Project acronym 100 Archaic Genomes
Project Genome sequences from extinct hominins
Researcher (PI) Svante PaeaeBO
Host Institution (HI) MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Country Germany
Call Details Advanced Grant (AdG), LS2, ERC-2015-AdG
Summary Neandertals and Denisovans, an Asian group distantly related to Neandertals, are the closest evolutionary relatives of present-day humans. They are thus of direct relevance for understanding the origin of modern humans and how modern humans differ from their closest relatives. We will generate genome-wide data from a large number of Neandertal and Denisovan individuals from across their geographical and temporal range as well as from other extinct hominin groups which we may discover. This will be possible by automating highly sensitive approaches to ancient DNA extraction and DNA libraries construction that we have developed so that they can be applied to many specimens from many sites in order to identify those that contain retrievable DNA. Whenever possible we will sequence whole genomes and in other cases use DNA capture methods to generate high-quality data from representative parts of the genome. This will allow us to study the population history of Neandertals and Denisovans, elucidate how many times and where these extinct hominins contributed genes to present-day people, and the extent to which modern humans and archaic groups contributed genetically to Neandertals and Denisovans. By retrieving DNA from specimens that go back to the Middle Pleistocene we will furthermore shed light on the early history and origins of Neandertals and Denisovans.
Summary
Neandertals and Denisovans, an Asian group distantly related to Neandertals, are the closest evolutionary relatives of present-day humans. They are thus of direct relevance for understanding the origin of modern humans and how modern humans differ from their closest relatives. We will generate genome-wide data from a large number of Neandertal and Denisovan individuals from across their geographical and temporal range as well as from other extinct hominin groups which we may discover. This will be possible by automating highly sensitive approaches to ancient DNA extraction and DNA libraries construction that we have developed so that they can be applied to many specimens from many sites in order to identify those that contain retrievable DNA. Whenever possible we will sequence whole genomes and in other cases use DNA capture methods to generate high-quality data from representative parts of the genome. This will allow us to study the population history of Neandertals and Denisovans, elucidate how many times and where these extinct hominins contributed genes to present-day people, and the extent to which modern humans and archaic groups contributed genetically to Neandertals and Denisovans. By retrieving DNA from specimens that go back to the Middle Pleistocene we will furthermore shed light on the early history and origins of Neandertals and Denisovans.
Max ERC Funding
2 350 000 €
Duration
Start date: 2016-11-01, End date: 2021-10-31
Project acronym ACoolTouch
Project Neural mechanisms of multisensory perceptual binding
Researcher (PI) James Francis Alexander Poulet
Host Institution (HI) MAX DELBRUECK CENTRUM FUER MOLEKULARE MEDIZIN IN DER HELMHOLTZ-GEMEINSCHAFT (MDC)
Country Germany
Call Details Consolidator Grant (CoG), LS5, ERC-2015-CoG
Summary Sensory perception involves the discrimination and binding of multiple modalities of sensory input. This is especially evident in the somatosensory system where different modalities of sensory input, including thermal and mechanosensory, are combined to generate a unified percept. The neural mechanisms of multisensory binding are unknown, in part because sensory perception is typically studied within a single modality in a single brain region. I propose a multi-level approach to investigate thermo-tactile processing in the mouse forepaw system from the primary sensory afferent neurons to thalamo-cortical circuits and behaviour.
The mouse forepaw system is the ideal system to investigate multisensory binding as the sensory afferent neurons are well investigated, cell type-specific lines are available, in vivo optogenetic manipulation is possible both in sensory afferent neurons and central circuits and we have developed high-resolution somatosensory perception behaviours. We have previously shown that mouse primary somatosensory forepaw cortical neurons respond to both tactile and thermal stimuli and are required for non-noxious cooling perception. With multimodal neurons how, then, is it possible to both discriminate and bind thermal and tactile stimuli?
I propose 3 objectives to address this question. We will first, perform functional mapping of the thermal and tactile pathways to cortex; second, investigate the neural mechanisms of thermo-tactile discrimination in behaving mice; and third, compare neural processing during two thermo-tactile binding tasks, the first using passively applied stimuli, and the second, active manipulation of thermal objects.
