When we begin to study mathematics, we learn that the operation of multiplication on numbers satisfies some basic rules. One of these rules, known as associativity, says that for any three numbers a, b and c, we get the same result if we multiply a and b and then multiply the result by c or if we multiply a by the result of multiplying b and c. This leads to the abstract algebraic notion of a monoid, which is a set (in this case the set of natural numbers) equipped with a binary operation (in this case multiplication) that is associative and has a unit (in this case the number 1). If we continue to study mathematics, we encounter a new kind of multiplication, no longer on numbers but on sets, which is known as Cartesian product. Given two sets A and B, their Cartesian product is the set A x B whose elements are the ordered pairs (a, b), where a is an element of A and b is an element of B. Pictorially, the Cartesian product of two sets is a grid with coordinates given by the elements of the two sets. This operation satisfies some rules, analogous to those for the multiplication of numbers, but a little more subtle. For example, if we are given three sets A, B and C, then the set A x (B x C) is isomorphic (rather than equal) to the set (A x B) x C. Here, being isomorphic means that we they are essentially the same by means of a one-to-one correspondence between the elements A x (B x C) and those of (A x B) x C. This construction leads to the notion of a monoidal category, which amounts to a collection of objects and maps between them (in this case the collection of all sets and functions between them) equipped with a multiplication (in this case the Cartesian product) that is associative and has a unit (in this case the one-element set) up to isomorphism. Monoidal categories, introduced in the '60s, have been extremely important in several areas of mathematics (including logic, algebra, and topology) and theoretical computer science. In logic and theoretical computer science, they connect to linear logic, in which one keeps track of the resources necessary to prove a statement. This project is about the next step in this sequence of abstract notions of multiplication, which is given by the notion of a monoidal bicategory. In a bicategory, we have not only objects and maps but also 2-maps, which can be thought of as "maps between maps" and allow us to capture how different maps relate to each other. In a monoidal bicategory, we have a way of multiplying their objects, maps and 2-maps, subject to complex axioms. Monoidal bicategories, introduced in the '90s, have potential for applications even greater than that of monoidal categories, as they allow us to keep track of even more information. We seek to realise this potential by advancing the theory of monoidal bicategories. We will prove fundamental theorems about them, develop new connections to linear logic and theoretical computer science and investigate examples that are of interest in algebra and topology. Our work connects to algebra via an important research programme known as "categorification", which is concerned with replacing set-based structures (like monoids) with category-based structures (like monoidal categories) in order to obtain more subtle invariants. Our work links to topology via the notion of an operad, which is a flexible tool used to describe algebraic structures in which axioms do not hold as equalities, but rather up to weak forms of isomorphism. Overall, this project will bring the theory of monoidal bicategories to a new level and promote interdisciplinary research within mathematics and with theoretical computer science.

Advanced nanotools including atomic force microscopy, optical microscopy and correlative microscopy are enabling techniques for discoveries and knowledge generation in nanoscale science and technology. Many R&D efforts have been directed towards the performance improvement of such kinds of techniques for soft matter. However, the greatest challenge faced by these leading edge techniques is the realization of high spatiotemporal resolution, non-invasive, multi-scale and multi-dimensional imaging and manipulation. We therefore propose NanoRAM, a 10 ESR Marie Sklodowska Curie Action Doctoral Network by close collaboration between academic and industrial partners around the theme of innovative nanotools and their industrial applications. NanoRAM will train a new generation of ESRs in the development and application of newly developed manipulation and characterisation nanotools in soft matter research. ESRs will be cross-pollinated with concepts and skills in instrumentation and soft matter characterisation, in particular in fast nanomechanical spectroscopy, nano-robotics, correlative super-resolution nanoscopy, nano biomechanics and mechanotransduction. These skills are applied to reveal for the first time the fast, high resolution, multi-level and 3D information for single cell biomechanics and nanomedicine. Excellent training in new scientific and complementary skills, combined with international and intersectoral work experience, will instil an innovative, creative and entrepreneurial mind-set in ESRs, maximising economic benefits based on scientific discoveries. These specialised, highly trained ESRs will have greatly enhanced career prospects and qualifications for access to responsibility job positions in the private and public sectors. The ultimate goal of NanoRAM is to consolidate Europe as the world leader in innovative nanotool techniques and their emerging applications in soft matter fields such as biomechanics, mechanobiology, and nanomedicines.

