With a Consolidator Grant, the ERC enables promising early career researchers (seven to twelve years into their post-doc phase) to consolidate their academic independence.
Funding period
2024–2028
Abstract
In DIONISOS, we aim to develop new analytical relationships for ion- and heat-transport in ionic conductors, and thus heal significant inconsistencies of the current understanding. Currently ion- and heat transport are interpreted as unrelated phenomena; ion transport being based on local jumps, whereas heat transport being mediated by dynamic lattice vibrations called phonons.
Funding period
2023–2028
Abstract
In many relevant real-world problems it is of fundamental importance to approximately compute evaluations of high-dimensional functions. Standard deterministic approximation methods often suffer in this context from the so-called curse of dimensionality in the sense that the number of computational operations of the approximation method grows at least exponentially in the problem dimension. It is the key objective of the ERC-funded MONTECARLO project to employ multilevel Monte Carlo and stochastic gradient descent type methods to design and analyse algorithms which provably overcome the curse of dimensionality in the numerical approximation of several high-dimensional functions; these include solutions of certain stochastic optimal control problems of some nonlinear partial differential equations and of certain supervised learning problems.
Funding period
2022–2027
Abstract
Partial differential equations are fundamental to describing processes in which one variable is dependent on two or more others – most situations in real life. Stochastic partial differential equations (SPDEs) describe physical systems subject to random effects. In the description of scaling limits of interacting particle systems and in quantum field theories analysis, the randomness is due to fluctuations related to noise terms on all length scales. The presence of a non-linear term can lead to divergencies. Funded by the European Research Council, the GE4SPDE project will describe the global behaviour of solutions of some of the most prominent examples of semi-linear SPDEs, building on the systematic treatment of the renormalisation procedure used to deal with these divergencies.
Funding period
2021–2026
Abstract
The earliest society in the ancient world, Babylonia went through two major regime changes and was consecutively ruled by three empires: the Assyrian, the Chaldean and the (first) Persian. But little is known about how imperial rule was negotiated locally and how the strategies that rulers and the ruled applied in pursuit of their interests interacted and led to instability or stability. The EU-funded GoviB project will explore the politics and authority in the ancient city of Babylon. By analysing newly available textual and archaeological material, the project will shed light on what causes states to be stable or instable and how regime changes fail or succeed.
Funding Period
2019–2025
Abstract
Equality can be defined as the condition of being equal and as the right of different groups of people to have a similar social position and receive the same treatment. While all major national and international human rights instruments include norms protecting equality, there is no agreement about what equality exactly means or entails. Within this legal context, the EU-funded EQUALITY project will study the extent to which legal equality guarantees tolerate inequality. Specifically, the project will analyse how courts conceptualise equality in constitutional and international human rights law. For instance, it will consider the factors that influence the courts when deciding cases involving inequality.
Funding period
2022–2024 (startet 2018 at the Technical University of Munich)
Abstract
The Langlands programme is a far-reaching web of conjectural or proven correspondences joining the fields of representation theory and of number theory. It is one of the centerpieces of arithmetic geometry, and has in the past decades produced many spectacular breakthroughs, for example the proof of Fermat’s Last Theorem by Taylor and Wiles. The most successful approach to prove instances of Langlands’ conjectures is via algebraic geometry, by studying suitable moduli spaces such as Shimura varieties. Their cohomology carries actions both of a linear algebraic group (such as GLn) and a Galois group associated with the number field one is studying. A central tool in the study of the arithmetic properties of these moduli spaces is the Newton stratification, a natural decomposition based on the moduli description of the space. Recently the theory of Newton strata has seen two major new developments: Representation-theoretic methods and results have been successfully established to describe their geometry and cohomology. Furthermore, an adic version of the Newton stratification has been defined and is already of prime importance in new approaches within the Langlands programme. This project aims at uniting these two novel developments to obtain new results in both contexts with direct applications to the Langlands programme, as well as a close relationship and dictionary between the classical and the adic stratifications. It is subdivided into three parts which mutually benefit from each other: Firstly we investigate the geometry of Newton strata in loop groups and Shimura varieties, and representations in their cohomology. Secondly, we study corresponding geometric and cohomological properties of adic Newton strata. Finally, we establish closer ties between the two contexts. Here we want to obtain analogues to results on one side for the other, but more importantly aim at a direct comparison that explains the similar behaviour directly.
