Group theory is a field in mathematics which investigates algebraic structures called groups, which can be used to describe the symmeties of any object. Thus, group theory has wide-reaching applications in virology, quantum computing, cyber security and communications theory. Groups are also used in finding and reducing symmetries within search problems, which is vital in modern Artificial Intelligence. So finding groups, their properties and computing fundamental group operations as fast as possible, is at the core of many UK world leading research areas and will have wide reaching impact in economic successes. There is an inherit circular improvement that will come from the research in algorithms in group theory, as one of the computational techniques used in finding subgroups, their properties or computing operations is a type of search algorithm itself. Thus, improving search in groups will improve the search for other applications as well. The current search techniques in groups are advanced but are still struggling with scaling issues. We are proposing to use search techniques commonly used in graph search problems and apply them to group theoretical search algorithms. Such techniques are (1) (learned) nogood clauses during search which then will inform further search steps, (2) restarting the search from the top at well defined intervals, and (3) using weighted orderings on the search decisions. We have found that using these techniques in graph problems sped up the search by at least two orders of magnitude. We expect the performance improvements to be the same or better across the board in group problems. Further, these techniques allow for a simple way of parallelising the current sequential algorithms, without the need to design/engineer a whole new algorithm. Speeding up algorithms which solve group problems and enabling them to be easily parallelisable will further impact applications such as virology, where group theory is used to describe the structural and geometrical properties of viruses.

In contrast to the bulk semiconductors, spatially confined van der Waals (vdWs) layered materials possess strong Coulomb interaction, high exciton binding energy, reduced charge screening and low electron-phonon coupling, leading to a slower hot carrier (HC) cooling. Efficient direct interlayer HC transfer has been observed in vdWs heterostructures without phonon emission due to momentum conservation at K-point. In a graphene-based vdWs heterostructure, considerably high optical absorbance leads to the enhanced photocarrier density, which invokes the hot-phonon bottleneck effect, leading to prolonged HC cooling in graphene. The aforementioned advantages of suitably designed vdWs heterostructures are certainly advantageous for fabrication of efficient HC solar cells (HCSCs), restricting the ultrafast thermalization of HCs and exceeding the Shockley-Queisser limit. In this work, low bandgap (~1-1.5 eV) transition metal dichalcogenides (TMDs) of various layer thicknesses (transition metal: Mo, W; chalcogenide: S, Se, Te) with high optical absorbance will be grown and integrated with graphene having ultraclean interface for the fabrication of HCSCs. HC dynamics including the type of HC, temperature, HC lifetime, and carrier multiplication will be investigated by time- and angle-resolved photoemission spectroscopy to probe the solar light driven HC photovoltaic characteristics. Optimized graphene/TMD vdWs heterostructures will be integrated with proper energy selective contacts (ESCs) and metal electrodes with appropriate work functions for the efficient HCs collection in HCSCs. The thickness of the ESCs will be tuned for the maximum HCs tunneling to the metal electrodes through the ESCs. Demonstration of HC-driven photovoltaics will be carried out by current-voltage (I-V) measurements with various energetic laser illuminations. Large area HCSCs will be realized with wafer-scale growth of vdWs materials and I-V measurements under solar simulator (1-SUN AM1.5).

Traditional relational data management systems are challenged by the abundance of highly interconnected heterogeneous data. This led to a surge in the popularity of graph databases in many industry and academic areas. For example, graph datasets with world-wide multi-omics data for genomic analyses and contact tracing were collaboratively curated during the pandemic (EU Datathon, CovidGraph, Covid-19 Knowledge Graph). Other critical societal graph databases use-cases include finance, telecommunications, journalism, and intelligent transportation. However, when processing geo-distributed graph data at scale, custom distribution models are needed, whose support still poses practical challenges. These are: replication, to mitigate slow and unreliable networks; sharding, to horizontally partition large graphs; and partial replication, to favor access locality, replicating data close to clients. Moreover, local-first models provide high availability, combining sharding and replication for read and write access to a relevant data subset, even when disconnected. While distribution mechanisms, such as Replicated Data Types (RDTs), have become well-established for local-first key-value stores, their usage in graph databases is largely unexplored. This is a more complex setting, due to its stronger demands to compositionally maintain connectivity invariants. VERDI proposes a novel interdisciplinary methodology to reliably devise such foundational distribution devices, cross-cutting the areas of databases, distributed systems, formal methods, and programming languages. It comprises four work packages (WPs). WP1 will build a unified formal foundation for prototyping and extracting correct-by-construction graph RDTs (GRDTs). WP2 will tailor these to provably enforce complex invariants under weak consistency models. WP3 will extend GRTDs with parametricity and transactional support and WP4 will evaluate their performance on a decentralized graph-based ledger industrial use-case.