Cultural diplomacy (CD) has emerged as a key strategy for nations to build bilateral ties and address global issues. The networks at local, national, and international levels in CD form a crucial infrastructure to operationalise CD programmes. For instance, great power countries such as the UK, US, China, and France all administer their institutions for cultural diplomacy (British Council, Fulbright, and Confucius Institute) via its own global network that enables the top-down programme design to be implemented in foreign local contexts. In addition to these formal networks at a global scale, there are informal networks of professionals in certain sectors (e.g., museums), or for a specific cultural or art form. However, these networks, initiated and operated by actors with different purposes, are a double-edged sword. On one hand, they have the potential to effectively unite international actors to tackle global issues such as rising populism and protectionism through the development of mutual understanding and international collaboration. On the other hand, they can potentially perpetuate disparities between regions (e.g., West and East, Global North and South) and actors (e.g., early career and established individuals) due to monopolies of information and resources. This duality of CD networks and their impacts have yet to attract sufficient academic research attention. Existing research largely focuses on the instrumentality of CD and how they are mis(used) as a propaganda/economic tool by various actors (with a focus on the nation-state perspective). Networks within CD have not been analysed to understand how they affect different aspects of CD activities such as efficiency (of resource allocation), flexibility (to adapt to different foreign contexts), inclusivity (to include various actors and reflect their interests), and sustainability (to have long-lasting impacts). To fill this research gap and contribute to future network-building practices in CD, this project seeks to discuss the following questions in the proposed events: 1. How do networks form and what are their different types (e.g., spatial, content-oriented, or actor-specific) and what are their functionalities? 2. What are the limitations of existing networks, and what kinds of networks are absent but much needed? 3. How do network-building practices in CD converge and diverge in different geopolitical and sociocultural contexts, and what are the implications for researchers and cultural administrators? To investigate the above questions, four global events have been planned to bring together a mix of academics (ECRs and senior researchers), cultural practitioners, and policymakers. This cross-disciplinary, sectoral, and national discussion is expected to contribute to: 1. A definition of cultural diplomacy networks, 2. An articulation of a CD network mechanism specifying goals, contexts, assumptions, and behaviours/actions needed to achieve the desired outcome, and 3. A plan for follow-up research and grant application to apply new methods and pursue new research agendas generated from the four events. To operationalise this project, the PI is intellectually and practically supported by three steering committee members and their institutions in the US, France, and China (see CfS and LoS). Additionally, an advisory board consisting of senior researchers and research platforms will mentor the ECR on the steering committee and share their connections for the networking events. This community of ECRs and senior researchers is the vital intellectual infrastructure for this project and follow-up research.

Programming is intrinsically based on the use of limited resources, such as memory and processing power of computers. Various abstractions of resources play an important role throughout computer science, but they are conceptualised in very different, and apparently unrelated ways. In particular, there is a big gap between studies focussing on precise quantitative issues of what we can do and how efficiently we can do it with limited resources, and those which concern more conceptual aspects, which underpin modern high-level programming languages, and application-oriented programming. In this project, building on some recent breakthrough developments which relate these different aspects, we aim to develop a unified theory of resources which will apply to all these aspects, and allow a flow of ideas between them. This will provide new tools and methods for computer scientists, and lead both to new kinds of results, and more general versions of existing ones.

Our everyday understanding of perception is that our sense organs enable us to see, touch, smell, taste and hear. The vocabulary of five distinct senses ramifies through descriptions of thought ("I see what you mean") emotion ("I was touched by her suffering") and aesthetics ("That's not to my taste"). Traditionally, philosophers have also thought that the five senses producing distinctive, separate conscious experiences. Equally, until recently, scientists have also studied each of the senses in isolation. But modern neuroscience is radically changing our understanding. Each sense organ contains many kinds of sensory receptors (think of all the different feelings from your skin). Everyday experiences - watching a film, eating a meal, walking along the street - involve different senses, working together. But most remarkable is a mass of recent research showing highly specific sensory interactions, in which one sense modifies the experience of another. Imagine listening to a syllable (say /ba/) spoken over and over, while watching a video of someone mouthing a different syllable (say /ga/), you actually hear the sound differently. Equally, the voice of a ventriloquist seems to come from the mouth of a doll some distance away. Somehow, what we see changes what we hear, presumably through processes that normally help us to associate sounds and sights correctly. Flavour provides the most surprising examples of sensory interaction, What we call the "taste" of food and drink is largely determined by smell rather than taste, but it also depends on the temperature and texture of food and drink, and its colour, and even the sounds that accompany eating. For instance, white noise reduces sensitivity to flavour (the so-called "aircraft food effect"). Equally, your sense of your own body can be changed by what you see and feel. If you look at a model hand being stroked with a brush, while your own hand, out of sight, is simultaneously stroked, you will soon feel that the model hand is part of you. The traditional view that information flows in one direction from basic sensation to perception, memory and action, has also been overturned. Recognising a spoken word, a familiar face, or a favourite piece of music draws on previous knowledge. Perception is influenced by memory, expectation, emotion and attention. Further, since our head, hands and eyes are constantly in motion, the brain must somehow stitch together perception from a sequence of sensory "snapshots". A comprehensive account of perception needs to begin with the relationships and interactions between the sensory modalities that produce our awareness of the world and of ourselves in it. Although the science of perception is moving very fast, it lacks the conceptual framework that philosophical thinking can bring to understanding the relationship between brain processes and experience. Our plan is for philosophers, psychologists and neuroscientists to work together in entirely new ways, including planning laboratory experiments together, to help us to understand how the brain puts together different sensory information, under the influence of past experience and expectation, to create the seamless flow of conscious experience, to identify objects and events in the world, to give us an sense of our own body, and to enable us to control our actions. We believe that our work will have wide impact beyond our university departments. It will help in the design of new forms of prosthetic devices to help deaf and blind people, and those who suffer untreatable pain, changes in body image or reduction in the sense of smell. It will inform the rapidly advancing technology of enhancement of sensory experience, cast light on the appreciation of the visual and performing arts, and stimulate new forms of preparation and presentation of food, and new understanding of the way in which people choose what products to buy, what works of art they prefer and what food they eat.