Funding period
2020–2024 (started 2018 at the Imperial College London)
Abstract
The present proposal is concerned with the analysis of the Einstein equations of general relativity, a non-linear system of geometric partial differential equations describing phenomena from the bending of light to the dynamics of black holes. The theory has recently been confirmed in a spectacular fashion with the detection of gravitational waves. The main objective of the proposal is to consolidate my research group by developing novel mathematical techniques that will fundamentally advance our understanding of the Einstein equations. Here the proposal builds on mathematical progress in the last decade resulting from achievements in the fields of partial differential equations, differential geometry, microlocal analysis and theoretical physics.
Funding period
2019–2024
Abstract
Organofluorine compounds, organic molecules containing carbon-fluorine bonds, are widely used to make high-impact pharmaceuticals, imaging agents, agrochemicals and various materials. Numerous pharmaceuticals are fluorinated to impart enhanced metabolic and oxidative stability, lipophilicity and membrane permeability. However, we have likely only seen the tip of the iceberg when it comes to the potential of organofluorine compounds. The roadblock has been limitations in controlling fluorination sites and the resulting 2D and 3D molecular architecture. RECON is working to unlock the potential of complex fluorinated compounds with rational design of structure for highly specific and unique function. Even better, these methods rely on cost-effective and commercially available fluoride feedstock.
Funding period
2018–2023
Abstract
Light is an excellent external regulatory element that can be applied to cells and organisms with high spatio-temporal precision and without interfering with cellular processes. Optochemical biology exploits small photo-responsive chemical groups to cage and activate or to switch biomolecular functions in response to light of a defined wavelength. Caged antisense agents have enabled down-regulation of gene expression with spatio-temporal control at the messenger-RNA (mRNA) level in vivo, however approaches for triggering translation of exogenous mRNA lack efficient turn-on effects. To explore the effects of conditional and transient ectopic gene expression in a developing organism it is vital to fully abrogate and restore translational efficiency. The goal of this project is to bring eukaryotic mRNA under the control of light to trigger efficient ectopic translation with spatio-temporal resolution in cells and in vivo. To achieve this, eukaryotic mRNA will be photo-caged at its 5′ cap using a highly promiscuous methyltransferase capable of transferring very bulky moieties from synthetic analogs of the cosubstrate S-adenosylmethionine (AdoMet). A single 5′ cap modification will block translation of the respective mRNA. Its light-triggered removal will release unmodified capped RNA, which in cells will be efficiently remethylated to form the canonical 5′ cap resulting in uncompromised translation. In addition to labeling and tracking subpopulations of cells, we will use our technology to control and to manipulate cell fate by locally producing proteins responsible for cell death, genome engineering, and cell migration. We will use cultured cells and one-cell stage zebrafish embryos that can be easily injected with mRNA to study the function of ectopic gene expression in early development. Our approach will overcome current limitations of photo-inducible mRNA translation and enable us to manipulate a developing organism at the molecular level.
Funding period
2018–2021
Abstract
Epithelial polarity is one of the most fundamental types of cellular organization, and correct cellular polarization is vital for all epithelial tissue. Failure to establish polarity leads to severe phenotypes, from catastrophic developmental deficiencies to life-threatening diseases such as cancer. Despite knowing much about the signalling and trafficking machinery vital for polarity, we lack quantitative knowledge about the intracellular mechanical processes which organize and stabilize epithelial polarity. This presents a critical knowledge gap, as any elaborated understanding of intracellular organization needs to include the forces and viscoelastic mechanical properties that position organelles and proteins. As such, the main aim of POLARIZEME is to determine the intracellular mechanical processes relevant for epithelial polarization, thus providing a mechanical understanding of polarity. We will combine advanced optical tweezers technology with cutting-edge molecular biology tools to rigorously test new intracellular transport concepts such as the active, diffusion-like forces that can position organelles or the recently introduced cortical actin flows that can drag polarity-defining proteins around the cell. Thus we propose (i) to quantify active forces and intracellular mechanics and their relation to organelle positioning, (ii) to quantify polarized cortical and cytoplasmic flows, and (iii) to measure the forces and mechanical obstacles relevant for direct vesicle trafficking. These quantitative biophysics experiments will be supported by mathematical modelling and the development of two new instruments which (a) allow for automated intracellular mechanics measurements over extended time periods and (b) combine multi-view light-sheet microscopy with optical tweezers and UV ablation. Overall, we will provide a new access to understand and describe polarity by merging the physical and biological aspects of its initiation, maintenance and stability.