At each stage we will perform cell type-specific neural recordings and causal optogenetic manipulations in awake and behaving mice. Our multi-level approach will provide a comprehensive investigation into how the brain performs multisensory perceptual binding: a fundamental yet unsolved problem in neuroscience.
Summary
Sensory perception involves the discrimination and binding of multiple modalities of sensory input. This is especially evident in the somatosensory system where different modalities of sensory input, including thermal and mechanosensory, are combined to generate a unified percept. The neural mechanisms of multisensory binding are unknown, in part because sensory perception is typically studied within a single modality in a single brain region. I propose a multi-level approach to investigate thermo-tactile processing in the mouse forepaw system from the primary sensory afferent neurons to thalamo-cortical circuits and behaviour.
The mouse forepaw system is the ideal system to investigate multisensory binding as the sensory afferent neurons are well investigated, cell type-specific lines are available, in vivo optogenetic manipulation is possible both in sensory afferent neurons and central circuits and we have developed high-resolution somatosensory perception behaviours. We have previously shown that mouse primary somatosensory forepaw cortical neurons respond to both tactile and thermal stimuli and are required for non-noxious cooling perception. With multimodal neurons how, then, is it possible to both discriminate and bind thermal and tactile stimuli?
I propose 3 objectives to address this question. We will first, perform functional mapping of the thermal and tactile pathways to cortex; second, investigate the neural mechanisms of thermo-tactile discrimination in behaving mice; and third, compare neural processing during two thermo-tactile binding tasks, the first using passively applied stimuli, and the second, active manipulation of thermal objects.
At each stage we will perform cell type-specific neural recordings and causal optogenetic manipulations in awake and behaving mice. Our multi-level approach will provide a comprehensive investigation into how the brain performs multisensory perceptual binding: a fundamental yet unsolved problem in neuroscience.
Max ERC Funding
1 999 877 €
Duration
Start date: 2016-09-01, End date: 2021-08-31
Project acronym Autonomous CLL-BCRs
Project Role of autonomous B cell receptor signalling and external antigen in the pathogenesis of chronic lymphocytic leukaemia (CLL)
Researcher (PI) Hassan JUMAA-WEINACHT
Host Institution (HI) UNIVERSITAET ULM
Country Germany
Call Details Advanced Grant (AdG), LS6, ERC-2015-AdG
Summary The proposed project aims at investigating the molecular mechanisms that activate B cell antigen receptor (BCR) signalling in chronic lymphocytic leukaemia (CLL). While it is widely accepted that the unbroken BCR expression in CLL cells is indicative for a key role in disease development, the mechanisms that induce BCR activation and survival of malignant cells are still elusive. Using a unique reconstitution system, we have recently shown that CLL-derived BCRs possess the exceptional capacity for cell-autonomous signalling independent of external antigen. Crystallographic analyses confirmed our model that CLL-BCRs bind to intrinsic motifs in nearby BCRs on the very same cell. In addition to the BCR, several pathogenic factors influence the biological behaviour of CLL cells, but the functional hierarchy and the effect on BCR signalling are insufficiently understood. Here, we aim at investigating the structural cause of autonomous signalling as well as the characterization of important signalling pathways and their mechanistic action in CLL pathogenesis.
By combining crystallography with the measurement of autonomous signalling of wild type and mutated receptors in our unique reconstitution system, we will generate a structure-function relationship for CLL-BCRs. By generating new animal models and by employing classical as well as cutting-edge approaches of biochemistry and molecular/cellular immunology, we will comprehensively characterize the signalling pathways that are activated by autonomous signalling and might be important for CLL pathogenesis.
These systematic efforts are necessary to understand how various biological mechanisms operate and ultimately activate downstream pathways that result in a lymphoproliferative disease. In addition, a cohesive model of CLL pathogenesis, which elucidates the hierarchical order of pathogenic factors and their interaction with BCR signalling, may well lead to novel disease-specific preventive or therapeutic intervention.
