Three core questions bind this proposal together: how to foster growth; how to share growth and how to sustain growth 1 HOW CAN WE FOSTER GROWTH? We plan to develop a new Growth Programme focussing on bolstering innovation in its widest sense, both technological and organisational. It will co-ordinate the Centre's growth work agenda and follow up the LSE Growth Commission's policy proposals. Next, the Trade programme will analyse the impact of globalisation with a targeted focus on how to make a dramatic improvement in British export performance. A core policy question is what the UK's future relationship with other countries will be, in particular with the European Union (EU) and South-East Asia. Third, the Education and Skills programme will examine human capital investment by analysing the recent transformation of the educational system using new tools of competition and organisation theory. Two core questions are: have educational reforms worked - especially for the disadvantaged - and, what can be done to improve the intermediate skills base, a long-standing area of UK weakness. 2 HOW CAN WE SHARE THE BENEFITS OF GROWTH? A problem with growth in the decades prior to the global financial crisis was that prosperity was shared very unequally. To study the spatial dimensions of inequality, we propose a new Urban programme. This will emphasise cities as key economic units and address why so much UK growth is concentrated in the South East.This is a key policy issue in the light of the commitment to decentralise power within England by all main UK parties. Following the City Growth Commission, the policy focus will be how local policy makers can help their cities prosper. Alongside the large productivity fall since the crisis, there has been a big fall in real wages - something unique in post-war UK recessions. Some wage stagnation occurred also in the run-up to the crisis, as it has over a longer time in the US. The Labour programme will examine these changes and whether they are linked to the declining share of GDP going to employees across the world. We will look at earnings, income and wealth inequalities across individuals, but also on why women's progress has stalled. In all these aspects, we are interested not just in explaining why growth is unequally shared, but also how we could design institutions and policies that generate a "double dividend" of more growth and less inequality. 3 WHAT KIND OF GROWTH DO WE WANT? Increasing GDP per capita remains important as UK average incomes track this over the long run. But growth must be sustainable, it must deal with environmental challenges, it should expand not undermine people's happiness and it should not be at the expense of social cohesion. Dealing with climate change requires both containing demand for greenhouse gases and stimulating clean technologies and we propose a wide portfolio of green growth projects directed to this. Of course, it is not just technology that affects people's lives - it is also the beliefs and norms that regulate the interactions between people. Growth involves change that has significant impacts on people's lives and neighbourhoods, often causing great stress. Our Community programme will investigate the impact of economic changes (both direct and indirect through changes like immigration) on social cohesion, and will help to develop policies to ensure that growth benefits all communities. CEP has been at the forefront of looking beyond GDP and our Wellbeing programme will ambitiously develop a model of subjective well-being over the life-course, in order to show the quantitative causal impact of factors like parenting, schooling, employment, income and health. Without such knowledge it is impossible for policy-makers to aim effectively at greater wellbeing, even if that is their objective.

Climate change is arguably the biggest challenge facing people this century, and changes to the intensity and frequency of climatic and hydrologic extremes will have large impacts on our communities. The 2017 Climate Change Risk Assessment identified floods and windstorms as likely to have a strong impact on key infrastructure sectors in the UK with climate change. Extreme rainfall is becoming more intense with warming, and short-duration bursts within storms appears to be increasing at a higher rate. However, we still don't understand how changes in large scale atmospheric patterns, the storm track, the release of energy from evaporation and other factors will influence the profile of the storm in time and as well as their frequencies and how long they last for. This is partly due to the fact that most scientific studies have concentrated on 'peak intensity' changes over fixed durations, e.g. daily, multi-day, hourly, etc. Alongside this, most studies look at the likely range of change even though the most important risks rarely lie within this range. Instead, the most important risks are often associated with the 'plausible worst case' scenario. In STORMY-WEATHER we are producing a new methodology based on different 'storm' types to understand the drivers behind the changes and to produce a set of physically-plausible high-impact storm hazard storylines and metrics that people can use to plan for the future. These will use the latest climate projections. We use climate models to tell us about what weather in the future will be like and these computer models are based on fundamental physical laws and complicated mathematical equations which necessarily simplify real processes. One of the simplifications that really seems to matter is that of deep convection (imagine the type of processes that cause a thunderstorm). However, computers are so powerful now that we are able to produce models that work on smaller and smaller scales, and recently we have developed models which we call "convection-permitting" where we stop using these simplifications of deep convection. These "convection-permitting" models are not necessarily better at simulating mean rainfall or rainfall occurrence but they are much better at simulating intense rainfall over short time periods (less than one day) which cause flooding, in particular flash-flood events. They are also better at simulating the increase in heavy rainfall with temperature rise that we can observe; therefore we are more confident in their projections of changes in heavy rainfall for the future. We will use these new models as well as global climate models more commonly used to assess the uncertainty in our projections of the future. We will consider changing temperatures as the potential driver of change to storm hazards, including precipitation and wind as joint hazards. Our storm-type approach will help clarify hazard from different rainfall mechanisms and their scaling rates with temperature, alongside combined wind and rain hazard from storms, as well as their changing nature with warming; characteristics that are vital for planning for impacts (e.g. flooding, infrastructure failure, transport and energy systems, etc.) The focus on storm properties is balanced against the need to understand the impact of potential changes to large-scale circulation patterns on storm hazards, e.g. frequency/persistence changes, and, in particular, the possibility of circulation-driven changes to the dominant event type across regions. Ultimately, we need better information on how extreme weather events might change in the future on which to make adaptation decisions and STORMY-WEATHER intends to provide this important advance, alongside translating this information into useful tools and metrics for use in climate change adaptation.

