Privacy and confidentiality in patient records, diagnostic outputs and treatment requires novel application of research related to data security and anonymisation.
H2: Improve prevention and public health H3: Optimise diagnosis and treatment Number Theory research plays a key role in encryption and security technologies. It is especially relevant to the following Connected, Healthy, Productive and Resilient Ambitions: C1: Enable a competitive, data-driven economy C3: Deliver intelligent technologies and systems C4: Ensure a safe and trusted cyber society C5: Design for an inclusive, innovative and confident digital society This are will continue to underpin all of the Prosperity Outcomes, due to its support for data science and robotics and autonomous systems. The Pure Mathematics Centre for Doctoral Training (CDT) is training the next generation of researchers in Geometry and Number Theory. GCHQ) and the Heilbronn and Clay Institutes. The research community remains relatively small, with researchers typically located in the south of England, due to the location of the main security services (e.g. to string theory, cryptology and theoretical computer science) is key to maintaining this area’s health in the UK (Evidence source 4,5). Sustaining these and strengthening interdisciplinary links (e.g. The area has intradisciplinary links to all areas of pure mathematics, in particular through representation theory, algebraic geometry, additive combinatorics and probability theory. Other applications include communications technology and, more generally, engineering and physics (Evidence source 4,5). Number Theory has strong links to all areas of pure mathematics, especially algebra and geometry in relation to the Langlands programme. Number Theory’s role can be underlined by the case studies highlighted in the Research Excellence Framework (REF) 2014 exercise which were provided by Government Communications Headquarters (GCHQ), (Evidence source 3).
Number Theory contributes significantly to ongoing research in cryptography, an area of national importance as it plays a key role in information security (especially cyber-security), (Evidence source 1,2). The number of speakers from UK-based research institutions invited to give plenary talks at the International Congress of Mathematics is a further reflection of success. The partnerships between academic Number Theory research and the Heilbronn and Clay Institutes emphasise the potential opportunities for transformative research in this area.
Number Theory researchers have received numerous European Research Council and Clay Institute awards. The UK continues to be world-leading in many aspects of Number Theory, with a particular focus on: L-functions Diophantine geometry and number theory in the Langlands programme.
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