I will visit 2 international centres of excellence, namely the group of Prof. Keisuke Goda at the University of Tokyo (Japan) and the group of Prof. Charles Schroeder at the University of Illinois at Urbana-Champaign (USA) to i) learn two state-of the art techniques and ii) to establish new collaborations combining the unique activities carried out in my lab at Swansea University, developed under EP/S036490/1, with their pioneering technologies spanning the fields of artificial intelligence applied to microfluidics (Japan) and passive 3D flow control of objects in Stokes flow (USA). The group of Prof. Goda has pioneered the use of artificial intelligence to enable rapid detection of different cell-line populations. The group of Prof. Schroeder has recently developed a microfluidic platform using the proprietary Stokes Trap technique (developed earlier by the same group) to trap and manipulate objects in 3D flows. During my visits, we will achieve the following overall goals: i) Employ my expertise in generating strings of equally-spaced particles in simple microfluidic geometries, further enhanced under EP/S036490/1, to transform the image activated cell-sorter developed by the group of Prof. Goda; and ii) employ my expertise in controlling the encapsulation of particles in viscoelastic liquids within microfluidic geometries to study particle-particle interactions within compartmentalised droplets trapped using the Stokes trap. The impact of this travel can be quantified as: i) establish two new collaborations between the UK and several world-leading research groups, who are currently at the forefront of their field of study; and ii) apply for joint grant applications based on the preliminary data developed during this project. Furthermore, we foresee a clear pathway to develop new technologies aimed at transforming healthcare, thanks to the long-term involvement of companies within our network portfolio.

The classification of algebraic varieties up to birational equivalence has long been a fundamental problem of Algebraic Geometry.Two varieties are birationally equivalent if they become isomorphic after removing a small subset. It is possible to produce ever larger varieties by simple birational operations (such as blowing up subvarieties), and hence classifying varieties amounts to finding a best, or ``minimal , representative for a birational equivalence class. The Minimal Model Program (MMP) is a still incomplete project started in the 1970s, which given an algebraic variety X, performs a finite number of elementary steps to produce an end product of pure geometric type. These pure geometric type are minimal models on the one hand, and Fano varieties on the other.Minimal models, as their name indicates, realise the hope of being a best (minimal) match for their equivalence class. Fano varieties are close to projective spaces, and should be thought of as the higher dimensional analogue of the sphere in the Uniformisation theorem for Riemann surfaces. Assuming the MMP, the problem of classification of varieties is reduced to understanding the elementary steps of the MMP and its possible outcomes. There remain a number of open questions to achieve completion of the MMP in higher dimensions. In dimension 3, the MMP was completed in the 80s, yet our understanding of its products is partial at best. Some very natural questions remain unanswered. For instance, since the end product of the MMP is not unique, when are two possible end products of the MMP birational? Is it possible to tell which end products are rational, i.e. birational to projective space? My research aims at answering these questions for Fano 3-folds. The MMP produces varieties that are mildly singular-- in dimension 3, these singularities are isolated points. My research shows that when a Fano has ``many'' singular points it tends to acquire many birational maps to other Fano 3-folds, and therefore behave like projective space. What ``many'' means in this context is topological: a Fano has many singular points if these singular points actually lie on a surface S contained in X that is not a hyperplane section of X. My research project argues that, conversally, if there is no such surface lying on X, X behaves as if it was nonsingular. Surprisingly, for Fanos of small degree, this often implies that they are only birational to very few other Fano 3-folds and are therefore nonrational.

Re4Rail project aims to build new technological enablers for sustainable asset management throughout the life cycle of railway granular media (RGM). The technological enablers include a health monitoring system (during service for repair) and circularity management (through end-of-life reuse, recycle and repurpose) aiming for zero carbon emissions of RGM, of which railway ballast and sub-ballast provide crucial support to track systems. Re4Rail will be achieved by establishing an innovative AI & digital twin-based automated technology for real-time RGM defect diagnosis and prognosis (Re4Tech). The applicant will conduct Re4Rail under the supervision of world-renown scientists at University of Birmingham (UoB), and secondment supervisors across sectors at Loram Finland Oy (non-academic) and at University of Illinois Urbana-Champaign (academic). Not only will Re4Rail revolutionise the smart maintenance and circular economy for RGM, but it will also enact the applicant's new competency in artificial intelligence, digital transformation, and geophysics, and endorse my employability skills in both academia and industry within UK and Europe. It also opens a new door of using novel data science tools (AI and digital twin) in solving challenging engineering issues (RGM digitalisation and sustainability) towards accomplishing global common goal (zero carbon emissions). Re4Tech will reduce RGM-related costs by 55% (expected) through the following improvements: (i) Re4Tech will classify and guide materials circularity optimisation, which will reduce the inspection and maintenance frequencies by 80% (expected); (ii) increase RGM operational life by 50% (expected); and (iii) reduce usage of raw granular materials by 40% (expected). Re4Rail will reduce carbon emissions by 70% (expected) throughout its life cycle, plus reducing inspection and maintenance frequencies. Re4Rail will empower Europe to certainly become a world leader in digital maintenance of railway towards net zero by 2030.

