ERC FUNDED PROJECTS

Algebras of operators on Hilbert spaces were originally introduced as the right framework for the mathematical description of quantum mechanics. In modern mathematics the scope has much broadened due to the highly versatile nature of operator algebras. They are particularly useful in the analysis of groups and their actions. Amenability is a finiteness property which occurs in many different contexts and which can be characterised in many different ways. We will analyse amenability in terms of approximation properties, in the frameworks of abstract C*-algebras, of topological dynamical systems, and of discrete groups. Such approximation properties will serve as bridging devices between these setups, and they will be used to systematically recover geometric information about the underlying structures. When passing from groups, and more generally from dynamical systems, to operator algebras, one loses information, but one gains new tools to isolate and analyse pertinent properties of the underlying structure. We will mostly be interested in the topological setting, and in the associated C*-algebras. Amenability of groups or of dynamical systems then translates into the completely positive approximation property. Systems of completely positive approximations store all the essential data about a C*-algebra, and sometimes one can arrange the systems so that one can directly read of such information. For transformation group C*-algebras, one can achieve this by using approximation properties of the underlying dynamics. To some extent one can even go back, and extract dynamical approximation properties from completely positive approximations of the C*-algebra. This interplay between approximation properties in topological dynamics and in noncommutative topology carries a surprisingly rich structure. It connects directly to the heart of the classification problem for nuclear C*-algebras on the one hand, and to central open questions on amenable dynamics on the other.

1 596 017 €

Start date: 2019-10-01, End date: 2024-09-30

Many complex phenomena in the sciences are described by nonlinear partial differential equations, the solutions of which exhibit oscillations and concentration effects on multiple temporal or spatial scales. Our aim is to use methods from applied analysis to contribute to the understanding of the interplay of effects on different scales. The central question is to determine those quantities on the microscale which are needed to for the correct description of the macroscopic evolution. We aim to develop a mathematical framework for analyzing and modeling coupled systems with multiple scales. This will include Hamiltonian dynamics as well as different types of dissipation like gradient flows or rate-independent dynamics. The choice of models will be guided by specific applications in material modeling (e.g., thermoplasticity, pattern formation, porous media) and optoelectronics (pulse interaction, Maxwell-Bloch systems, semiconductors, quantum mechanics). The research will address mathematically fundamental issues like existence and stability of solutions but will mainly be devoted to the modeling of multiscale phenomena in evolution systems. We will focus on systems with geometric structures, where the dynamics is driven by functionals. Thus, we can go much beyond the classical theory of homogenization and singular perturbations. The novel features of our approach are - the combination of different dynamical effects in one framework, - the use of geometric and metric structures for coupled partial differential equations, - the exploitation of Gamma-convergence for evolution systems driven by functionals.

1 390 000 €

Start date: 2011-04-01, End date: 2017-03-31

Angiogenesis research has focused on the sprouting of new capillaries. The mechanisms of vessel maturation are much less well understood. Yet, the maintenance of a mature, quiescent, and organotypically-differentiated layer of endothelial cells (ECs) lining the inside of all blood vessels is vital for human health. The goal of ANGIOMATURE is to identify, validate, and implement novel mechanisms of vascular maturation and organotypic EC differentiation that are active during development, maintenance of vascular stability in adults, and undergo changes in aging. We recently identified previously unrecognized gene expression signatures of vascular maturation in a genome-wide screen of ECs isolated from newborn and adult mice. Epigenetic mechanisms were identified that control the EC transcriptome through gain and loss of DNA methylation as well as EC differentiation and signaling specification. These findings pave the way for groundbreaking novel opportunities to study vascular maturation. By characterizing functionally diverse types of blood vessels, including continuous ECs in lung and brain and sinusoidal ECs in liver and bone marrow, the ANGIOMATURE project will (1) determine up to single cell resolution the transcriptional and epigenetic program(s) of vascular maturation and organotypic differentiation during adolescence, (2) analyze the functional consequences of such program(s) in differentiated ECs and their adaptation to challenge, and (3) study changes of maturation and differentiation program(s) and vascular responses during aging. We will towards this end employ an interdisciplinary matrix of approaches involving omics, systems biology, conditional gene targeting, organoid cell culture, and experimental pathology to create a high-resolution structural and functional organotypic angioarchitectural map. The project will thereby yield transformative mechanistic insights into vital biological processes that are most important for human health and healthy aging.

