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

The suite of graphene’s unique properties and applications can be enormously enhanced by its functionalization. As non-covalently functionalized graphenes do not target all graphene’s properties and may suffer from limited stability, covalent functionalization represents a promising way for controlling graphene’s properties. To date, only a few well-defined graphene derivatives have been introduced. Among them, fluorographene (FG) stands out as a prominent member because of its easy synthesis and high stability. Being a perfluorinated hydrocarbon, FG was believed to be as unreactive as the two-dimensional counterpart perfluoropolyethylene (Teflon®). However, our recent experiments showed that FG is not chemically inert and can be used as a viable precursor for synthesizing graphene derivatives. This surprising behavior indicates that common textbook grade knowledge cannot blindly be applied to the chemistry of 2D materials. Further, there might be specific rules behind the chemistry of 2D materials, forming a new chemical discipline we tentatively call 2D chemistry. The main aim of the project is to explore, identify and apply the rules of 2D chemistry starting from FG. Using the knowledge gained of 2D chemistry, we will attempt to control the chemistry of various 2D materials aimed at preparing stable graphene derivatives with designed properties, e.g., 1-3 eV band gap, fluorescent properties, sustainable magnetic ordering and dispersability in polar media. The new graphene derivatives will be applied in sensing, imaging, magnetic delivery and catalysis and new emerging applications arising from the synergistic phenomena are expected. We envisage that new applications will be opened up that benefit from the 2D scaffold and tailored properties of the synthesized derivatives. The derivatives will be used for the synthesis of 3D hybrid materials by covalent linking of the 2D sheets joined with other organic and inorganic molecules, nanomaterials or biomacromolecules.

1 831 103 €

Start date: 2016-06-01, End date: 2021-05-31

"Two-dimensional (2D) nanosheets, which possess a high degree of anisotropy with nanoscale thickness and infinite length in other dimensions, hold enormous promise as a novel class of ultrathin 2D nanomaterials with various unique functionalities and properties, and exhibit great potential in energy storage and conversion systems that are substantially different from their respective 3D bulk forms. Here I propose a strategy for the synthesis and processing of various 2D nanosheets across a broad range of inorganic, organic and polymeric materials with molecular-level or thin thickness through both the top-down exfoliation of layered materials and the bottom-up assembly of available molecular building blocks. Further, I aim to develop the synthesis of various 2D-nanosheet based composite materials with thickness of less than 100 nm and the assembly of 2D nanosheets into novel hierarchal superstrucutures (like aerogels, spheres, porous particles, nanotubes, multi-layer films). The structural features of these 2D nanomaterials will be controllably tailored by both the used layered precursors and processing methodologies. The consequence is that I will apply and combine defined functional components as well as assembly protocols to create novel 2D nanomaterials for specific purposes in energy storage and conversion systems. Their unique characters will include the good electrical conductivity, excellent mechanical flexibility, high surface area, high chemical stability, fast electron transport and ion diffusion etc. Applications will be mainly demonstrated for the construction of lithium ion batteries (anode and cathode), supercapacitors (symmetric and asymmetric) and fuel cells. As the key achievements, I expect to establish the delineation of reliable structure-property relationships and improved device performance of 2D nanomaterials."

1 500 000 €

Start date: 2012-09-01, End date: 2017-08-31

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