ERC FUNDED PROJECTS

The traditional (Riemann) approach to analytic number theory uses the zeros of zeta functions. This requires the associated multiplicative function, say f(n), to have special enough properties that the associated Dirichlet series may be analytically continued. In this proposal we continue to develop an approach which requires less of the multiplicative function, linking the original question with the mean value of f. Such techniques have been around for a long time but have generally been regarded as “ad hoc”. In this project we aim to show that one can develop a coherent approach to the whole subject, not only reproving all of the old results, but also many new ones that appear inaccessible to traditional methods. Our first goal is to complete a monograph yielding a reworking of all the classical theory using these new methods and then to push forward in new directions. The most important is to extend these techniques to GL(n) L-functions, which we hope will now be feasible having found the correct framework in which to proceed. Since we rarely know how to analytically continue such L-functions this could be of great benefit to the subject. We are developing the large sieve so that it can be used for individual moduli, and will determine a strong form of that. Also a new method to give asymptotics for mean values, when they are not too small. We wish to incorporate techniques of analytic number theory into our theory, for example recent advances on mean values of Dirichlet polynomials. Also the recent breakthroughs on the sieve suggest strong links that need further exploration. Additive combinatorics yields important results in many areas. There are strong analogies between its results, and those for multiplicative functions, especially in large value spectrum theory, and its applications. We hope to develop these further. Much of this is joint work with K Soundararajan of Stanford University.

2 011 742 €

Start date: 2015-08-01, End date: 2020-07-31

A key synthetic challenge of widespread interest in chemical science involves the creation of well-defined 2D functional materials that exist on a length-scale of nanometers to microns. In this ambitious 5 year proposal we aim to tackle this issue by exploiting the unique opportunities made possible by recent developments with the living crystallization-driven self-assembly (CDSA) platform. Using this solution processing approach, amphiphilic block copolymers (BCPs) with crystallizable blocks, related amphiphiles, and polymers with charged end groups will be used to predictably construct monodisperse samples of tailored, functional soft matter-based 2D nanostructures with controlled shape, size, and spatially-defined chemistries. Many of the resulting nanostructures will also offer unprecedented opportunities as precursors to materials with hierarchical structures through further solution-based “bottom-up” assembly methods. In addition to fundamental studies, the proposed work also aims to make important impact in the cutting-edge fields of liquid crystals, interface stabilization, catalysis, supramolecular polymers, and hierarchical materials.

2 499 597 €

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

Quantum optics, the study of how discrete packets of light (photons) and matter interact, has led to the development of remarkable new technologies which exploit the bizarre properties of quantum mechanics. These quantum technologies are primed to revolutionize the fields of communication, information processing, and metrology in the coming years. Similar to contemporary technologies, the future quantum machinery will likely consist of a semiconductor platform to create and process the quantum information. However, to date the demanding requirements on a quantum photonic platform have yet to be satisfied with conventional bulk (three-dimensional) semiconductors. To surmount these well-known obstacles, a new paradigm in quantum photonics is required. Initiated by the recent discovery of single photon emitters in atomically flat (two-dimensional) semiconducting materials, 2DQP aims to be at the nucleus of a new approach by realizing quantum optics with ultra-stable (coherent) quantum states integrated into devices with electronic and photonic functionality. We will characterize, identify, engineer, and coherently manipulate localized quantum states in this two-dimensional quantum photonic platform. A vital component of 2DQP’s vision is to go beyond the fundamental science and achieve the ideal solid-state single photon device yielding perfect extraction - 100% efficiency - of on-demand indistinguishable single photons. Finally, we will exploit this ideal device to implement the critical building block for a photonic quantum computer.

1 999 135 €

Start date: 2018-01-01, End date: 2022-12-31

The field of C-H bond activation has evolved at an exponential pace in the last 15 years. What appeals most in those novel synthetic techniques is clear: they bypass the pre-activation steps usually required in traditional cross-coupling chemistry by directly metalating C-H bonds. Many C-H bond functionalizations today however, rely on poorly atom and step efficient oxidants, leading to significant and costly chemical waste, thereby seriously undermining the overall sustainability of those methods. As restrictions in sustainability regulations will further increase, and the cost of certain chemical commodities will rise, atom efficiency in organic synthesis remains a top priority for research. The aim of 2O2ACTIVATION is to develop novel technologies utilizing O2 as sole terminal oxidant in order to allow useful, extremely sustainable, thermodynamically challenging, dehydrogenative C-N and C-O bond forming coupling reactions. However, the moderate reactivity of O2 towards many catalysts constitutes a major challenge. 2O2ACTIVATION will pioneer the design of new catalysts based on the ultra-simple propene motive, capable of direct activation of O2 for C-H activation based cross-couplings. The project is divided into 3 major lines: O2 activation using propene and its analogues (propenoids), 1) without metal or halide, 2) with hypervalent halide catalysis, 3) with metal catalyzed C-H activation. The philosophy of 2O2ACTIVATION is to focus C-H functionalization method development on the oxidative event. Consequently, 2O2ACTIVATION breakthroughs will dramatically shortcut synthetic routes through the use of inactivated, unprotected, and readily available building blocks; and thus should be easily scalable. This will lead to a strong decrease in the costs related to the production of many essential chemicals, while preserving the environment (water as terminal by-product). The resulting novels coupling methods will thus have a lasting impact on the chemical industry.

1 489 823 €

Start date: 2017-03-01, End date: 2022-02-28