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 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
Project acronym MATHEF
Project Mathematical Thermodynamics of Fluids
Researcher (PI) Eduard Feireisl
Host Institution (HI) MATEMATICKY USTAV AV CR V.V.I.
Call Details Advanced Grant (AdG), PE1, ERC-2012-ADG_20120216
Summary "The main goal of the present research proposal is to build up a general mathematical theory describing the motion of a compressible, viscous, and heat conductive fluid. Our approach is based on the concept of generalized (weak) solutions satisfying the basic physical principles of balance of mass, momentum, and energy. The energy balance is expressed in terms of a variant of entropy inequality supplemented with an integral identity for the total energy balance.
We propose to identify a class of suitable weak solutions, where admissibility is based on a direct application of the principle of maximal entropy production compatible with Second law of thermodynamics. Stability of the solution family will be investigated by the method of relative entropies constructed on the basis of certain thermodynamics potentials as ballistic free energy.
The new solution framework will be applied to multiscale problems, where several characteristic scales become small or extremely large. We focus on mutual interaction of scales during this process and identify the asymptotic behavior of the quantities that are filtered out in the singular limits. We also propose to study the influence of the geometry of the underlying physical space that may change in the course of the limit process. In particular, problems arising in homogenization and optimal shape design in combination with various singular limits are taken into account.
The abstract approximate scheme used in the existence theory will be adapted in order to develop adequate numerical methods. We study stability and convergence of these methods using the tools developed in the abstract part, in particular, the relative entropies."
Summary
"The main goal of the present research proposal is to build up a general mathematical theory describing the motion of a compressible, viscous, and heat conductive fluid. Our approach is based on the concept of generalized (weak) solutions satisfying the basic physical principles of balance of mass, momentum, and energy. The energy balance is expressed in terms of a variant of entropy inequality supplemented with an integral identity for the total energy balance.
We propose to identify a class of suitable weak solutions, where admissibility is based on a direct application of the principle of maximal entropy production compatible with Second law of thermodynamics. Stability of the solution family will be investigated by the method of relative entropies constructed on the basis of certain thermodynamics potentials as ballistic free energy.
The new solution framework will be applied to multiscale problems, where several characteristic scales become small or extremely large. We focus on mutual interaction of scales during this process and identify the asymptotic behavior of the quantities that are filtered out in the singular limits. We also propose to study the influence of the geometry of the underlying physical space that may change in the course of the limit process. In particular, problems arising in homogenization and optimal shape design in combination with various singular limits are taken into account.
The abstract approximate scheme used in the existence theory will be adapted in order to develop adequate numerical methods. We study stability and convergence of these methods using the tools developed in the abstract part, in particular, the relative entropies."
Max ERC Funding
726 320 €
Duration
Start date: 2013-05-01, End date: 2018-04-30
Project acronym TRANSARREST
Project Keeping gene expression in check: eliciting the role of transcription in the maintenance of genome integrity
Researcher (PI) Maria Fousteri
Host Institution (HI) BIOMEDICAL SCIENCES RESEARCH CENTER ALEXANDER FLEMING
Call Details Starting Grant (StG), LS1, ERC-2012-StG_20111109
Summary Genomic integrity is essential for accurate gene expression and epigenetic inheritance. On the other hand, a prolonged transcriptional arrest can challenge genome stability, contributing to genetic and epigenetic defects and the mechanisms of ageing and disease.
Here we aim to identify the molecular mechanisms that couple transcriptional arrest to chromatin alteration and repair. We wish to explore the idea that transcription suppresses cellular toxicity and preserves genetic and epigenetic inheritance.
Towards these goals our work will be focused on:
1. Deciphering the molecular events impinging on the manner cells respond when the progress of a transcribing RNA polymerase II is blocked.
2. Exploring a novel, so far unanticipated function of key players of the transcription-associated repair pathways, such as the Cockayne Syndrome (CS) proteins, not related to repair.
3. Understanding the role of transcription in chemotherapeutic-driven toxicity.
4. Investigating novel post-translational modifications of CS and determining their function.
These objectives will be addressed using advanced proteomics and genome wide technologies in combination with biochemical and cellular techniques in normal human cells and a large battery of patient-derived cell lines. Our rational is that better understanding of CS function will help reach our ultimate goal, which is to identify the regulatory cascades involved in the interplay between genomic stability and transcription. The novel key idea put forward in this proposal is that active transcription itself directly contributes to genome integrity. While the role of DNA damage-driven transcription blockage in promoting repair is well established, the protective role of active transcription in genome stability is entirely unexplored.
If successful, the proposed studies may help reveal the underlying causes of related disorders and explain their clinical features.
Summary
Genomic integrity is essential for accurate gene expression and epigenetic inheritance. On the other hand, a prolonged transcriptional arrest can challenge genome stability, contributing to genetic and epigenetic defects and the mechanisms of ageing and disease.
Here we aim to identify the molecular mechanisms that couple transcriptional arrest to chromatin alteration and repair. We wish to explore the idea that transcription suppresses cellular toxicity and preserves genetic and epigenetic inheritance.
Towards these goals our work will be focused on:
1. Deciphering the molecular events impinging on the manner cells respond when the progress of a transcribing RNA polymerase II is blocked.
2. Exploring a novel, so far unanticipated function of key players of the transcription-associated repair pathways, such as the Cockayne Syndrome (CS) proteins, not related to repair.
3. Understanding the role of transcription in chemotherapeutic-driven toxicity.
4. Investigating novel post-translational modifications of CS and determining their function.
These objectives will be addressed using advanced proteomics and genome wide technologies in combination with biochemical and cellular techniques in normal human cells and a large battery of patient-derived cell lines. Our rational is that better understanding of CS function will help reach our ultimate goal, which is to identify the regulatory cascades involved in the interplay between genomic stability and transcription. The novel key idea put forward in this proposal is that active transcription itself directly contributes to genome integrity. While the role of DNA damage-driven transcription blockage in promoting repair is well established, the protective role of active transcription in genome stability is entirely unexplored.
If successful, the proposed studies may help reveal the underlying causes of related disorders and explain their clinical features.
Max ERC Funding
1 500 000 €
Duration
Start date: 2012-11-01, End date: 2018-10-31
