One of the central questions in number theory is the solution of diophantine equation: to determine the set of all rational solutions of a system of polynomial equations with rational coefficients. The name diophantine is derived from name of Diophantus of Alexandria, of the third century AD, whose influential books "Arithmetica" shaped the development of number theory. From the point of view of algebraic geometry, the equations that Diophantus studied mostly define curves and his goal was to determine the set of integral (or rational) solutions. By virtue of many celebrated results, the case of rational points on curves is theoretically well-understood, and the motto "Geometry Determines Arithmetic" is fully justified. Indeed, an algebraic curve has a unique discrete invariant, its genus, taking non-negative integral values. If a curve has genus zero, then the question of determining whether it has rational points or not is completely algorithmic, and the set of all its rational points can be efficiently determined. If a curve has genus one, then the question of determining whether it has a rational point or not is typically feasible in concrete cases. There is a procedure to decide whether a curve of genus one has a point, but, if the curve does not have points, it is not known whether this procedure necessarily terminates. The finiteness of this procedure essentially relies on the finiteness of the Tate-Shafarevich groups. If a curve of genus one admits a point, then the set of its rational points can be endowed with a very natural structure of an abelian group. This group is finitely generated over number fields by the Mordell-Weil Theorem; explicit generators can again be found subject essentially to the Birch--Swinnerton-Dyer Conjecture. Finally, curves of genus at least two only have finitely many rational points, by Faltings' celebrated proof of the Mordell Conjecture. The situation is entirely different in higher dimensions. Bombieri and Lang formulated a conjecture implying that the distribution of rational points on varieties shares many similarities with the case of curves. Conjecture (Bombieri-Lang). The set of rational points of a smooth projective variety of general type over a number field is not Zariski dense. While this conjecture is very appealing, already in the case of surfaces, there is very little supporting evidence for it. The overall goal of this project is to study algebraic surfaces, mostly of general type, of special arithmetic interested, with the aim of gathering evidence for the Bombieri-Lang Conjecture. For this purpose we will compute the Picard groups and automorphism groups of various surfaces. We will use this information to look for curves of genus at most one on the surfaces, and determine the rational points on such curves. All this data will provide clues on possible modular interpretations of the surfaces: we will try to establish the modularity of these surfaces, trying first among moduli spaces of Abelian varieties and moduli spaces of vector bundles.

"Epoxyketones are an important class of bacterial nonribosomal peptides that target the proteolytic -subunit of the proteasome. They inspired the development of carfilzomib, an epoxyketone approved in 2012 for the treatment of multiple myeloma. Oprozimib, a second-generation orally available anticancer epoxyketone, and KZR-616, an epoxyketone that selectively targets the immune proteasome, are currently in phase II clinical trials. All three are manufactured via chemical synthesis, which is costly and unsustainable. We aim to develop cheaper and more sustainable biocatalytic approaches for epoxyketone production. We have investigated the biosynthesis of TMC-86A and eponemycin, two closely related epoxyketones produced by Actinobacteria. The biosynthetic gene clusters for these metabolites have been cloned using transformation-associated recombination (TAR) in yeast and expressed in a heterologous host. TAR-based methods have been used to create in-frame deletions in each of the biosynthetic genes and characterisation of the metabolites accumulated in each of the mutants has provided extensive insights into the nature and order of each of the biosynthetic steps. We have also shown using in vitro biochemical methods that the epoxyketone pharmacophore of these metabolites is assembled from the -dimethyl--keto acid product of a hybrid nonribosomal peptide synthetase-polyketide synthase (NRPS-PKS) by an unusual trifunctional flavin-dependent decarboxylase-dehydrogenase-monooxygenase (epoxyketone synthase). This enzyme has been shown to accept several analogues of the natural substrate. In this project, we aim to determine the X-ray crystal structure of the epoxyketone synthase, providing a basis for rational engineering to further broaden its substrate tolerance, and develop a mutasynthesis approach for the production of epoxyketones that are structurally related to the compounds currently undergoing clinical trials."

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The 2D Experimental Pilot Line (2D-EPL) project will establish a European ecosystem for prototype production of Graphene and Related Materials (GRM) based electronics, photonics and sensors. The project will cover the whole value chain including tool manufacturers, chemical and material providers and pilot lines to offer prototyping services to companies, research centers and academics. The 2D-EPL targets to the adoption of GRM integration by commercial semiconductor foundries and integrated device manufacturers through technology transfer and licensing. The project is built on two pillars. In Pillar 1, the 2D-EPL will offer prototyping services for 150 and 200 mm wafers, based on the current state of the art graphene device manufacturing and integration techniques. This will ensure external users and customers are served by the 2D-EPL early in the project and guarantees the inclusion of their input in the development of the final processes by providing the specifications on required device layouts, materials and device performances. In Pillar 2, the consortium will develop a fully automated process flow on 200 and 300 mm wafers, including the growth and vacuum transfer of single crystalline graphene and TMDCs. The knowledge gained in Pillar 2 will be transferred to Pillar 1 to continuously improve the baseline process provided by the 2D-EPL. To ensure sustainability of the 2D-EPL service after the project duration, integration with EUROPRACTICE consortium will be prepared. It provides for the European actors a platform to develop smart integrated systems, from advanced prototype design to small volume production. In addition, for the efficiency of the industrial exploitation, an Industrial Advisory Board consisting mainly of leading European semiconductor manufacturers and foundries will closely track and advise the progress of the 2D-EPL. This approach will enable European players to take the lead in this emerging field of technology.