Workshop on Emerging Mathematical Foundations for Design; Washington, DC; Summer 2020

本研讨会旨在扩大可用于解决复杂工程设计问题的数学工具的范围。具体地说，该研讨会通过使用有针对性的协作和写作练习来帮助探索和弥合三个领域--工程设计、数学和计算机科学--之间的语言和概念障碍，这些练习旨在揭示数学和计算机科学的新的发展领域，可以被改编和应用于解决现实世界的工程问题。该研讨会还寻求通过加强学生的教育成果，并为美国学术和工业劳动力提供一条途径，在未来几十年增长和开发这些新的数学工具，从而在这些交叉领域培养新一代研究生。与没有研讨会相比，这个研讨会以更快的速度推进了NSF促进科学进步的使命，将先进的数学工具转化为工程研究和实践。这个为期数天的研讨会将聚集三组人：(1)工程/系统设计研究人员，(2)数学家、统计学家和计算机科学家，以及(3)来自这些领域的研究生。会议的目的是进行一系列“翻译”练习，在这些练习中，具有工程设计和系统工程(EDSE)研究人员通常不存在或使用的学科领域知识的数学家、统计学家和计算机科学家与工程设计和系统工程(EDSE)研究人员结对并以小组形式与EDSE研究人员合作，将关键思想或结果从未被探索的数学领域--具体地说，从表示理论的不同领域--翻译成EDSE研究人员可以在EDSE问题的背景下解释的语言。这些练习包括改编自科学传播技术的有针对性的写作练习，以及来自具有代表性和不同工程学科的研究生的入门讲座和范例问题解决练习。研讨会的主要目标是激发数学和计算科学中尚未探索的领域之间的新兴趣和联系，从而(1)EDSE研究界在这些新的科学领域有具体、易于理解的立足点；(2)数学家、统计学家和计算科学家看到他们的工作在更广泛的EDSE兴趣问题中的具体应用；以及(3)研讨会促进CMMI和DMS之间的趋同研究和CESS方向，扩大对工程设计问题感兴趣的人的池，以及这些研究人员解决这些紧迫问题所需的可用的数学工具。研讨会的具体成果包括一套白皮书，向EDSE、数学和计算机科学受众介绍来自一个数学领域的关键思想，并举例说明工程师在人类技术前沿设计产品或系统时出现的当前问题。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This workshop aims to expand the scope of mathematical tools available to solve complex engineering design problems. Specifically, the workshop helps explore and bridge language and conceptual barriers between three fields--Engineering Design, Mathematics, and Computer Science--through the use of targeting collaboration and writing exercises designed to uncover new growing areas of mathematics and computer science can be adapted and applied to solved real-world engineering problems. The workshop also seeks to train a new generation of graduate students in these intersecting areas by strengthening educational outcomes for students and providing a pathway for the US academic and industrial workforce to grow and develop these new mathematical tools over future decades. This workshop advances NSF's mission to promote the progress of science by transitioning advanced mathematical tools into engineering research and practice at an accelerated rate compared to what would be possible without the workshop. This multi-day workshop will bring together three groups of people: (1) Engineering/System Design Researchers, (2) Mathematicians, Statisticians, and Computer Scientists, and (3) graduate students from across those areas. The meeting's purpose is to perform a series of "translation" exercises wherein Mathematicians, Statisticians, and Computer Scientists with knowledge of subject areas not typically present in or used by Engineering Design and Systems Engineering (EDSE) researchers, work in pairs and small groups with EDSE researchers to "translate" key ideas or results from under-explored areas of mathematics--specifically, from different areas of Representation Theory--to a language that EDSE researchers can interpret in the context of EDSE problems. These exercises include both targeted writing exercises adapted from science communication techniques as well as introductory lectures and example problem-solving exercises by graduate students from representative and diverse engineering disciplines. The key goal of the workshop is to spark new interest and connections between unexplored areas of Mathematics and Computational Science such that (1) the EDSE research community has concrete, easy-to-understand footholds into those new scientific areas; (2) Mathematicians, Statisticians, and Computational Scientists see concrete applications of their work in problems of broader EDSE interest; and (3) the workshop promotes convergence research between the CMMI and DMS and CISE directorates, expanding the pool of people interested in Engineering Design problems and the available mathematical tools those researchers have to address those pressing problems. The concrete deliverables from the workshop include a set of white-papers that introduce the key ideas from one area of mathematics to EDSE, and Mathematics and Computer Science audiences with examples of current problems that occur when engineers design products or systems at the Human-Technology Frontier.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.