Summary
The proposed project aims at investigating the molecular mechanisms that activate B cell antigen receptor (BCR) signalling in chronic lymphocytic leukaemia (CLL). While it is widely accepted that the unbroken BCR expression in CLL cells is indicative for a key role in disease development, the mechanisms that induce BCR activation and survival of malignant cells are still elusive. Using a unique reconstitution system, we have recently shown that CLL-derived BCRs possess the exceptional capacity for cell-autonomous signalling independent of external antigen. Crystallographic analyses confirmed our model that CLL-BCRs bind to intrinsic motifs in nearby BCRs on the very same cell. In addition to the BCR, several pathogenic factors influence the biological behaviour of CLL cells, but the functional hierarchy and the effect on BCR signalling are insufficiently understood. Here, we aim at investigating the structural cause of autonomous signalling as well as the characterization of important signalling pathways and their mechanistic action in CLL pathogenesis.
By combining crystallography with the measurement of autonomous signalling of wild type and mutated receptors in our unique reconstitution system, we will generate a structure-function relationship for CLL-BCRs. By generating new animal models and by employing classical as well as cutting-edge approaches of biochemistry and molecular/cellular immunology, we will comprehensively characterize the signalling pathways that are activated by autonomous signalling and might be important for CLL pathogenesis.
These systematic efforts are necessary to understand how various biological mechanisms operate and ultimately activate downstream pathways that result in a lymphoproliferative disease. In addition, a cohesive model of CLL pathogenesis, which elucidates the hierarchical order of pathogenic factors and their interaction with BCR signalling, may well lead to novel disease-specific preventive or therapeutic intervention.
Max ERC Funding
2 256 250 €
Duration
Start date: 2016-11-01, End date: 2021-10-31
Project acronym BrainModes
Project Personalized whole brain simulations: linking connectomics and dynamics in the human brain
Researcher (PI) Petra Ritter
Host Institution (HI) CHARITE - UNIVERSITAETSMEDIZIN BERLIN
Country Germany
Call Details Consolidator Grant (CoG), LS5, ERC-2015-CoG
Summary Background. We have detailed maps of brain structure and function, yet are lacking understanding of how the highly connected units interact and give rise to mental processes. The Virtual Brain (TVB), a whole brain simulation framework, aims to bridge that gap. Yet it is still developing. We are proposing here breakthrough advances that reveal mechanisms of brain function and foster collaboration between research groups. Vision. Clinical applications that simulate individual patient brains and predict trajectories of recovery or decline or test therapies to select the best one for that person. Goal. Using biologically realistic brain models and multimodal functional and structural imaging data to elucidate control mechanisms of the human brain in aging. A database collects key data and allows identifying most generic models and mechanisms below the spatial and temporal resolution of non-invasive imaging techniques taking into account the complex interaction in the brain that without a model would be impossible to keep track of. Objectives. 1) Parameter optimization for large parameter space search and a library of dynamical regimes linking dynamical regimes and underlying mechanisms to biological (cognitive) age. 2) Identifying the role of intrinsic plasticity for network reconfigurations in the resting state and its age dependency. 3) Model based identification of task related plasticity mechanisms and their functional consequences for network reconfigurations in coordination learning in aging. 4) An interactive tool that provides access to the dynamical regimes library and makes pre-computed simulations easily accessible allowing researchers to benefit and learn from existing work. Impact. Understanding development, aging and brain disorders from the perspective of disruption of information processing architectures provides an opportunity for new interventions that re-establish control in brain pathology hence posing a breakthrough in the health and biotech sector.
Summary
Background. We have detailed maps of brain structure and function, yet are lacking understanding of how the highly connected units interact and give rise to mental processes. The Virtual Brain (TVB), a whole brain simulation framework, aims to bridge that gap. Yet it is still developing. We are proposing here breakthrough advances that reveal mechanisms of brain function and foster collaboration between research groups. Vision. Clinical applications that simulate individual patient brains and predict trajectories of recovery or decline or test therapies to select the best one for that person. Goal. Using biologically realistic brain models and multimodal functional and structural imaging data to elucidate control mechanisms of the human brain in aging. A database collects key data and allows identifying most generic models and mechanisms below the spatial and temporal resolution of non-invasive imaging techniques taking into account the complex interaction in the brain that without a model would be impossible to keep track of. Objectives. 1) Parameter optimization for large parameter space search and a library of dynamical regimes linking dynamical regimes and underlying mechanisms to biological (cognitive) age. 2) Identifying the role of intrinsic plasticity for network reconfigurations in the resting state and its age dependency. 3) Model based identification of task related plasticity mechanisms and their functional consequences for network reconfigurations in coordination learning in aging. 4) An interactive tool that provides access to the dynamical regimes library and makes pre-computed simulations easily accessible allowing researchers to benefit and learn from existing work. Impact. Understanding development, aging and brain disorders from the perspective of disruption of information processing architectures provides an opportunity for new interventions that re-establish control in brain pathology hence posing a breakthrough in the health and biotech sector.