2 338 918 €

Start date: 2018-08-01, End date: 2023-07-31

Despite improved therapy, cardiovascular diseases remain the most prevalent diseases in the European Union and the incidence is rising due to increased obesity and ageing. The fine-tuned regulation of vascular functions is essential not only for preventing atherosclerotic diseases, but also after tissue injury, where the coordinated growth and maturation of new blood vessels provides oxygen and nutrient supply. On the other hand, excessive vessel growth or the generation of immature, leaky vessels contributes to pathological angiogenesis. Thus, the regulation of the complex processes governing vessel growth and maturation has broad impacts for several diseases ranging from tumor angiogenesis, diabetic retinopathy, to ischemic cardiovascular diseases. MicroRNAs (miRs) are small noncoding RNAs, which play a crucial role in embryonic development and tissue homeostasis. However, only limited information is available regarding the role of miRs in the vasculature. MiRs regulate gene expression by binding to the target mRNA leading either to degradation or to translational repression. Because miRs control patterns of target genes, miRs represent an attractive and promising therapeutic target to interfere with complex processes such as neovascularization and repair of ischemic tissues. Therefore, the present application aims to identify miRs in the vasculature, which regulate vessel growth and vessel remodelling and may, thus, serve as therapeutic targets in ischemic diseases. Since ageing critically impairs endothelial function, neovascularization and vascular repair, we will specifically identify miRs, which are dysregulated during ageing in endothelial cells and pro-angiogenic progenitor cells, in order to develop novel strategies to rescue age-induced impairment of neovascularization. Beyond the specific scope of the present application, the principle findings may have impact for other diseases, where deregulated vessel growth causes or accelerates disease states.

2 375 394 €

Start date: 2009-03-01, End date: 2014-02-28

The proposal consists of an extensive research program to advance the understanding of singular integral operators of Harmonic Analysis in various situations on the borderline of the existing theory. This is to be achieved by a creative combination of techniques from Analysis and Probability. On top of the standard arsenal of modern Harmonic Analysis, the main probabilistic tools are the martingale transform inequalities of Burkholder, and random geometric constructions in the spirit of the random dyadic cubes introduced to Nonhomogeneous Analysis by Nazarov, Treil and Volberg. The problems to be addressed fall under the following subtitles, with many interconnections and overlap: (i) sharp weighted inequalities; (ii) nonhomogeneous singular integrals on metric spaces; (iii) local Tb theorems with borderline assumptions; (iv) functional calculus of rough differential operators; and (v) vector-valued singular integrals. Topic (i) is a part of Classical Analysis, where new methods have led to substantial recent progress, culminating in my solution in July 2010 of a celebrated problem on the linear dependence of the weighted operator norm on the Muckenhoupt norm of the weight. The proof should be extendible to several related questions, and the aim is to also address some outstanding open problems in the area. Topics (ii) and (v) deal with extensions of the theory of singular integrals to functions with more general domain and range spaces, allowing them to be abstract metric and Banach spaces, respectively. In case (ii), I have recently been able to relax the requirements on the space compared to the established theories, opening a new research direction here. Topics (iii) and (iv) are concerned with weakening the assumptions on singular integrals in the usual Euclidean space, to allow certain applications in the theory of Partial Differential Equations. The goal is to maintain a close contact and exchange of ideas between such abstract and concrete questions.

1 100 000 €

Start date: 2011-11-01, End date: 2016-10-31

Dysregulation of capillary permeability is a severe problem in critically ill patients, but the mechanisms involved are poorly understood. Further, there are no targeted therapies to stabilize leaky vessels in various common, potentially fatal diseases, such as systemic inflammation and sepsis, which affect millions of people annually. Although a multitude of signals that stimulate opening of endothelial cell-cell junctions leading to permeability have been characterized using cellular and in vivo models, approaches to reverse the harmful process of capillary leakage in disease conditions are yet to be identified. I propose to explore a novel autocrine endothelial permeability regulatory system as a potentially universal mechanism that antagonizes vascular stabilizing ques and sustains vascular leakage in inflammation. My group has identified inflammation-induced mechanisms that switch vascular stabilizing factors into molecules that destabilize vascular barriers, and identified tools to prevent the barrier disruption. Building on these discoveries, my group will use mouse genetics, structural biology and innovative, systematic antibody development coupled with gene editing and gene silencing technology, in order to elucidate mechanisms of vascular barrier breakdown and repair in systemic inflammation. The expected outcomes include insights into endothelial cell signaling and permeability regulation, and preclinical proof-of-concept antibodies to control endothelial activation and vascular leakage in systemic inflammation and sepsis models. Ultimately, the new knowledge and preclinical tools developed in this project may facilitate future development of targeted approaches against vascular leakage.