The Hub will reduce disaster risk for the poor in tomorrow's cities. The failure to integrate disaster risk resilience into urban planning and decision-making is a persistent intractable challenge that condemns hundreds of millions of the World's poor to continued cyclical destruction of their lives and livelihoods. It presents a major barrier to the delivery of the Sustainable Development Goals in expanding urban systems. Science and technology can help, but only against complex multi-hazard context of urban life and the social and cultural background to decision-making in developing countries. Science-informed urbanisation, co-produced and properly integrated with decision support for city authorities, offers the possibility of risk-sensitive development for millions of the global poor. This is a major opportunity - some 60% of the area expected to be urban by 2030 is yet to be built. Our aim is to catalyse a transition from crisis management to risk-informed planning in four partner cities and globally through collaborating International governance organisations. The Hub, co-designed with local and international stakeholders from the start, will deliver this agenda through integrated research across four urban systems - Istanbul, Kathmandu, Nairobi and Quito - chosen for their multi-hazard exposure, and variety of urban form, development status and governance. Trusted core partnerships from previous Global Challenge Research Fund, Newton Fund and UK Research Council projects provide solid foundations on which city based research projects have been built around identified, existing, policy interventions to provide research solutions to specific current development problems. We have developed innovative, strategic research and impact funds and capable management processes constantly to monitor progress and to reinforce successful research directions and impact pathways. In each urban system, the Hub will reduce risk for 1-4 million people by (1) Co-producing forensic examinations of risk root causes, drivers of vulnerability and trend analysis of decision-making culture for key, historic multi-hazard events. (2) Combining quantitative, multi-hazard intensity, exposure and vulnerability analysis using advances in earth observation, citizen science, low cost sensors and high-resolution surveys with institutional and power analysis to allow multi-hazard risk assessment to interface with urban planning culture and engineering. (3) Convene diverse stakeholder groups-communities, schools, municipalities private enterprise, national agencies- around new understanding of multi-hazard urban disaster risk stimulating engagement and innovation in making risk-sensitive development choices to help meet the SDGs and Sendai Framework. Impact will occur both within and beyond the life of the Hub and will raise the visibility of cities in global risk analysis and policy making. City Partnerships, integrating city authorities, researchers, community leaders and the private sector, will develop and own initiatives including high-resolution validated models of multi-hazard risk to reflect individual experience and inform urban development planning, tools and methods for monitoring, evaluation and audit of disaster risk, and recommendations for planning policy to mitigate risks in future development. City partnerships will collaborate with national and regional city networks, policy champions and UN agencies using research outputs to structure city and community plans responding to the Sendai Framework and targeted SDG indicators, and build methods and capacity for reporting and wider critique of the SDG and Sendai reporting process. Legacy will be enabled through the ownership of risk assessment and resilience building tools by city and international partners who will identify need, own, modify and deploy tools beyond the life of the Hub.