Max ERC Funding
1 870 588 €
Duration
Start date: 2016-08-01, End date: 2021-07-31
Project acronym CHRiSHarMa
Project Commutators, Hilbert and Riesz transforms, Shifts, Harmonic extensions and Martingales
Researcher (PI) Stefanie Petermichl
Host Institution (HI) JULIUS-MAXIMILIANS-UNIVERSITAT WURZBURG
Country Germany
Call Details Consolidator Grant (CoG), PE1, ERC-2015-CoG
Summary This project aims to develop two arrays of questions at the heart of harmonic
analysis, probability and operator theory:
Multi-parameter harmonic analysis.
Through the use of wavelet methods in harmonic analysis, we plan to shed new
light on characterizations for boundedness of multi-parameter versions of
classical Hankel operators in a variety of settings. The classical Nehari's theorem on
the disk (1957) has found an important generalization to Hilbert space
valued functions, known as Page's theorem. A relevant extension of Nehari's
theorem to the bi-disk had been a long standing problem, finally solved in
2000, through novel harmonic analysis methods. It's operator analog remains
unknown and constitutes part of this proposal.
Sharp estimates for Calderon-Zygmund operators and martingale
inequalities.
We make use of the interplay between objects central to
Harmonic analysis, such as the Hilbert transform, and objects central to
probability theory, martingales. This connection has seen many faces, such as
in the UMD space classification by Bourgain and Burkholder or in the formula
of Gundy-Varapoulos, that uses orthogonal martingales to model the behavior of
the Hilbert transform. Martingale methods in combination with optimal control
have advanced an array of questions in harmonic analysis in recent years. In
this proposal we wish to continue this direction as well as exploit advances
in dyadic harmonic analysis for use in questions central to probability. There
is some focus on weighted estimates in a non-commutative and scalar setting, in the understanding of discretizations
of classical operators, such as the Hilbert transform and their role played
when acting on functions defined on discrete groups. From a martingale
standpoint, jump processes come into play. Another direction is the use of
numerical methods in combination with harmonic analysis achievements for martingale estimates.
Summary
This project aims to develop two arrays of questions at the heart of harmonic
analysis, probability and operator theory:
Multi-parameter harmonic analysis.
Through the use of wavelet methods in harmonic analysis, we plan to shed new
light on characterizations for boundedness of multi-parameter versions of
classical Hankel operators in a variety of settings. The classical Nehari's theorem on
the disk (1957) has found an important generalization to Hilbert space
valued functions, known as Page's theorem. A relevant extension of Nehari's
theorem to the bi-disk had been a long standing problem, finally solved in
2000, through novel harmonic analysis methods. It's operator analog remains
unknown and constitutes part of this proposal.
Sharp estimates for Calderon-Zygmund operators and martingale
inequalities.
We make use of the interplay between objects central to
Harmonic analysis, such as the Hilbert transform, and objects central to
probability theory, martingales. This connection has seen many faces, such as
in the UMD space classification by Bourgain and Burkholder or in the formula
of Gundy-Varapoulos, that uses orthogonal martingales to model the behavior of
the Hilbert transform. Martingale methods in combination with optimal control
have advanced an array of questions in harmonic analysis in recent years. In
this proposal we wish to continue this direction as well as exploit advances
in dyadic harmonic analysis for use in questions central to probability. There
is some focus on weighted estimates in a non-commutative and scalar setting, in the understanding of discretizations
of classical operators, such as the Hilbert transform and their role played
when acting on functions defined on discrete groups. From a martingale
standpoint, jump processes come into play. Another direction is the use of
numerical methods in combination with harmonic analysis achievements for martingale estimates.