1 999 770 €

Start date: 2018-05-01, End date: 2023-04-30

This proposal aims to unravel mysteries at the frontier of number theory and other areas of mathematics and physics. The main focus will be to understand and exploit “modularity” of q-hypergeometric series. “Modular forms are functions on the complex plane that are inordinately symmetric.” (Mazur) The motivation comes from the wide-reaching applications of modularity in combinatorics, percolation, Lie theory, and physics (black holes). The interplay between automorphic forms, q-series, and other areas of mathematics and physics is often two-sided. On the one hand, the other areas provide interesting examples of automorphic objects and predict their behavior. Sometimes these even motivate new classes of automorphic objects which have not been previously studied. On the other hand, knowing that certain generating functions are modular gives one access to deep theoretical tools to prove results in other areas. “Mathematics is a language, and we need that language to understand the physics of our universe.”(Ooguri) Understanding this interplay has attracted attention of researchers from a variety of areas. However, proofs of modularity of q-hypergeometric series currently fall far short of a comprehensive theory to describe the interplay between them and automorphic forms. A recent conjecture of W. Nahm relates the modularity of such series to K-theory. In this proposal I aim to fill this gap and provide a better understanding of this interplay by building a general structural framework enveloping these q-series. For this I will employ new kinds of automorphic objects and embed the functions of interest into bigger families A successful outcome of the proposed research will open further horizons and also answer open questions, even those in other areas which were not addressed in this proposal; for example the new theory could be applied to better understand Donaldson invariants.

1 240 500 €

Start date: 2014-01-01, End date: 2019-04-30

Supramolecular assemblies – formed by the self-assembly of hundreds of protein subunits – are part of bacterial nanomachines involved in key cellular processes. Important examples in pathogenic bacteria are pili and type 3 secretion systems (T3SS) that mediate adhesion to host cells and injection of virulence proteins. Structure determination at atomic resolution of such assemblies by standard techniques such as X-ray crystallography or solution NMR is severely limited: Intact T3SSs or pili cannot be crystallized and are also inherently insoluble. Cryo-electron microscopy techniques have recently made it possible to obtain low- and medium-resolution models, but atomic details have not been accessible at the resolution obtained in these studies, leading sometimes to inaccurate models. I propose to use solid-state NMR (ssNMR) to fill this knowledge-gap. I could recently show that ssNMR on in vitro preparations of Salmonella T3SS needles constitutes a powerful approach to study the structure of this virulence factor. Our integrated approach also included results from electron microscopy and modeling as well as in vivo assays (Loquet et al., Nature 2012). This is the foundation of this application. I propose to extend ssNMR methodology to tackle the structures of even larger or more complex homo-oligomeric assemblies with up to 200 residues per monomeric subunit. We will apply such techniques to address the currently unknown 3D structures of type I pili and cytoskeletal bactofilin filaments. Furthermore, I want to develop strategies to directly study assemblies in a native-like setting. As a first application, I will study the 3D structure of T3SS needles when they are complemented with intact T3SSs purified from Salmonella or Shigella. The ultimate goal of this proposal is to establish ssNMR as a generally applicable method that allows solving the currently unknown structures of bacterial supramolecular assemblies at atomic resolution.

1 456 000 €

Start date: 2014-05-01, End date: 2019-04-30

DNA double-strand breaks are perhaps the most harmful DNA damages and result in carcinogenic chromosome aberrations. Cells protect their genome by activating a complex signaling and repair network, collectively denoted DNA damage response (DDR). A key initial step of the DDR is the activation of the 360 kDa checkpoint kinase ATM (ataxia telangiectasia mutated) by the multifunctional DSB repair factor Mre11-Rad50-Nbs1 (MRN). MRN senses and tethers DSBs, processes DSBs for further resection, and recruits and activates ATM to trigger the DDR. A mechanistic basis for the activities of the core DDR sensor MRN has not been established, despite intense research over the past decade. Our recent breakthroughs on structures of core Mre11-Rad50 and Mre11-Nbs1 complexes enable us now address three central questions to finally clarify the mechanism of MRN in the DDR: - How does MRN interact with DNA or DNA ends in an ATP dependent manner? - How do MRN and associated factors such as CtIP process blocked DNA ends? - How do MRN and DNA activate ATM? We will employ an innovative structural biology hybrid methods approach by combining X-ray crystallography, electron microscopy and small angle scattering with crosslink mass spectrometry and combine the structure-oriented techniques with validating in vitro and in vivo functional studies. The anticipated outcome will clarify the structural mechanism of one of the most important but enigmatic molecular machineries in maintaining genome stability and also help understand the molecular defects associated with several prominent cancer predisposition and neurodegenerative disorders.

2 498 019 €

Start date: 2013-05-01, End date: 2018-04-30