beginning to be understood. Today it is clear that Homologcal Mirror Symmetry (HMS) as a categorical correspondence works and it is time for developing direct geometric applications to classical problems - rationality of algebraic varieties and Hodge conjecture. This the main goal of the proposal. But in order to attack the above problems we need to generalize HMS and explore its connection to new developments in modern Hodge theory. In order to carry the above program we plan to further already working team Vienna, Paris, Moscow, MIT.
Max ERC Funding
1 060 800 €
Duration
Start date: 2009-01-01, End date: 2013-12-31
Project acronym InterAct-MemNP
Project Interaction and actuation of lipid membranes with magnetic nanoparticles
Researcher (PI) Erik Reimhult
Host Institution (HI) UNIVERSITAET FUER BODENKULTUR WIEN
Call Details Starting Grant (StG), LS9, ERC-2012-StG_20111109
Summary Cell membranes contain a large part of the delicate machinery of life and comprise the barriers controlling access to and from the interior of the cell. With the increasing use of nanoparticles (NPs) in medical imaging, drug delivery, cosmetics and materials the need is great and increasing to understand how NPs physically interact with cell membranes. On the one hand it is important to understand mechanisms to control risks of novel nanomaterials and to design therapeutic agents which can enter cells specifically and non-destructively. On the other hand, the structure and function of biological membranes inspire development of biomimetic smart materials for biotechnological applications which exploit or are modeled on biological membranes, but given enhanced functionality and external control of properties through incorporation of functional NPs.
The aim of the proposed work is to develop understanding of the biophysical interaction of functional NPs with lipid membranes, in particular NP incorporation into and penetration through lipid membranes. Further, the aim is, based on that knowledge, to understand and control the self-assembly of superparamagnetic NPs into synthetic and cell lipid membranes to actuate them and control their physical properties in pursuit of novel biomimetic smart materials and cell analytical methods.
The required level of control for this research has until recently been beyond the reach of existing NP systems (lack of synthetic control, stability and characterization) and methodology (lipid membrane models and high resolution techniques for their investigation). However, it can now be achieved using the Fe3O4 NP platform and surface-based and vesicular membrane model systems of tuned composition that I have developed. Using the same platform, breakthrough magneto-responsive biomimetic smart materials with application in drug delivery and cell manipulation with novel mechanisms of actuation will be self-assembled and investigated.
Summary
Cell membranes contain a large part of the delicate machinery of life and comprise the barriers controlling access to and from the interior of the cell. With the increasing use of nanoparticles (NPs) in medical imaging, drug delivery, cosmetics and materials the need is great and increasing to understand how NPs physically interact with cell membranes. On the one hand it is important to understand mechanisms to control risks of novel nanomaterials and to design therapeutic agents which can enter cells specifically and non-destructively. On the other hand, the structure and function of biological membranes inspire development of biomimetic smart materials for biotechnological applications which exploit or are modeled on biological membranes, but given enhanced functionality and external control of properties through incorporation of functional NPs.
The aim of the proposed work is to develop understanding of the biophysical interaction of functional NPs with lipid membranes, in particular NP incorporation into and penetration through lipid membranes. Further, the aim is, based on that knowledge, to understand and control the self-assembly of superparamagnetic NPs into synthetic and cell lipid membranes to actuate them and control their physical properties in pursuit of novel biomimetic smart materials and cell analytical methods.
The required level of control for this research has until recently been beyond the reach of existing NP systems (lack of synthetic control, stability and characterization) and methodology (lipid membrane models and high resolution techniques for their investigation). However, it can now be achieved using the Fe3O4 NP platform and surface-based and vesicular membrane model systems of tuned composition that I have developed. Using the same platform, breakthrough magneto-responsive biomimetic smart materials with application in drug delivery and cell manipulation with novel mechanisms of actuation will be self-assembled and investigated.
Max ERC Funding
1 483 487 €
Duration
Start date: 2013-01-01, End date: 2017-12-31
Project acronym isoineqintgeo
Project Isoperimetric Inequalities and Integral Geometry
Researcher (PI) Franz Ewald Schuster
Host Institution (HI) TECHNISCHE UNIVERSITAET WIEN
Call Details Starting Grant (StG), PE1, ERC-2012-StG_20111012
Summary "Among several trends in convex geometric analysis, two have undergone an explosive development in recent years: the theory of affine isoperimetric and analytic inequalities, and the enhanced understanding of fundamental concepts of the subject as a whole lent by the theory of valuations. The proposal concerns both of these trends.
The connections between convex body valued valuations and isoperimetric inequalities (like, the Petty projection inequality or affine Sobolev inequalities and their Lp extensions) have attracted the interest of first-rate research groups in the world. However, the underlying bigger picture behind these strong relations has yet to be discovered. A goal of the proposed research program is to systematically exploit the ""valuations point of view"" to reshape not only the way (affine) isoperimetric inequalities are thought of and applied but also the way these powerful inequalities are established.
Through the introduction of new algebraic structures on the space of translation invariant scalar valued valuations substantial inroads have been made towards a fuller understanding of the integral geometry of groups acting transitively on the sphere. An aim of the proposed program is to introduce a corresponding algebraic machinery in the theory of convex body valued valuations which would provide the means to attack long standing major open problems in the area of affine isoperimetric inequalities.
It is the PI's strong belief that over the next years it will become clear that many classical inequalities from affine geometry hold in a much more general setting than is currently understood. This will not only lead to the discovery of new inequalities but also should reveal the full strength of affine inequalities compared to their counterparts from Euclidean geometry. The proposed research goals of this ERC grant proposal would therefore represent a huge step towards advancing these developments that will alter two main subjects at the same time."
Summary
"Among several trends in convex geometric analysis, two have undergone an explosive development in recent years: the theory of affine isoperimetric and analytic inequalities, and the enhanced understanding of fundamental concepts of the subject as a whole lent by the theory of valuations. The proposal concerns both of these trends.
The connections between convex body valued valuations and isoperimetric inequalities (like, the Petty projection inequality or affine Sobolev inequalities and their Lp extensions) have attracted the interest of first-rate research groups in the world. However, the underlying bigger picture behind these strong relations has yet to be discovered. A goal of the proposed research program is to systematically exploit the ""valuations point of view"" to reshape not only the way (affine) isoperimetric inequalities are thought of and applied but also the way these powerful inequalities are established.
Through the introduction of new algebraic structures on the space of translation invariant scalar valued valuations substantial inroads have been made towards a fuller understanding of the integral geometry of groups acting transitively on the sphere. An aim of the proposed program is to introduce a corresponding algebraic machinery in the theory of convex body valued valuations which would provide the means to attack long standing major open problems in the area of affine isoperimetric inequalities.
It is the PI's strong belief that over the next years it will become clear that many classical inequalities from affine geometry hold in a much more general setting than is currently understood. This will not only lead to the discovery of new inequalities but also should reveal the full strength of affine inequalities compared to their counterparts from Euclidean geometry. The proposed research goals of this ERC grant proposal would therefore represent a huge step towards advancing these developments that will alter two main subjects at the same time."
Max ERC Funding
982 461 €
Duration
Start date: 2012-11-01, End date: 2017-10-31