Max ERC Funding
1 523 963 €
Duration
Start date: 2017-01-01, End date: 2021-12-31
Project acronym Extinction Genomics
Project Exploring and exploiting the potential of extinct genome sequencing
Researcher (PI) Marcus Thomas Pius Gilbert
Host Institution (HI) KOBENHAVNS UNIVERSITET
Country Denmark
Call Details Consolidator Grant (CoG), LS2, ERC-2015-CoG
Summary Palaeogenomics is the nascent discipline concerned with sequencing and analysis of genome-scale information from historic, ancient, and even extinct samples. While once inconceivable due to the challenges of DNA damage, contamination, and the technical limitations of PCR-based Sanger sequencing, following the dawn of the second-generation sequencing revolution, it has rapidly become a reality. Indeed, so much so, that popular perception has moved away from if extinct species’ genomes can be sequenced, to when it will happen - and even, when will the first extinct animals be regenerated. Unfortunately this view is naïve, and does not account for the financial and technical challenges that face such attempts. I propose an exploration of exactly what the limits on genome reconstruction from extinct or otherwise historic/ancient material are. This will be achieved through new laboratory and bioinformatic developments aimed at decreasing the cost, while concomitantly increasing the quality of genome reconstruction from poor quality materials. In doing so I aim to build a scientifically-grounded framework against which the possibilities and limitations of extinct genome reconstruction can be assessed. Subsequently genomic information will be generated from a range of extinct and near-extinct avian and mammalian species, in order to showcase the potential of reconstructed genomes across research questions spanning at least three different streams of research: De-extinction, Evolutionary Genomics, and Conservation Genomics. Ultimately, achievement of these goals requires formation of a dedicated, closely knit team, focusing on both the methodological challenges as well as their bigger picture application to high-risk high-gain ventures. With ERC funding this can become a reality, and enable palaeogenomics to be pushed to the limits possible under modern technology.
Summary
Palaeogenomics is the nascent discipline concerned with sequencing and analysis of genome-scale information from historic, ancient, and even extinct samples. While once inconceivable due to the challenges of DNA damage, contamination, and the technical limitations of PCR-based Sanger sequencing, following the dawn of the second-generation sequencing revolution, it has rapidly become a reality. Indeed, so much so, that popular perception has moved away from if extinct species’ genomes can be sequenced, to when it will happen - and even, when will the first extinct animals be regenerated. Unfortunately this view is naïve, and does not account for the financial and technical challenges that face such attempts. I propose an exploration of exactly what the limits on genome reconstruction from extinct or otherwise historic/ancient material are. This will be achieved through new laboratory and bioinformatic developments aimed at decreasing the cost, while concomitantly increasing the quality of genome reconstruction from poor quality materials. In doing so I aim to build a scientifically-grounded framework against which the possibilities and limitations of extinct genome reconstruction can be assessed. Subsequently genomic information will be generated from a range of extinct and near-extinct avian and mammalian species, in order to showcase the potential of reconstructed genomes across research questions spanning at least three different streams of research: De-extinction, Evolutionary Genomics, and Conservation Genomics. Ultimately, achievement of these goals requires formation of a dedicated, closely knit team, focusing on both the methodological challenges as well as their bigger picture application to high-risk high-gain ventures. With ERC funding this can become a reality, and enable palaeogenomics to be pushed to the limits possible under modern technology.
Max ERC Funding
2 000 000 €
Duration
Start date: 2016-04-01, End date: 2021-03-31
Project acronym GCB-PRID
Project Post-transcriptional Regulation of Germinal Center B Cell Responses in Immunity and Disease
Researcher (PI) Marc Schmidt-Supprian
Host Institution (HI) KLINIKUM RECHTS DER ISAR DER TECHNISCHEN UNIVERSITAT MUNCHEN
Country Germany
Call Details Consolidator Grant (CoG), LS6, ERC-2015-CoG
Summary Antibodies secreted by B cells of the adaptive immune system establish an essential barrier against bacteria and viruses and their presence is the hallmark of protective vaccinations. B cells are licensed for their tasks during germinal center (GC) reactions and differentiation into antibody-secreting plasma cells. Unfortunately, B cell-derived autoantibodies and proinflammatory cytokines can cause or contribute to autoimmune diseases.
While major transcription factor networks regulating protective (or pathogenic) GCB cell responses have been identified and characterized, little is known about the post-transcriptional regulation by RNA-binding proteins (RBP), whose number rivals that of transcription factors.
