Centre for Analysis and Nonlinear Partial Differential Equations

非线性偏微分方程（PDE）在从机翼周围的空气流动到金融市场行为的现实情况建模中具有普遍适用性。它们也是描述数学物理和微分几何定律的自然语言。他们的研究对纯粹的数学家提出了深刻的智力挑战，以及在特定应用中需要精确数值数据的重要计算问题。尽管英国在国际上具有重要意义，在几个方面的研究活动也很活跃，包括近年来的重大突破，但英国在这一领域似乎落后于其竞争对手。目前的建议是建立一个分析和非线性偏微分方程中心，由爱丁堡大学和爱丁堡赫瑞瓦特大学共同管理。该中心将通过一系列具体行动改善英国目前的地位：-任命在英国代表性不足的领域的杰出研究人员-一个向英国和英国以外的研究人员开放的教学研讨会计划-两个关于非线性PDE当前趋势和发展的主要研究研讨会-一个实质性的访问计划，将世界上最好的研究人员带到英国进行高调的讲座并建立新的研究联系-发展该提议来自麦克斯韦数学研究所，该研究所是一个新的合资企业，结合了爱丁堡大学和赫瑞瓦特大学的数学科学实力。麦克斯韦研究所由苏格兰基金委员会和科学技术办公室资助，旨在成为数学科学研究和研究生培训的卓越中心，提供一个能够吸引和培养来自世界各地最优秀的数学人才的环境。麦克斯韦研究所是五个联合研究项目之一，其他项目涵盖工程和地球科学领域的广泛主题。目前的竞标将利用麦克斯韦研究所的地位以及其他联合研究计划，在这些领域开发非线性PDE的新合作和应用。该提案的另一个显著特征是国际数学科学中心（ICMS）的存在，该中心是爱丁堡和赫瑞瓦特大学数学家于1990年共同倡议成立的。从那时起，ICMS在举办高水平国际教学和研究讲习班方面建立了声誉，它提供的基础设施将对组织拟议的讲习班至关重要。与此同时，这些讲习班扩大了ICMS目前的活动，并将增加其国际声誉。新的研究小组将由科学指导委员会管理，该委员会由爱丁堡大学和赫瑞瓦特大学各两名数学家组成，还包括至少一名来自工业界的代表和至少一名来自海外的代表。将定期征求委员会的意见，特别是关于讲习班和访问方案的意见。

Nonlinear partial differential equations (PDE) are of universal applicability in the modelling of real-life situations from the flow of air around a wing to the behaviour of financial markets. They are also a natural language for describing the laws of mathematical physics and differential geometry. Their study poses profound intellectual challenges to pure mathematicians as well as important computational problems where accurate numerical data is required in specific applications. Despite its international importance and intense research activity on several fronts, including important breakthroughs in recent years, the UK appears to lag behind its competitors in this area.The present proposal is to establish the Centre for Analysis and Nonlinear Partial Differential Equations, run jointly by the University of Edinburgh and Heriot--Watt University at Edinburgh. This centre will improve the UK's current position through a number of specific actions:--- appointment of outstanding researchers in areas under-represented in the UK--- a programme of instructional workshops open to researchers in the UK and beyond--- two major research workshops on current trends and developments in nonlinear PDE--- a substantial visitor programme to bring the world's best researchers to the UK to give high-profile lectures and establish new research contacts--- development of new research links with industry and other interested parties--- development of new undergraduate and graduate courses in analysis aimed at meeting the needs of the next generation of researchersThe proposal comes from the Maxwell Institute of Mathematics, which is a new joint venture combining the strength of mathematical sciences at the University of Edinburgh and Heriot-Watt University. Funded by the Scottish Funding Council and the Office of Science and Technology, the Maxwell Institute aims to be a pre-eminent centre for research and post-graduate training in the mathematical sciences, offering an environment able to attract and foster the very best mathematical talent from around the world. The Maxwell Institute is one of five joint research initiatives, the others covering a wide range of topics in engineering and geoscience. The present bid will take advantage of the Maxwell Institute's position alongside the other joint research initiatives to develop new collaborations and applications of nonlinear PDE in these areas.The other distinctive feature of this proposal is the presence of the International Centre for Mathematical Sciences (ICMS) which is a joint initiative of the mathematicians at Edinburgh and Heriot-Watt which was set up in 1990. Since then ICMS has developed a reputation for the running of high-level international instructional and research workshops, and the infrastructure it provides will be crucial in organizing the proposed workshops. At the same time, these workshops provide a broadening of ICMS's current activities and will add to its international reputation.The new research grouping will be managed by a Scientific Steering Committee composed of two mathematicians from each of University of Edinburgh and Heriot-Watt University, and also including at least one representative from industry and at least one person from overseas. The committee will be regularly consulted, especially on the workshop and visitor programmes.