The remarkable idea that matter is made up of discrete units, indiscernible to the eye, can be traced back at least as far as ancient Greece. In the centuries since philosophers and scientists have grappled with the myriad questions this atomic theory of matter raises. This research project is guided by one such question: How does matter, consisting of a multitude of interacting particles, exhibit such a rich array of patterns and structures? Over the course of the past century, the field of statistical physics has emerged to deal with precisely this question. The essence of the problem, to understand the relationship between order and disorder, is so fundamental that it is central to a number of scientific fields. The overarching goal of this project is to show how the tools and intuitions from statistical physics provide a unified framework for solving problems in combinatorics, computer science, and geometry. These investigations will also have the reciprocal benefit of shedding new light on old problems in statistical physics itself. The starting point for this research project is one of the oldest mathematical models of a gas or liquid known as the hard sphere model: simply throw identical non-overlapping spheres into a fixed box at random. As the number of spheres increases, one might expect the spheres to begin to follow a crystalline pattern so that they can all fit inside the box. This shift from randomness to structure is known as a phase transition in physics and it suggests a remarkable fact about matter: the freezing of a gas to a solid occurs for purely geometric reasons. However, mathematically proving that a phase transition in the hard sphere model actually occurs is a major unsolved problem. This problem is intimately related to a problem in geometry that dates back to Kepler in 1611: If you want to fit as many identical spheres into a box as possible, what is the best way to arrange them? This puzzle, known as the sphere packing problem, remained unsolved for almost 400 years. This project proposes the hard sphere model as a key to a deeper understanding of the sphere packing problem. One aim of this project is to prove the existence of particularly dense sphere packings in high-dimensional space. The second part of this research project concerns the study of phase transitions in computer science. Simulating the hard sphere model is one of the oldest challenges in computer science. Indeed the Metropolis Algorithm, one of the most influential algorithms of the 20th century, was developed for precisely this purpose. There is a fascinating connection between the computational complexity of simulating the hard sphere model and the physical phase (gaseous or solid) of the system. Algorithms, such as the Metropolis Algorithm, tend to do well in the gaseous regime, but begin to fail when the system begins to freeze. One theme of this project will be to show that phase transitions need not be an obstacle for the design of successful algorithms. In fact, we will show that the very mechanisms that drive phase transitions can be exploited to design efficient algorithms that work in the ordered, 'frozen' regime. The third part of this project aims to bridge the fields of statistical physics and the mathematical field of combinatorics. A central object of study in combinatorics is known as a graph: a collection of nodes and edges between them. Graphs can be used to encode a vast array of information e.g. people in a social network, neurons communicating in a brain, or a system of interacting particles. A major theme in both statistical physics and combinatorics is to understand the relationship between structure and randomness and both fields have independently developed intricate tools to study the very same phenomena. I plan to combine two powerful methods, one from statistical physics and one from combinatorics, in order to make progress on classical problems in both fields.

Progress in nanotechnology relies upon the production of nanoparticles. During the past decade many recipes have been introduced for the synthesis of nanoparticles from the solution phase, including particles of different composition, shape, and architecture such as core and shell structures. In spite of this extensive work we lack a molecular level understanding of the nucleation and growth of nanoparticles that could lead to their rational, rather than empirical, design. We propose a new approach based upon a combination of X-ray probes and interfacial localization of the evolving nanoparticle structure.Most of the solution phase routes to metal nanoparticles exploit the reduction of the metal ion by a reducing agent. This agent (or another species) can act as a capping ligand, defining the particle size. The study of the growth process of metal nanoparticles is greatly simplified if reactants (i.e., metal ion and reducing agent) are physically separated from one another, by their locaton in two (immiscible) liquid phases. Nucleation and growth of the nanoparticles then takes place at the interface between these two liquid phases. Such localization allows for the use of X-ray absorption, which would not readily detect particles dispersed homogeneously across a solution volume, but can be applied in the interfacial case because the particles are highly concentrated at the interface. X-ray absorption spectroscopy probes the local geometric and electronic structure in non-crystalline systems, including determination of the chemical species and the chemical state of the atoms. In addition to this spectroscopic probe, we propose to use a structural probe, X-ray surface scattering, to study the in-plane and out-of-plane structure, including the shape, size, and organization of the particles, as well as the depletion of reactant species near the interface. We propose to combine these X-ray techniques with electrochemical control of the interfacial reaction at the liquid/liquid interface, both to monitor the progress in particle growth as well as to investigate the influence of the applied potential in controlling particle production.The proposed collaboration of scientists from the UK and the USA will use state-of-the-art X-ray spectroscopy, surface scattering and electrochemistry techniques. The PI from the USA has expertise combining X-ray surface scattering with in situ electrochemical control of the liquid-liquid interface. ThePIs from the UK have combined expertise in synchrotron X-ray spectroscopy and in the growth and characterization of metal nanoparticles at the liquid-liquid interface. This unusual and complementary set of techniques and approaches will be used to investigate the nucleation and growth of metalnanoparticles with the aim of understanding these processes at the molecular level in order to provide the basis for a rational approach to their synthesis.A molecular-level understanding of metal nanoparticle nucleation and growth will allow for the production of nanoparticles with designed properties. This should influence the development of applications of nanoparticles in a number of areas, including the design of new materials for catalytic,opto-electronic, and coating applications.The proposed collaboration utilizing state-of-the-art X-ray spectroscopy and surface scattering, as well as electrochemical analysis will provide a rare, possibly unique, collection of techniques and approaches. There are not many researchers with expertise in both X-ray spectroscopy and surfacescattering, in spite of the complementarity of these techniques in characterizing materials. Similarly, experts in synchrotron X-ray techniques are rarely familiar with a broad range of analytical chemistry techniques. The opportunity for cross training in these areas will provide early career researchers with a unique perspective at the beginning of their careers.