Capacity building in Africa via technology-driven research in algebraic and arithmetic geometry

我们拟议的项目旨在通过在英国数学家和撒哈拉以南非洲新兴科学家及其研究小组之间建立深入、有意义的合作，以解决与非洲发展背景相关的技术挑战中出现的一系列问题，从而在非洲大陆建立数学研究能力。我们解决这些问题的方法将涉及抽象数学的工具包。我们的目标是在非洲伙伴及其研究小组中积累使用理论方法解决应用问题的专门知识。我们的能力建设方案侧重于应用代数和算术几何方面的合作研究。这是一个快速发展的领域，旨在将抽象几何的复杂工具应用于研究应用中出现的多项式方程组。我们将解决的具体研究目标来自功率流、系统生物学、机器人学和密码学领域。所有这些调查思路都可以应对在与发展有关的背景下出现的具体挑战。控制和了解电力网络中的潮流可以提高电力系统的稳定性，从而提高电力系统的可靠性，而不必采取昂贵的预防性过度工程。更好地从理论上理解与特定疾病有关的信号通路，可以更有效地进行实验设计，在非洲背景下具有很高的应用潜力。机器人学的理论进步带来了更好的具体运动学结构的实用设计建议，然后可以在新兴的当地机器人实验室进行测试。密码学，包括更复杂的版本，如椭圆曲线密码术，为信息安全提供了有效的协议，并被广泛应用于银行部门，包括移动转账，这是一个非洲处于世界领先地位的行业。在英国，我们的能力建设研究计划将由一组在代数和算术几何及其应用领域的高水平研究记录以及国际研究开发经验的研究人员领导。在非洲方面，我们将与非洲伙伴的核心小组合作，这些核心小组是我们已经认识的新兴领导人，他们活跃在代数、代数和算术几何领域的研究。我们将通过公开征集更多的非洲参与者加入我们的能力建设研究计划。我们提议的项目将包括两个阶段。在该项目的第一阶段，将分别在东非和西非举办两个为期10天的强化讲习班。在该项目的第二阶段，我们将在英国接待大约非洲科学家访问英国，而调查人员将访问非洲合作伙伴部门。我们的能力建设计划将使非洲数学家能够抽出时间并专注于与发展相关的特定领域的研究，这些领域对他们来说大多是新的。通过对他们的研究小组的影响，这将导致这些调查领域的当地专业知识的可持续增长。因此，我们将建立重要的研究能力，能够应对与发展相关的挑战。

Our proposed project aims to build mathematics research capacity on the African continent by establishing deep, meaningful collaborations between UK mathematicians and emerging Sub-Saharan African scientists and their research groups to tackle a range of problems arising in technological challenges relevant to the African development context. Our approach to these problems will involve the toolkit of abstract mathematics. Our objective is to build up expertise among African partners and their research groups in using theoretical approaches to attack applied problems.Our capacity building programme is focused around collaborative research in applied algebraic and arithmetic geometry. This is a fast-developing area that aims to apply the sophisticated tools of abstract geometry to the study of systems of polynomial equations arising in applications. The specific research objectives we will tackle come from the areas of power flows, systems biology, robotics and cryptography. All these lines of inquiry can address specific challenges arising in development-related contexts. Controlling and understanding power flow in electrical networks leads to improvements in the robustness and hence the reliability of an electrical system without having to resort to expensive precautionary over-engineering. A better theoretical understanding of signalling pathways connected to specific diseases enables more efficient experimental design, with a high potential for applications in an African context. Theoretical progress in robotics leads to suggestions for better practical design of specific kinematical constructions, that can then be tested in emerging local robotics labs. Cryptography, including more sophisticated versions such as elliptic curve cryptography, allows for efficient protocols for information security, and is widely used in the banking sector including mobile money transfers, an industry in which Africa is a world leader.On the UK side, our capacity building research programme will be led by a group of Investigators with a track record in high-level research in the fields of algebraic and arithmetic geometry and their applications, and experience of research development in an international context. On the African side, we will work with a core group of African Partners, emerging leaders already known to us and active in research in the fields of algebra and algebraic and arithmetic geometry. We will recruit further African participants via open calls to join our capacity building research programme.Our proposed project will consist of two phases. In the first phase of the project, two intensive, 10-day workshops will be held in East and West Africa, respectively. In the second phase of the project, we will host about African scientists in the UK for visits to the UK, whereas Investigators will visit African partner departments.Our capacity building programme will allow African mathematicians to find the time and focus to embark on research in specific development-related areas, which are mostly novel for them. Via the impact on their research groups, this will lead to a sustainable increase in local expertise in these lines of inquiry. We will thus build crucial research capacity able to tackle challenges relevant in the context of development.