Abstract: Many contemporary challenges in the engineering sciences concern the inference of global features from local data. This passage from local-to-global data is as subtle as it is fundamental; however, it is not unprecedented. In the mathematical sciences, several types of local-to-global challenges were overcome with new techniques -- from topology, homological algebra, and sheaves. This talk will outline both the vision and the first steps of exporting homological and sheaf-theoretic tools for data in the engineering sciences, with examples drawn from sensor networks, signal processing, target tracking, and network optimization.
Prof. Ghrist has a BS in Mechanical Engineering from the University of Toledo, and an MS & Ph.D. in Applied Mathematics from Cornell University. He has held positions at the University of Texas, Austin; Georgia Institute of Technology; and the University of Illinois, Urbana-Champaign. Currently, he is the Andrea Mitchell University Professor of Mathematics and Electrical & Systems Engineering at the University of Pennsylvania. Prof. Ghrist’s work focuses on topological methods in applied mathematics, with applications in networks, robotics, sensing, and more. His work has been honored by an NSF PECASE award in 2004, a Scientific American "SciAm50 Top Research Innovation" award in 2007, and the Chauvenet prize in 2013.