Abstract: Group theory has been a cornerstone of physics for more than a century. Applications of Lie groups in engineering and biology are much more recent. This talk reviews how group theory and noncommutative harmonic analysis have been used by the speaker in robotics and DNA statistical mechanics. These problems involve the representation theory of the Euclidean motion group. Moreover, recent problems in crystallographic packing problems are formulated as a search in quotients of the Euclidean motion group modulo discrete subgroups. Geometric and measure-theoretic issues in these problems are presented.
Introduction: Gregory S. Chirikjian received undergraduate degrees from Johns Hopkins University in 1988, and the Ph.D. degree from the California Institute of Technology, Pasadena, in 1992. Since 1992, he has been on the faculty of the Department of Mechanical Engineering, Johns Hopkins University, where he has been a full professor since 2001. From 2004-2007 he served as department chair.
He also has held courtesy appointments in several departments and programs, including Computer Science. His research interests include robotics, applications of group theory in a variety of engineering disciplines, and the mechanics of biological macromolecules. He is a 1993 National Science Foundation Young Investigator, a 1994 Presidential Faculty Fellow, and a 1996 recipient of the ASME Pi Tau Sigma Gold Medal. In 2008 he became a Fellow of the ASME, and in 2010 he became a Fellow of the IEEE. He is the author of more than 250 journal and conference papers and primary author on four books: Engineering Applications of Noncommutative Harmonic Analysis (2001) and Stochastic Models, Information Theory, and Lie Groups, Vols. 1+2. (2009,2011); Harmonic Analysis for Engineers and Applied Scientists (2016). Since January 2019 he has been serving as Professor and the Head of the Department of Mechanical Engineering at the National University of Singapore.