Spintronics is the area of research dedicated to the study of how 'spin'--the quantum mechanical currency of magnetism--can be used realize new types of information transport, storage, and processing system which surpass the capabilities of those currently found in our computers and other electronic devices. Over the quarter century since its conception this field has branched in many directions. Some have already delivered spectacular real-world impact: spintronic magnetic field sensors are, for example, the bedrock of contemporary hard-disc technology and key players in the choreography of the information age. Others hold exciting promise as the basis for technologies of the future: a host of spintronic sub-disciplines feature among the most active and innovative areas of contemporary solid-state physics research. Today, with many spintronic sub-fields now well-developed, there is mounting interest in unlocking the rich and subtle physics which connects them. Against this background, this proposal is about recognizing and investigating a new and exciting frontier: the interface between magnonics and magnon spintronics, and quantum information. The field of magnonics is the area of magnetics dedicated to the science of quasi-particles known as magnons. In certain magnetic systems, magnons are able to play the role of microscopic spin-carrying tokens which can be generated and transmitted over relatively long distances (up to centimetres) and at high speed (many tens of kilometres per second). Magnon spintronics, magnonics' emerging sister discipline, is concerned with structures and devices which involve the passing of spin-information between magnons and electrons, the familiar workhorses of conventional electronics. As appreciation of the interplay between magnonic and electronic spin-transport deepens, so excitement surrounding its possible contribution to next-generation information technology heightens. To date however, work in magnonics and magnon spintronics has focused on the study of room-temperature magnon and magnon/electron systems in the classical limit. As a result, the field of experimental quantum measurement and information processing has yet to explore what the magnonic theatre has to offer. This project will develop the first experimental systems dedicated to a broad and systematic investigation of magnonics and magnon spintronics at the quantum level. Building on this, it will take the maiden steps towards accessing the new physical insight and potential technological opportunity at the interface between the rich physics of magnonic and magnon spintronic systems, and the techniques of contemporary quantum measurement and information processing. If successful, it will define and open up an entirely new field of research: quantum magnon spintronics.

Strings in programming languages are sequences of characters that represent any kind of text. They are a fundamental aspect of information representation: user names, passwords, or indeed any kind of text are handled as strings. The manipulation of strings, however, can also lead to subtle programming errors, that can have consequences for program correctness as well as information security. For example, a malicious user may enter computer code as their username. If the system is not sufficiently secure, this code can allow the user to hack the system. The Open Web Application Security Project lists this kind of attack among the top 10 application security risks. Despite this kind of attack being well-known, it has proved surprisingly difficult to avoid due to the complex nature of computer programs. Ideally, programming mistakes will be caught during testing. However, manual testing is a tedious and time-consuming process which requires the developer to imagine every possible user input. Automatic test-case generation can take this burden away from the developer and allow more complete testing to be done more efficiently. However, this relies on the tools used for test-case generation to be able to accurately reason about how software will run. This project will focus on how software deals with strings. Typically "regular expressions" are used for this purpose. However, current research takes an idealised view of regular expressions that omits many important features of the regular expressions provided by modern programming languages. We will address this shortcoming both in the theory of computer science and in practice. In particular, we will create a test-case generation tool-chain that will provide better test-case generation for software dealing with strings. These tools will be tested on real-world industrial code provided by Prodo.ai.