We postulate that RBPs exercise critical post-transcriptional control over germinal center B (GCB) and plasmacytic cell physiology and we aim to identify and molecularly characterize these regulatory mechanisms.
To this end, we will complement sophisticated genetic mouse models with novel cell culture systems. We will monitor RBP activity with fluorescent sensors and use proteomics to reveal RBPs regulating the protein abundance of critical mediators of GCB and plasmacytic cell fates. In addition, we will conduct genetic screens to uncover relevant functions of a short list of 40 RBPs, whose protein expression we found to differ significantly between GCB and mantle zone B cells. Ultimately, we will use cellular immunology and RNA biochemistry to elucidate how these RBPs exert their post-transcriptional control.
Through the integrated power of our multi-disciplinary approach we will thus pinpoint and investigate the functions of key RBPs regulating the biology of GCB and plasmacytic cells. GCB-PRID promises to uncover profoundly new insights into post-transcriptional regulation of adaptive immunity. Thereby, this groundbreaking research aims to reveal novel molecular targets for the treatment of autoimmune diseases, whose incidence is steadily on the rise.
Summary
Antibodies secreted by B cells of the adaptive immune system establish an essential barrier against bacteria and viruses and their presence is the hallmark of protective vaccinations. B cells are licensed for their tasks during germinal center (GC) reactions and differentiation into antibody-secreting plasma cells. Unfortunately, B cell-derived autoantibodies and proinflammatory cytokines can cause or contribute to autoimmune diseases.
While major transcription factor networks regulating protective (or pathogenic) GCB cell responses have been identified and characterized, little is known about the post-transcriptional regulation by RNA-binding proteins (RBP), whose number rivals that of transcription factors.
We postulate that RBPs exercise critical post-transcriptional control over germinal center B (GCB) and plasmacytic cell physiology and we aim to identify and molecularly characterize these regulatory mechanisms.
To this end, we will complement sophisticated genetic mouse models with novel cell culture systems. We will monitor RBP activity with fluorescent sensors and use proteomics to reveal RBPs regulating the protein abundance of critical mediators of GCB and plasmacytic cell fates. In addition, we will conduct genetic screens to uncover relevant functions of a short list of 40 RBPs, whose protein expression we found to differ significantly between GCB and mantle zone B cells. Ultimately, we will use cellular immunology and RNA biochemistry to elucidate how these RBPs exert their post-transcriptional control.
Through the integrated power of our multi-disciplinary approach we will thus pinpoint and investigate the functions of key RBPs regulating the biology of GCB and plasmacytic cells. GCB-PRID promises to uncover profoundly new insights into post-transcriptional regulation of adaptive immunity. Thereby, this groundbreaking research aims to reveal novel molecular targets for the treatment of autoimmune diseases, whose incidence is steadily on the rise.
Max ERC Funding
1 998 066 €
Duration
Start date: 2016-09-01, End date: 2023-02-28
Project acronym GPSART
Project Geometric aspects in pathwise stochastic analysis and related topics
Researcher (PI) Peter Karl Friz
Host Institution (HI) TECHNISCHE UNIVERSITAT BERLIN
Country Germany
Call Details Consolidator Grant (CoG), PE1, ERC-2015-CoG
Summary "Recent years have seen an explosion of applications of geometric and pathwise ideas in probability theory, with motivations from fields as diverse as quantitative finance, statistics, filtering, control theory and statistical physics. Much can be traced back to Bismut, Malliavin (1970s) on the one-hand and then Doss, Sussman (1970s), Foellmer (1980s) on the other hand, with substantial new input from Lyons (from '94 on), followed by a number of workers, including Gubinelli (from '04 on) and the writer of these lines (also from '04 on). Most recently, the theory of such ``rough paths"" has been extended to ``rough fields"", notably in the astounding works of M. Hairer (from '13 on). The purpose of this project is to study a number of important problems in this field, going beyond the rough path setting, and with emphasis on geometric ideas.
(i) The transfer of concepts from rough path theory to the new world of Hairer's regularity structures.
(ii) Applications of geometric and pathwise ideas in quantitative finance.
(iii) Obtain a pathwise understanding of the geometry of Loewner evolution and more generally explore the use of rough path-inspired ideas in the world of Schramm-Loewner evolution.
