EPSRC Centre for Doctoral Training in Mathematical Analysis and its Applications:Maxwell Institute Graduate School in Analysis & Applications - MIGSAA

在这项提议中，我们寻求建立一个数学分析及其应用方面的博士培训中心。该中心的主要目的是在几年内在这一领域培训60多名新的博士生，并通过这样做来满足这一领域训练有素的研究人员已证明的技能需求。该中心将建立在严格的数学分析及其应用的基础上，重点放在三大主题下的非线性偏微分方程式：理论、随机和数值。其范围包括调和分析、大型离散结构的数学分析、应用分析、动力系统、随机分析、金融数学、应用概率和计算数学。将特别强调这些领域及其应用之间的联系和互动，并积极与业界合作--在制定学生项目、指导博士生、为学生制定工作安排以及更广泛的双向知识交流方面--将是CDT的一个关键特征。在该中心接受培训的数学家的需要体现在需要尖端的微分和/或随机模型的现实世界现象中，例如在石油开采、电网可再生能源战略、金融过程、气候变化的生态影响以及大脑内部的过程中。我们将提供一批具有多种技能的博士，并有能力应对数学建模中出现的复杂挑战：他们将能够分析和实施，并能够对当前和未来的挑战做出快速和灵活的反应。MIGSAA培训将建立在两个主要支柱上：出色的学术供应和早期职业发展，这些都是以发展强烈的同龄人意识为基础的。作为一个完全整合的四年制联合博士课程，它将提供比标准的英国数学博士模式更多的内容。初步的学术培训将建立在SMSTC提供的坚实基础上，并将以强大的教学和评估部分为特色。学生还将在第一年完成两个评估项目。这两个项目将跨越MIGSAA的领域，并将为第一年年底主要博士论文的选题提供坚实的基础。主要的博士项目将具有挑战性和实质性，将导致前沿的数学研究成果。二年级及以后的学生将获得一批特别设计的更高级的课程，以便学生在继续他们的主要研究项目的同时，继续巩固现有的知识和专业知识。学生将得到精心规划的补充研究活动的进一步支持，并将重点放在最广泛意义上的早期职业发展上。这将包括公众参与、有效协作、了解影响议程和负责任的创新、领导力、外联、媒体培训、行业参与和网络方面的培训。我们对MIGSAA的愿景的核心是它将培养的群体意识。从一年一度的上岗活动开始，通过提供连续的办公场所和专用的公共空间，参加SMSTC已经提供的队列环境将得到显著改善，一年级学生将被安置在爱丁堡市中心的ICMS。随后几年的队列活动包括：实际参加更高级别的课程、研究研讨会和通用技能课程；积极的工作组鼓励对等学习；年度住宿座谈会。

In this proposal we seek to establish a Centre for Doctoral Training in Mathematical Analysis and its Applications. The main purpose of the centre is to train upwards of 60 new PhD students in this area over several years, and in doing so address the proven skills need for highly-trained researchers in this area. The centre will be founded on rigorous mathematical analysis and its applications, with a strong focus on nonlinear partial differential equations, under three broad themes: theoretical, stochastic and numerical. Its scope includes harmonic analysis, mathematical analysis of large-scale discrete structures, applied analysis, dynamical systems, stochastic analysis, financial mathematics, applied probability and computational mathematics. There will be a special emphasis on the connections and interactions between these areas, and their applications, and active collaboration with industry -- in the formulation of student projects, in mentoring PhD students, in developing work placements for the students, and more broadly in two-way knowledge exchange -- will be a key feature of this CDT. The need for mathematicians trained in this centre is manifest in real-world phenomena where cutting-edge differential and/or stochastic models are needed, for example in oil extraction, in power grid renewable energy strategies, in finance processes, in ecological impacts of climate change, and in procceses inside the brain. We shall provide a flow of such PhDs with multiple skill sets and the ability to deal with the sophisticated challenges arising in mathematical modelling: they will be able to both analyse and implement and will be in a position to mount rapid and agile responses to current and future challenges. MIGSAA training will be constructed on two main pillars: outstanding academic provision and early-stage career development.These are underpinned by development of a strong sense of cohort. As a fully integrated joint 4 year PhD programme, it will offer much more than the standard UK Mathematics PhD model.Initial academic training will build upon the firm foundation provided by SMSTC, and will feature a strong taught and assessed component.Students will also complete two assessed projects during their first year. It is intended that the two projects will span the areas of MIGSAA, and will provide a firm basis for choosing the topic for the main PhD dissertation towards the end of Year 1. The main PhD project, which will be challenging and substantial, will lead to original research findings at the cutting edge of mathematical endeavour.A tranche of specially designed, more advanced courses will be available for students in Year 2 and beyond so that students will continue to consolidate the available knowledge and expertise as they continue on their main research project. Students will be further supported by a carefully-planned programme of complementary research activities.There will be a strong focus on early-stage career development in its broadest sense. This will include training in public engagement, effective collaboration, understanding the impact agenda and responsible innovation, leadership, outreach, media training, engagement with industry and networking. Central to our vision for MIGSAA is the sense of cohort which it will foster. Beginning with the annual induction event, the cohort environment already offered by participation in SMSTC will be significantly enhanced by provision of contiguous office accommodation and dedicated common spaces, with Year 1 students collocated at ICMS in central Edinburgh. For the later years cohort activities include: physical attendance at higher level courses, research seminars and generic skills courses; active working groups encouraging peer-to-peer learning; annual residential symposia.