Funding period
2017–2023
Abstract
Chemical transformations comprise the polarization of the reacting species. As a consequence, partially or fully charged reagents and intermediates are omnipresent in chemistry. Although anion-binding processes are well-known for their crucial role in molecular recognition, this type of phenomenon has only recently been utilized for catalysis. Since catalytic reactions are of utmost relevance to construct valuable chemicals and materials, this mode of catalytic chemical activation might be the key for the future design of original and more efficient synthetic transformations. However, the effects of anions in catalytic processes are still largely unknown. Aiming at providing a novel general synthetic toolbox, in this project I propose several anion-binding activation concepts to solve current challenging catalytic synthetic problems. To achieve this goal, structurally different chiral anion-binding catalysts will be developed and incorporated into the existing limited palette of catalyst library. Furthermore, I propose a significant expansion of the application scope of anion-binding catalysis based on the activation and modulation of anionic nucleophiles and oxidants to develop organocatalytic reactions such as halogenations and oxidations, including the asymmetric functionalization of C-H bonds. In addition, anion-binding processes will be used to facilitate key steps in cross-coupling reactions such as the transmetallation, as well as the photoactivity modulation of readily available photosensitizers and the introduction of asymmetric photocatalysis involving radical-anions.The proposed groundbreaking approaches will revolutionize not only anion-binding catalysis but also all the scientific areas relying on catalytic synthetic methods. Thus, the results derived from this project will have a tremendous impact in diverse fields such as catalysis, organic synthesis and material sciences, as well as in economical, environmental and industrial issues.
Funding period
2017–2021
Abstract
Quantum processors are envisioned to conquer ultimate challenges in information processing and to enable simulations of complex physical processes that are intractable with classical computers. Among the various experimental approaches to implement such devices, scalable technologies are particularly promising because they allow for the realization of large numbers of quantum components in circuit form. For upscaling towards functional applications distributed systems will be needed to overcome stringent limitations in quantum control, provided that high-bandwidth quantum links can be established between the individual nodes. For this purpose the use of single photons is especially attractive due to compatibility with existing fibre-optical infrastructure. However, their use in replicable, integrated optical circuits remains largely unexplored for non-classical applications.In this project nanophotonic circuits, heterogeneously integrated with superconducting nanostructures and carbon nanotubes, will be used to realize scalable quantum photonic chips that overcome major barriers in linear quantum optics and quantum communication. By relying on electro-optomechanical and electro-optical interactions, reconfigurable single photon transceivers will be devised that can act as broadband and high bandwidth nodes in future quantum optical networks. A hybrid integration approach will allow for the realization of fully functional quantum photonic modules which are interconnected with optical fiber links. By implementing quantum wavelength division multiplexing, the communication rates between individual transceiver nodes will be boosted by orders of magnitude, thus allowing for high-speed and remote quantum information processing and quantum simulation. Further exploiting recent advances in three-dimensional distributed nanophotonics will lead to a paradigm shift in nanoscale quantum optics, providing a key step towards optical quantum computing and the quantum internet.