(iv) Investigate the role of geometry in the pathwise analysis of non-linear evolution equations."
Summary
"Recent years have seen an explosion of applications of geometric and pathwise ideas in probability theory, with motivations from fields as diverse as quantitative finance, statistics, filtering, control theory and statistical physics. Much can be traced back to Bismut, Malliavin (1970s) on the one-hand and then Doss, Sussman (1970s), Foellmer (1980s) on the other hand, with substantial new input from Lyons (from '94 on), followed by a number of workers, including Gubinelli (from '04 on) and the writer of these lines (also from '04 on). Most recently, the theory of such ``rough paths"" has been extended to ``rough fields"", notably in the astounding works of M. Hairer (from '13 on). The purpose of this project is to study a number of important problems in this field, going beyond the rough path setting, and with emphasis on geometric ideas.
(i) The transfer of concepts from rough path theory to the new world of Hairer's regularity structures.
(ii) Applications of geometric and pathwise ideas in quantitative finance.
(iii) Obtain a pathwise understanding of the geometry of Loewner evolution and more generally explore the use of rough path-inspired ideas in the world of Schramm-Loewner evolution.
(iv) Investigate the role of geometry in the pathwise analysis of non-linear evolution equations."
Max ERC Funding
1 465 000 €
Duration
Start date: 2016-09-01, End date: 2022-02-28
Project acronym GrDyAp
Project Groups, Dynamics, and Approximation
Researcher (PI) Andreas Thom
Host Institution (HI) TECHNISCHE UNIVERSITAET DRESDEN
Country Germany
Call Details Consolidator Grant (CoG), PE1, ERC-2015-CoG
Summary Eversince, the study of symmetry in mathematics and mathematical physics has been fundamental
to a thourough understanding of most of the fundamental notions. Group theory in all its forms
is the theory of symmetry and thus an indispensible tool in many of the basic theoretical sciences.
The study of infinite symmetry groups is especially challenging, since most of the tools from the
sophisticated theory of finite groups break down and new global methods of study have to be found.
In that respect, the interaction of group theory and the study of group rings with methods from ring
theory, probability, Riemannian geometry, functional analyis, and the theory of dynamical systems
has been extremely fruitful in a variety of situations. In this proposal, I want to extend this line of
approach and introduce novel approaches to longstanding and fundamental problems.
There are four main interacting themes that I want to pursue:
(i) Groups and their study using ergodic theory of group actions
(ii) Approximation theorems for totally disconnected groups
(iii) Kaplansky’s Direct Finiteness Conjecture and p-adic analysis
(iv) Kervaire-Laudenbach Conjecture and topological methods in combinatorial group theory
The theory of `2-homology and `2-torsion of groups has provided a fruitful context to study global
properties of infinite groups. The relationship of these homological invariants with ergodic theory
of group actions will be part of the content of Part (i). In Part (ii) we seek for generalizations of
`2-methods to a context of locally compact groups and study the asymptotic invariants of sequences
of lattices (or more generally invariant random subgroups). Part (iii) tries to lay the foundation of a padic
analogue of the `2-theory, where we study novel aspects of p-adic functional analysis which help
to clarify the approximation properties of (Z/pZ)-Betti numbers. Finally, in Part (iv), we try to attack
various longstanding combinatorial problems in group theory with tools from algebraic topology and
p-local homotopy theory.
Summary
Eversince, the study of symmetry in mathematics and mathematical physics has been fundamental
to a thourough understanding of most of the fundamental notions. Group theory in all its forms
is the theory of symmetry and thus an indispensible tool in many of the basic theoretical sciences.
The study of infinite symmetry groups is especially challenging, since most of the tools from the
sophisticated theory of finite groups break down and new global methods of study have to be found.
In that respect, the interaction of group theory and the study of group rings with methods from ring
theory, probability, Riemannian geometry, functional analyis, and the theory of dynamical systems
has been extremely fruitful in a variety of situations. In this proposal, I want to extend this line of
approach and introduce novel approaches to longstanding and fundamental problems.