CRUST takes advantage of the UK's leadership in uncertainty evaluation of earthquake source and ground motion (Goda [PI] and University of Bristol/Cabot Research Institute) and on-shore tsunami impact research (Rossetto [Co-I] and University College of London/EPICentre [Earthquake and People Interaction Centre]) to develop an innovative cross-hazard risk assessment methodology for cascading disasters that promotes dynamic decision-making processes for catastrophe risk management. It cuts across multiple academic fields, i.e. geophysics, engineering seismology, earthquake engineering, and coastal engineering. The timeliness and critical needs for cascading multi-hazards impact assessments have been exemplified by recent catastrophes. CRUST fills the current gap between quasi-static, fragmented approaches for multi-hazards and envisaged, dynamic, coherent frameworks for cascading hazards. CRUST combines a wide range of state-of-the-art hazard and risk models into a comprehensive methodology by taking into account uncertainty associated with predictions of hazards and risks. The work will provide multi-hazards risk assessment guidelines and tools for policy-makers and engineering/reinsurance industries. The proposal capitalises on a breakthrough technology for generating long-waves achieved by Rossetto. CRUST is composed of four work packages (WPs): WP1-'Ground shaking risk modelling due to mega-thrust subduction earthquakes'; WP2-'Tsunami wave and fragility modelling due to mega-thrust subduction earthquakes'; WP3-'Integrated multi-hazards modelling for earthquake shaking and tsunami'; and WP4-'Case studies for the Hikurangi and Cascadia subduction zones'. In WP1-WP3, the research adopts the 2011 Tohoku earthquake as a case study site, since this event offers extensive datasets for strong motion data, tsunami inundation, and building damage survey results, together with other geographical and demographical information (e.g. high-resolution bathymetry data and digital elevation model). The aims of WP1 are: to generate strong motion time-histories based on uncertain earthquake slips, reflecting multiple asperities (large slip patches) over a fault plane (WP1-1); to characterise spatiotemporal occurrence of aftershocks using global catalogues of subduction earthquakes (WP1-2); and to conduct probabilistic seismic performance assessment of structures subjected to mainshock-aftershock sequences (WP1-3). WP2 comprises tsunami wave profile and inundation simulation using uncertain earthquake slips (WP2-1); characterisation of tsunami loads to structures in coastal areas through large-scale physical experiments using an innovative long wave generation system at HR Wallingford (WP2-2); and development of analytical tsunami fragility models in comparison with field observations and experiments (WP2-3). The WP2 will be conducted in collaboration with academic collaborators from Kyoto University and Tohoku University (Japan). WP3 integrates the model components developed from WP1 and WP2 into a comprehensive framework for multi-hazards risk assessment for the 2011 Tohoku earthquake and tsunami (WP3-1). Then, practical engineering tools for the multi-hazards method will be developed in WP3-2. Finally, in WP4, the developed multi-hazards methodology will be applied to the Hikurangi and Cascadia subduction zones. The assessments are done in a predictive mode, and these case studies will be conducted in close collaboration with academic partners, GNS Science (New Zealand) for the Hikurangi zone, and researchers at Western University and University of British Columbia (Canada) for the Cascadia zone.

Predicting high impact extreme events, such as severe climatic and economic events is a major societal challenge. Using innovative mathematical techniques this proposal determines phenomenological mechanisms that lead to the occurrence of extremes, and develops a theory that can be used to predict when such events occur in physical modelling applications. Using dynamical systems theory, the proposed research will use geometrical features of the underlying mathematical models to determine the future extreme behaviour. This goes beyond certain traditional approaches such as monitoring output time series data alone. The study of successive maxima (or minima) for stochastic processes is called Extreme Value Theory (EVT). This theory is extensively used in risk analysis to estimate probabilities of rare events and extremes, e.g. high river levels; hurricanes and market crashes. For physical systems modelled by deterministic dynamical systems, especially chaotic dynamical systems a corresponding theory of extremes is yet to be fully understood. These systems are highly sensitive and the time series of observations can be highly correlated. A key question that we address is when to modify the theory for independent, identically distributed random variables in the case of understanding extremes for deterministic systems. Conversely when are certain probabilistic limit laws (such as Poisson laws) a good description of the extreme phenomenon? Ergodic theory approaches have been very successful in understanding the long-term evolution of these systems. Recent approaches have focused on time series observations which have a unique maxima at a distinguished point in phase space, and whose level set geometries coincide with balls in the ambient (usually Euclidean) metric. However extremes of other physically relevant functions (with geometries beyond nested balls), are also important in applications. This includes energy-like functions or wind speed functionals which play a role in measuring the destructiveness of storms. We therefore go beyond existing methodologies and develop a theory of extremes for physically relevant observable functions. We then apply this theory to explicit dynamical systems (both discrete and continuous) motivated by real-world mathematical models such as for the weather and climate.