Our goal is to construct generalisations of the Hitchin and Wess--Zumino--Witten (WZW) and Knizhnik--Zamolodchikov (KZ) connections, both in geometric and deformation quantisation, and of their associated monodromy representations. The Hitchin connection achieved the quantisation of compact Chern--Simons theory and resulted in the construction of a topological quantum field theory. A different projectively flat connection provides a viable mathematical definition of correlation functions in the WZW model for conformal field theory. The resulting projectively flat vector bundles are isomorphic, and their monodromies have far-reaching applications in low-dimensional topology/geometry (quantum invariants of knots/3-manifolds) and representation theory (of mapping class/quantum/braid groups). Our guiding viewpoint is that the connections of Hitchin/WZW can be derived from the quantisation of moduli spaces of connections on Riemann surfaces. We will extend this further, focusing on meromorphic connections with high-order poles (i.e., wild singularities), generalising the above bundles and their applications. The motivation for this project is twofold. First, there is now a complete understanding of the Poisson/symplectic nature of isomonodromic deformations of wild singularitites, which are naturally amenable to quantisation. The quantum theory is much less developed than the classical one, and this naturally motivates us to close the gap using the latter as a guide. Second, recent work related the genus-zero WZW connection---that is, the KZ connection---to a new version of the Hitchin connection, and this was then used for the quantisation of moduli spaces of parabolic bundles. We want to pursue extensions of this identification; in particular, we will use the new flat connections constructed on the deformation quantisation side as candidates for `wild' Hitchin connections, in the geometric quantisation of wild character varieties: a complete novelty.

Eddy Current Testing (ECT) is an industrial procedure used to assess the reliability of the most critical facilities of nuclear power plants. Prior to practical usage, ECT requires a delicate phase of calibration and validation via numerical simulations. However, in the current state-of-the-art, they are limited by two critical issues: the poor precision of the results, and the limited geometrical modeling flexibility. This project will use the recently introduced Discrete de Rham (DDR) simulation method to overcome at once both these issues, focusing on three specific aims: laying the mathematical foundations of DDR methods for ECT simulation, building the practical computational tools to implement this method in a simulator, and using the simulator on real-life ECT scenarios. The project has a strong multidisciplinary nature, involving a combination of numerical analysis and engineering, and its originality and innovation lie on this interdisciplinary approach. The mathematical analysis of DDR methods for ECT is a complete novelty and represents a mine of mathematical problems in numerical analysis. The development of the EffECT simulation (open-source) will require both the transfer of the candidate’s engineering knowledge to the host institution and the training of the candidate on the very specific DDR mathematical methods. The project will thus make the candidate able to speak to different communities, improving his career prospects as an independent researcher. The planned communication activities of the project will target people both inside and outside academia, helping the latter to appreciate the effectiveness of the interaction between fundamental mathematical research and engineering in solving real-life problems. The arising results have the potential to increase the safety and efficiency of nuclear power plants and open new horizons in fundamental and applied level of numerical analysis of DDR methods, as well as other cutting-edge simulation methods.

The current exponential growth of energy consumption by electronic devices is not sustainable in the long term and has detrimental effects on global climate change, it requires solutions to reduce energy waste. One novel approach is the Artificial Neural Network (ANN), which is more efficient in performing several tasks as learning, pattern recognition and vision than the usual electronics and sequential algorithms. However, ANN lacks specific hardware to reach its potential. Recently, a lot of effort has been done to find memory devices to implement truly efficient neuromorphic hardware. High endurance and retention time, and low write energy, low write time and voltage are required. This research program proposes to create these memory devices with III-Sb compound semiconductor nanostructures since they are expected to have all these properties. In addition, their optoelectronic properties will allow the manipulation of memory states using light, which will provide unrivaled functionalities to the ANN that use these novels III-Sb memories.

The main goal of this project is the development of new polymeric catalysts and new catalytic membranes, designed to carry out high-end chemical oxidation in aqueous streams. Catalytic membranes are means to perform chemical transformation at the solid/ fluid interface and they are ideal interfacial reactors and contactors, simultaneously catalyzing and directing the heterogeneous phase reaction between substrates and oxidant agents. These systems have a key role in the future process industry and in water treatment since they enable oxidation reactions whilst reducing reagents and waste. Current systems employ inorganic and often high-value catalysts, which are generally of high cost, and prone to leaching causing loss of performance in time. I propose the first fully polymeric catalytic membrane made exclusively of bio-inspired iron coordination polymers. This research will lead to key scientific breakthroughs by: i) creating new non-heme catalytic polymers that mimic the activity of biological enzymes and that can be efficiently deployed to cast membranes for heterogeneous reaction; ii) designing and fabricating polymeric membranes consisting of the catalytic macromolecules and with suitable surface and morphological properties to precisely guide and enhance the contact among the reagents and with the catalyst; iii) successfully applying these systems maintaining high catalytic rate and yield and to understand the mechanisms and pathways of transformation of compounds, especially water micropollutants. These innovations will enable membrane robustness, long-term efficiency, and low cost. In particular, the potential of the new catalysts, membranes, and membrane reactors will be exemplified in the purification of contaminated streams to produce safe water. Thus, this new system represents a platform for a plethora of further advances in the field of oxidation processes applied to chemistry, engineering, and the environment.

Wine spoilage poses a significant threat to the global wine industry, leading to substantial economic losses and jeopardising its sustainability. This sector is already under strain, contending with issues including climate change, global competition, increasing production costs, declining consumption and evolving consumer preferences. Volatile Sulphur Compounds (VSCs) influence wine quality with their abundance and low perception threshold. While some VSCs enhance wine aromatic complexity, most of them cause negative wine faults such as aromas of cabbage and rotten eggs leading to discarded wine and substantial economic losses. Despite their significance, current methods for detecting and quantifying VSCs (particularly light VSCs) are inadequate. Additionally, a comprehensive model of sulfur metabolism is lacking. This project aims to develop innovative strategies for the accurate quantification, assessment, and management of VSCs during wine fermentation. The specific objectives are: (1) to identify VSC origins and characterise their production dynamics using a novel real-time monitoring device; (2) to assess sulfur compound flux distribution within yeast metabolic networks; and (3) to create the first model-based strategies for predicting and controlling VSC formation. The project includes a secondment to experts at the CSIC in Spain, where I will refine the model. This experience will significantly enhance my skills in analytical techniques and metabolic modelling while expanding my professional network and career prospects. The results of the project will offer valuable tools for both researchers in yeast metabolism and the wine industry, leading to improvements in quality control and production efficiency to mitigate the challenges faced. This pioneering research will provide a solid foundation for future projects in yeast metabolism and winemaking where the developed tools can be utilised.