There are four main interacting themes that I want to pursue:
(i) Groups and their study using ergodic theory of group actions
(ii) Approximation theorems for totally disconnected groups
(iii) Kaplansky’s Direct Finiteness Conjecture and p-adic analysis
(iv) Kervaire-Laudenbach Conjecture and topological methods in combinatorial group theory
The theory of `2-homology and `2-torsion of groups has provided a fruitful context to study global
properties of infinite groups. The relationship of these homological invariants with ergodic theory
of group actions will be part of the content of Part (i). In Part (ii) we seek for generalizations of
`2-methods to a context of locally compact groups and study the asymptotic invariants of sequences
of lattices (or more generally invariant random subgroups). Part (iii) tries to lay the foundation of a padic
analogue of the `2-theory, where we study novel aspects of p-adic functional analysis which help
to clarify the approximation properties of (Z/pZ)-Betti numbers. Finally, in Part (iv), we try to attack
various longstanding combinatorial problems in group theory with tools from algebraic topology and
p-local homotopy theory.
Max ERC Funding
2 000 000 €
Duration
Start date: 2016-10-01, End date: 2021-09-30
Project acronym GrInflaGal
Project Gravity, Inflation, and Galaxies: Fundamental Physics with Large-Scale Structure
Researcher (PI) Fabian Schmidt
Host Institution (HI) MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Country Germany
Call Details Starting Grant (StG), PE9, ERC-2015-STG
Summary Over the past two decades, a data-driven revolution has occurred in our understanding of the origin and evolution of our Universe and the structure within it. During this period, cosmology has evolved from a speculative branch of theoretical physics into precision science at the intersection of gravity, particle- and astrophysics. Despite all we have learned, we still do not understand why the Universe accelerates, and how the structure in the Universe originated. Recent breakthrough research, with leading contributions by the PI of this proposal, has shown that we can make progress on these questions using observations of the large-scale structure and its tracers, galaxies. This opens up a fascinating, new interdisciplinary research field: probing Gravity and Inflation with Galaxies. The goal of the proposed research is to first, probe our theory of gravity, General Relativity, on cosmological scales. Second, it aims to shed light on the origin of the initial seed fluctuations out of which all structure in the Universe formed, by constraining the physics and energy scale of inflation. While seemingly unrelated, the main challenge in both research directions consists in understanding the nonlinear physics of structure formation, which is dominated by gravity on scales larger than a few Mpc. By making progress in this understanding, we can unlock a rich trove of information on fundamental physics from large-scale structure. The research goals will be pursued on all three fronts of analytical theory, numerical simulations, and confrontation with data. With space missions, such as Planck and Euclid, as well as ground-based surveys delivering data sets of unprecedented size and quality at this very moment, the proposed research is especially timely. It will make key contributions towards maximizing the science output of these experiments, deepen our understanding of the laws of physics, and uncover our cosmological origins.
Summary
Over the past two decades, a data-driven revolution has occurred in our understanding of the origin and evolution of our Universe and the structure within it. During this period, cosmology has evolved from a speculative branch of theoretical physics into precision science at the intersection of gravity, particle- and astrophysics. Despite all we have learned, we still do not understand why the Universe accelerates, and how the structure in the Universe originated. Recent breakthrough research, with leading contributions by the PI of this proposal, has shown that we can make progress on these questions using observations of the large-scale structure and its tracers, galaxies. This opens up a fascinating, new interdisciplinary research field: probing Gravity and Inflation with Galaxies. The goal of the proposed research is to first, probe our theory of gravity, General Relativity, on cosmological scales. Second, it aims to shed light on the origin of the initial seed fluctuations out of which all structure in the Universe formed, by constraining the physics and energy scale of inflation. While seemingly unrelated, the main challenge in both research directions consists in understanding the nonlinear physics of structure formation, which is dominated by gravity on scales larger than a few Mpc. By making progress in this understanding, we can unlock a rich trove of information on fundamental physics from large-scale structure. The research goals will be pursued on all three fronts of analytical theory, numerical simulations, and confrontation with data. With space missions, such as Planck and Euclid, as well as ground-based surveys delivering data sets of unprecedented size and quality at this very moment, the proposed research is especially timely. It will make key contributions towards maximizing the science output of these experiments, deepen our understanding of the laws of physics, and uncover our cosmological origins.
Max ERC Funding
1 330 625 €
Duration
Start date: 2016-09-01, End date: 2022-08-31
