Noncommutative Harmonic Analysis in Robotics and Structural Biology
Many problems of interest in engineering and science involve probability distributions of rigid-body motions. In this talk, a variety of stochastic phenomena that evolve on the group of rigid-body motions will be discussed together with tools from harmonic analysis and Lie theory to solve the associated equations. These include mobile robot path planning, statistical mechanics of DNA, and problems in image processing. Current work on multi-robot team diagnosis and repair, information fusion, and self-replicating robots will also be discussed. In order to quantify the robustness of such robots, measures of the degree of environmental uncertainty that they can handle need to be computed. The entropy of the set of all possible arrangements (or configurations) of spare parts in the environment is such a measure, and has led us to study problems at the foundations of statistical mechanics and information theory. These, and other, topics in robotics and structural biology (such as methods for cross-modal information fusion between cryo-electron microscopy and small-angle x-ray scattering) lend themselves to the same mathematical tools, which will be discussed in this talk.
Speaker Biography: 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. 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 200 journal and conference papers and primary author on three books: Engineering Applications of Noncommutative Harmonic Analysis (2001) and Stochastic Models, Information Theory, and Lie Groups, Vols. 1+2. (2009,2011). In 2016 an expanded edition of his 2001 book came out as a Dover book under the new title: Harmonic Analysis for Engineers and Applied Scientists.