A common perception is that laboratory tests of fundamental physics necessarily require large particle colliders. However, thanks to the development of ultra high-intensity optical lasers and 4th generation light sources, new approaches are now possible that exploit the simultaneous interactions of multiple photons with matter and vacua via quantum field fluctuations. In this proposal, we will employ these high-field non-perturbative quantum optics processes to search for new fundamental particles. Since accelerator-based searches have not yet found new physics at high energies, ultra high-intensity optical lasers and 4th generation light sources offer a novel complementary approach for searches at optical and X-ray energies. This proposal addresses an important question in fundamental physics by developing a laboratory search for new particles beyond the Standard Model called axions. Our work will be able to probe axion masses bigger than a few eV up to a keV - a region that is currently inaccessible to laboratory searches. In the eV-keV mass range. the searches proposed here are the only model-independent ones, meaning that the experiments have full control over both the production and reconversion of axions within the same apparatus - without the need to assume that axions are produced by astrophysical objects (such as the Sun) or constitute a large fraction of the dark matter.

Physical phenomena observed in nature can be modelled by a wide range of mathematical theories. From shock waves in non-linear optics, to turbulence in hydrodynamics, and gravitational ripples caused by collapsing black holes, scientists have a strong grasp on the complex equations governing these phenomena. Nevertheless, solving these equations can be arduous, often done numerically or by taking the parameters of the theory to be small, hence approximating the results as a series of terms. This is a procedure called perturbation theory, and it plays a major role in fields ranging from mathematics to engineering. When the later terms of this series increase in magnitude, the series diverges. Despite this, summing a small number of such terms often gives a good approximation, and the series is called asymptotic. This behaviour, rather than problematic, is essential to build a complete understanding of physical observables. Hidden in it is a realm of phenomena so small that they disappear from perturbation theory (non-perturbative), but which can grow to eventually dominate our results, changing the physics. These phenomena are widely found in mathematical descriptions of nature, but the existing methods to study them are mostly problem specific, with varying rigour and practicality. A systematic, unified framework of asymptotics is still missing. A powerful method which studies the intimate relation between asymptotics and non-perturbative phenomena is resurgence theory. The proposed work aims to use resurgence to unify the different strands of research in asymptotics, bridging methods and disciplines, to obtain a comprehensive and practical theory of asymptotics. Blending the theoretical but powerful aspects of resurgence with practical, numerically driven theories of (exponential) asymptotics, we will be able to effectively construct full non-perturbative solutions to physical problems where only the perturbative series is known. The research will be conducted in great extend at the host organisation, the Applied Mathematics group at the University of Southampton, in collaboration with Prof C.J. Howls, as well as members of the String Theory group. A strong collaboration with project partners A.B. Olde Daalhuis (Edinburgh), J. King (Nottingham) and R.Schiappa (Lisbon) will be vital to the success of this project. Indeed, by combining the fellow's expertise in the systematic, practical implementations of resurgence theory with the project partners' broad knowledge in the field of exponential asymptotics and its applications, this proposal presents a clear path to achieve this goal. The physical problems that will be addressed during this project belong to a wide spectrum of research areas in mathematical sciences. Examples of these are: the formation of localised patterns in boundary value problems; the emergence of instabilities from time evolution in non-linear PDEs; asymptotic analysis of free energies of matrix models and gauge theories, and their dependence on coupling constant and rank of the gauge group; calculation of Stokes invariants for linear differential equations, from perturbative data or using integrability tools. These problems occur in the areas of continuum mechanics, mathematical analysis, non-linear systems and mathematical analysis. The scope and potential inter-disciplinary impact of this research is evident from the universality of the features controlling asymptotic behaviour, which this project is set to address.

