Complex Analysis: Techniques, Applications and Computations

该奖项支持美国早期职业数学家参加为期4个月的“复杂分析：技术、应用和计算”项目，该项目将于2019年9月2日至12月19日在艾萨克·牛顿数学科学研究所（英国剑桥）举行。该计划包括三个研讨会和大师班（由该领域的领导者进行的说明性讲座），并将为处于关键职业阶段的初级科学家提供参与其研究领域的研讨会和大师班的机会。研讨会为“复杂分析工具箱：新技术和新视角”，2019年9月9日至13日；“数学物理中的复杂分析及其应用”，2019年10月28日至11月1日；“计算复杂分析”，2019年12月9日至13日。复变量和解析函数理论在数学的各种应用和领域中起着基本的作用。在传统领域进行了几十年的经典工作，现在正在为许多令人兴奋的新方向的新的快速增长提供基础和灵感。INI计划将通过汇集在这些新发展前沿工作的主要研究人员来推进该领域，并将通过确定新技术，方法和见解中产生的最重要的科学挑战来帮助指导未来的努力。该计划还将重点阐明在过去几年中出现的复杂分析的不同分支之间意想不到的联系。为此，该计划将包括数学家以及物理学家和工程师在理论方面，计算方法，数学建模和应用工作。该奖项旨在支持参与研讨会，其次是更广泛的计划。主要影响将是初级研究人员的培训和职业发展。将科学领袖长期聚集在一起将为创造性合作提供一个协同论坛，这将特别有利于将得到支持的早期职业参与者。他们将有机会向资深同事学习，向社区展示他们的工作，并将为他们的研究项目带来新的想法，从而加强数学科学基础设施，作为该奖项的次要影响。组织者还将举行一个专题会议，讨论如何教授复杂分析，并探索课堂上的新创新，包括演示。这对于即将开始教学生涯的初级学员来说尤其有用。成立了一个多元化委员会，以确定有前途的多元化参与者（女性或代表性不足的少数民族），并让他们参与项目和讲习班。该计划的网站可在https://www.newton.ac.uk/event/cat上找到，其中包括有关讲习班的详细信息。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award supports the participation of early-career US-based mathematicians in the 4-month program "Complex Analysis: Techniques, Applications and Computations'' to be held at the Isaac Newton Institute (INI) for Mathematical Sciences (Cambridge, UK) from September 2 to December 19, 2019. The program includes three workshops and sets of masterclasses (expository lectures given by leaders in the field), and will give junior scientists, at a critical career stage, a chance to participate in a workshop and masterclass in their research area. The workshops are "The complex analysis toolbox: new techniques and perspectives", from September 9 to 13, 2019; "Complex analysis in mathematical physics and applications", from October 28 to November 1, 2019; and "Computational complex analysis", from December 9 to 13, 2019. Complex variable and analytic function theory play an elemental role in a diverse array of applications and areas of mathematics. The classical work carried out over decades in traditional fields is now providing the foundations and inspiration for new and rapid growth in many exciting new directions. The INI program will advance the field by bringing together key researchers working at the frontiers of these new developments and will help steer future endeavors by identifying the most important scientific challenges arising from the new techniques, methodologies and insights. The program will also focus on elucidating the unexpected connections between different branches of complex analysis that have been emerging over the past few years. To this end, the program will encompass mathematicians as well as physicists and engineers working on theoretical aspects, computational methods, mathematical modeling and applications.The award will be aimed at supporting participation in the workshops and secondarily the broader program. The main impact will be the training and career development of junior researchers. Bringing together scientific leaders for extended periods will provide a synergistic forum for creative collaboration, which will be particularly beneficial to the early-career participants who will be supported. They will have the opportunity to learn from senior colleagues and to highlight their work to the community, and will bring new ideas for their research programs back to the US, thereby enhancing the mathematical sciences infrastructure as a secondary impact of the award. The organizers will also hold a moderated session discussing how complex analysis is taught, and exploring new innovations in the classroom, including demonstrations. This will be particularly useful for junior participants who may be embarking on teaching careers. A diversity committee has been formed to identify promising diverse participants (female or underrepresented minorities) and involve them in the program and workshops. The website for the program can be found at https://www.newton.ac.uk/event/cat and includes details about the workshops.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.