Funding period
2017–2021
Abstract
Human Papillomavirus Type 16 (HPV16), the paradigm cancer-causing HPV type, is a small, nonenveloped, DNA virus characterized by its complex life cycle coupled to differentiation of squamous epithelia. Due to this complexity, how HPV16 infects cells is an understudied field of research. Our previous work to define the cellular pathways that are hijacked for initial infection revealed uptake by a novel endocytosis mechanism, and the requirement for mitosis for nuclear delivery. Our findings indicated that nuclear envelope breakdown was required to access the nuclear space, and that the virus associated with mitotic chromatin during metaphase. This prolonged mitosis, a process beneficiary for infection. The viral L2 protein as part of incoming viruses mimics this on its own. The aim of this proposal is to reveal how HPV16 differentially modulates or takes advantage of the mitotic machinery for nuclear import in cells, tissues or during aging, and whether malignant cellular consequences arise. On the viral side, we will define the minimal properties of L2 to mediate association with cell chromatin and mitosis prolongation. On the cellular side, we will identify the protein(s) that mediate recruitment, and how it occurs in a detailed temporal/spatial manner. To elucidate the mechanism of mitotic prolongation and consequences thereof, we will identify which regulatory complex of mitosis is targeted, how it is induced, and whether it causes DNA damage or segregation errors. Finally, we will ascertain the influence of tissue differentiation and aging on this process. Using systems biology, proteomics, virology, cell biology, biochemistry, and a wide range of microscopy approaches we will unravel the complex interactions between HPV and the host cell mitosis machinery. In turn, as viruses often serve as valuable tools to study cell function, this work is likely to uncover new insights into how cells spatially and temporally regulate mitosis in differentiation and aging.
Funding period
2015–2019
Abstract
Our proposed research lies at the interface of Geometry, Group Theory, Number Theory and Combinatorics. In recent years, striking results were obtained in those disciplines with the help of a surprise newcomer at the border between mathematics and logic: Model Theory. Bringing its unique point of view and its powerful formalism, Model Theory made a resounding entry into several different fields of mathematics. Here shedding new light on a classical phenomenon, there solving a long-standing open problem via a completely new method. Recent examples of concrete mathematical problems where Model Theory interacted in a fruitful manner abound: the local version of Hilbert's 5th problem by Goldbring and van den Dries, Szemeredi's theorems in combinatorics and graph theory, the André-Oort conjecture in diophantine geometry (Pila, Wilkie, Zannier), etc. In this vein, and building on Hrushovski's model-theoretic work, Green, Tao and myself recently settled a conjecture of Lindenstrauss pertaining to the structure of approximate groups. Our plan in this project is to put these methods into further use, to collaborate with model theorists, and to start looking through this prism at a small collection of familiar problems coming from combinatorics, group theory, analysis and spectral geometry of metric spaces, or from arithmetic geometry. Among them: extend our study of approximate groups to the general setting of locally compact groups, obtain uniform estimates on the spectrum of Cayley graphs of large finite groups, prove an analogue for character varieties of the Pink-Zilber conjectures in relation with rigidity theory for discrete subgroups of Lie groups, and clarify the links between uniform spectral gaps and height lower bounds in diophantine geometry with a view towards Lehmer's conjecture.
Funding period
2014–2018
Abstract
This project will develop novel techniques for solving inverse problems in life sciences, in particular related to dynamic imaging. Major challenges in this area are efficient four- dimensional image reconstruction under low SNR conditions and further the quantification of image series as obtained from molecular imaging or life microscopy techniques. We will tackle both of them in a rather unified framework as inverse problems for time-dependent (systems of) partial differential equations. In the solution of these inverse problems we will investigate novel approaches for the following aspects specific to the above-mentioned problems in the life sciences: 1. Solution of inverse problems for PDEs in complex time-varying geometries 2. Development of appropriate variational regularization models for dynamic images, including noise and motion models 3. Improved forward and inverse modelling of cellular and intracellular dynamics leading to novel inverse problems for nonlinear partial differential equations 4. Construction and implementation of efficient iterative solution methods for the arising 4D inverse problems and their variational formulation All tasks will be driven by concrete applications in biology and medicine and their success will be evaluated in applications to real problems and data. This is based on interdisciplinary work related to electrocardiology and developmental biology. The overall development of methods will however be carried out in a flexible and modular way, so that they become accessible for larger problem classes.
Funding period
2014–2019
Abstract
The project 'New isotope tracers for core formation in the terrestrial planets (ISOCORE)' will investigate the differentiation and volatile accretion history of the Earth. The two main research themes are (i) the mechanisms and timescales of accretion and core formation in the Earth, Moon and Mars, and (ii) the origin of Earth's volatiles (including water) with a particular focus on the time of volatile delivery to the Earth. The key concept of ISOCORE is to combine precise measurement of stable isotope fractionations in natural samples with a calibration of the fractionations in high temperature metal-silicate equilibration experiments. The work on the project will be subdivided into five strongly interlinked subprojects, all of which share the overarching goal of constraining core formation and volatile accretion on Earth and other planetary bodies.