ERC FUNDED PROJECTS

The sub-cellular processes that control the most critical aspects of life occur in three-dimensions (3D), and are intrinsically dynamic. While super-resolution microscopy has revolutionized cellular imaging in recent years, our current capability to observe the dynamics of life on the nanoscale is still extremely limited, due to inherent trade-offs between spatial, temporal and spectral resolution using existing approaches. We propose to develop and demonstrate an optical microscopy methodology that would enable live sub-cellular observation in unprecedented detail. Making use of multicolor 3D point-spread-function (PSF) engineering, a technique I have recently developed, we will be able to simultaneously track multiple markers inside live cells, at high speed and in five-dimensions (3D, time, and color). Multicolor 3D PSF engineering holds the potential of being a uniquely powerful method for 5D tracking. However, it is not yet applicable to live-cell imaging, due to significant bottlenecks in optical engineering and signal processing, which we plan to overcome in this project. Importantly, we will also demonstrate the efficacy of our method using a challenging biological application: real-time visualization of chromatin dynamics - the spatiotemporal organization of DNA. This is a highly suitable problem due to its fundamental importance, its role in a variety of cellular processes, and the lack of appropriate tools for studying it. The project is divided into 3 aims: 1. Technology development: diffractive-element design for multicolor 3D PSFs. 2. System design: volumetric tracking of dense emitters. 3. Live-cell measurements: chromatin dynamics. Looking ahead, here we create the imaging tools that pave the way towards the holy grail of chromatin visualization: dynamic observation of the 3D positions of the ~3 billion DNA base-pairs in a live human cell. Beyond that, our results will be applicable to numerous 3D micro/nanoscale tracking applications.

1 802 500 €

Start date: 2018-11-01, End date: 2023-10-31

Some of the most fascinating physical phenomena are experimentally observed in strongly correlated electron systems and, on the theoretical side, only poorly understood hitherto. The aim of the ERC project AbinitioDGA is the development, implementation and application of a new, 21th century method for the ab initio calculation of materials with such strong electronic correlations. AbinitioDGA includes strong electronic correlations on all time and length scales and hence is a big step beyond the state-of-the-art methods, such as the local density approximation, dynamical mean field theory, and the GW approach (Green function G times screened interaction W). It has the potential for an extraordinary high impact not only in the field of computational materials science but also for a better understanding of quantum critical heavy fermion systems, high-temperature superconductors, and transport through nano- and heterostructures. These four physical problems and related materials will be studied within the ERC project, besides the methodological development. On the technical side, AbinitioDGA realizes Hedin's idea to include vertex corrections beyond the GW approximation. All vertex corrections which can be traced back to a fully irreducible local vertex and the bare non-local Coulomb interaction are included. This way, AbinitioDGA does not only contain the GW physics of screened exchange and the strong local correlations of dynamical mean field theory but also non-local correlations beyond on all length scales. Through the latter, AbinitioDGA can prospectively describe phenomena such as quantum criticality, spin-fluctuation mediated superconductivity, and weak localization corrections to the conductivity. Nonetheless, the computational effort is still manageable even for realistic materials calculations, making the considerable effort to implement AbinitioDGA worthwhile.

1 491 090 €

Start date: 2013-01-01, End date: 2018-07-31

The rise of atmospheric O2 ~2,500 million years ago is one of the most profound transitions in Earth's history. Yet, despite its central role in shaping Earth's surface environment, the cause for the rise of O2 remains poorly understood. Tight coupling between the O2 cycle and the biogeochemical cycles of redox-active elements, such as C, Fe and S, implies radical changes in these cycles before, during and after the rise of O2. These changes, too, are incompletely understood, but have left valuable information encoded in the geological record. This information has been qualitatively interpreted, leaving many aspects of the rise of O2, including its causes and constraints on ocean chemistry before and after it, topics of ongoing research and debate. Here, I outline a research program to address this fundamental question in geochemical Earth systems evolution. The inherently interdisciplinary program uniquely integrates laboratory experiments, numerical models, geological observations, and geochemical analyses. Laboratory experiments and geological observations will constrain unknown parameters of the early biogeochemical cycles, and, in combination with field studies, will validate and refine the use of paleoenvironmental proxies. The insight gained will be used to develop detailed models of the coupled biogeochemical cycles, which will themselves be used to quantitatively understand the events surrounding the rise of O2, and to illuminate the dynamics of elemental cycles in the early oceans. This program is expected to yield novel, quantitative insight into these important events in Earth history and to have a major impact on our understanding of early ocean chemistry and the rise of O2. An ERC Starting Grant will enable me to use the excellent experimental and computational facilities at my disposal, to access the outstanding human resource at the Weizmann Institute of Science, and to address one of the major open questions in modern geochemistry.

1 472 690 €

Start date: 2013-09-01, End date: 2018-08-31

In a typical learning problem one tries to approximate an unknown function by a function from a given class using random data, sampled according to an unknown measure. In this project we will be interested in parameters that govern the complexity of a learning problem. It turns out that this complexity is determined by the geometry of certain sets in high dimension that are connected to the given class (random coordinate projections of the class). Thus, one has to understand the structure of these sets as a function of the dimension - which is given by the cardinality of the random sample. The resulting analysis leads to many theoretical questions in Asymptotic Geometric Analysis, Probability (most notably, Empirical Processes Theory) and Combinatorics, which are of independent interest beyond the application to Learning Theory. Our main goal is to describe the role of various complexity parameters involved in a learning problem, to analyze the connections between them and to investigate the way they determine the geometry of the relevant high dimensional sets. Some of the questions we intend to tackle are well known open problems and making progress towards their solution will have a significant theoretical impact. Moreover, this project should lead to a more complete theory of learning and is likely to have some practical impact, for example, in the design of more efficient learning algorithms.

750 000 €

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