Rising greenhouse gas (GHG) emissions are creating a serious threat to our planet, through their key impact of increasing temperatures. The 2015 Paris climate agreement, signed by 195 countries under the United Nations Framework Convention on Climate Change (UNFCCC), pledges to hold global average temperature increases to 2 'C above pre-industrial levels (c.1750). For context, in 2015, we passed the 1'C rise mark, and most climate models forecast a 2-4'C temperature rise by 2100, unless real actions are taken to reduce GHG emissions. In short, the situation is serious, and the window for staying within the 2'C target is closing. To reduce GHG emissions, a key part of government policy is to reduce the amount of energy we use. This is because most of our energy come from fossil fuels (i.e. oil, coal, gas), and burning them causes around 75% of the world's GHG emissions. The main policy for reducing energy use has been introducing energy efficient technologies, i.e. more efficient cars, lighting and heating systems. However, a key problem exists: to date energy efficiency has not reduced total energy consumption: in fact energy use globally is still rising, slightly behind economic output (Gross Domestic Product, GDP). Thus energy use and GDP have remained linked, or 'coupled' together. So a key question for the UK (and globally) is to work out exactly how to decouple energy-GDP: i.e. reduce energy use but allow economic growth. Studying the energy-GDP decoupling problem is the key aim of my research. Given the short time to reduce GHG emissions, we need to look at this problem from as many different angles as possible. This is where my research fits in: I work in an area of research that provides a different approach to looking at this problem compared to the mainstream (i.e. most common) methods. My research uses 'exergy analysis' to study the thermodynamic efficiency of energy use in a whole economy. Exergy is energy that is 'available for work'. Taking an example to illustrate exergy: though water in a hydroelectric dam has 'potential energy', it only becomes 'available for work' if there is a difference in water level between the two sides of the dam. If one side is 150m higher than the other, then physical 'work' (in this case hydroelectricity) can be extracted, but not if both water levels are 150m high. By studying how much energy is available for work as 'exergy' in an economy (for end uses such as transport, industrial machines, heating, cooling, lighting), we can calculate how (thermodynamically) energy efficient the whole economy is. This thermodynamic measure of energy efficiency (called exergy efficiency) can give us new insights into how much energy we are actually saving, versus how much we think we are going to save. This difference also tells us how much energy 'rebound' we have, i.e. the energy that is taken back by the economy. A better understanding of the size and role of these two factors - energy efficiency and energy rebound - holds the key to unpicking the energy-GDP decoupling puzzle. This is what my research sets out to achieve. The research is a five year project, based at the University of Leeds, where I will work with a 4 year PhD researcher and 3 year postdoctoral researcher, and other researchers who will contribute part time expertise. Our research in planned in three parts, 1. we will develop national exergy datasets into a global database, which 2. we will use to identify new insights and links of the key factors (energy efficiency and energy rebound) in the energy-GDP relationship, which lastly 3. will be used to test policies for achieving energy-GDP decoupling. We have several project partners outside of the University of Leeds, who we will work together with on sub-projects: The Bank of England; the UK Department for Business, Energy and Industrial Strategy (BEIS); Calvin College (USA) and Instituto Superior Técnico (Portugal). A steering group will provide advice during the project.

The lab in a bubble project is a timely investigation of the interaction of charged particles with radiation inside and in the vicinity of relativistic plasma bubbles created by intense ultra-short laser pulses propagating in plasma. It builds on recent studies carried out by the ALPHA-X team of coherent X-ray radiation from the laser-plasma wakefield accelerator and high field effects where radiation reaction becomes important. The experimental programme will be carried out using high power lasers and investigate new areas of physics where single-particle and collective radiation reaction and quantum effects become important, and where non-linear coupling and instabilities between beams, laser, plasma and induced fields develop, which result in radiation and particle beams with unique properties. Laser-plasma interactions are central to all problems studied and understanding their complex and often highly non-linear interactions gives a way of controlling the bubble and beams therein. To investigate the rich range of physical processes, advanced theoretical and experimental methods will be applied and advantage will be taken of know-how and techniques developed by the teams. New analytical and numerical methods will be developed to enable planning and interpreting results from experiments. Advanced experimental methods and diagnostics will be developed to probe the bubble and characterise the beams and radiation. An important objective will be to apply the radiation and beams in selected proof-of-concept applications to the benefit of society. The project is involves a large group of Collaborators and Partners, who will contribute to both theoretical and experimental work. The diverse programme is managed through a synergistic approach where there is strong linkage between work-packages, and both theoretical and experiential methodologies are applied bilaterally: experiments are informed by theory at planning and data interpretation stages, and theory is steered by the outcome of experimental studies, which results in a virtuous circle that advances understanding of the physics inside and outside the lab in a bubble. We also expect to make major advances in high field physics and the development of a new generation of compact coherent X-ray sources.