Distinguished Guest Lecturer: Herbert Edelsbrunner
Approximation and Convergence of the First Intrinsic Volume
The Steiner polynomial of a solid body in R^n is of degree n and describes the volume as a function of the thickening parameter (parallel body). The coefficient of the degree-i term is used to define the (n-i)-th intrinsic volume. Using an integral geometric approach, we modify the Crofton formula using persistent moments to get a measure for approximating bodies that converges to the intrinsic volume of the solid body. We have a proof of convergence for n-i = 1.
(Work with Florian Pausinger.)
Herbert Edelsbrunner is Professor at the Institute of Science and Technology Austria. He graduated from the Graz University of Technology, Austria, in 1982, he was faculty at the University of Illinois at Urbana-Champaign from 1985 through 1999, and Arts and Sciences Professor at Duke University from 1999 to 2012. He co-founded Geomagic in 1996, a software company in the field of Digital Shape Sampling and Processing.
His research areas are algorithms, computational geometry, computational topology, data analysis, and applications to biology. He has published four textbooks in the general area of computational geometry and topology. In 1991, he received the Alan T. Waterman Award from the US National Science Foundation. In 2006, he received an honorary degree from the Graz University of Technology. He is a member of the American Academy of Arts and Sciences, the Germany Academy of Sciences (the Leopoldina), the Academia Europaea, and the Austrian Academy of Sciences.