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

University Of Maryland, College Park, College Park MD

Investigators

Abstract

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.