Date(s) - 19/11/2018
11:00 am - 12:00 pm
Studio Villa Bosch
By Herbert Edelsbrunner, Institute of Science and Technology Austria (IST Austria)
We study classical questions in stochastic geometry, such as the expected density of p-simplices in the Delaunay mosaic of a Poisson point process in d-dimensional Euclidean space. Using a discrete Morse theory approach, we distinguish between critical and non-critical of the radius function and determine their expected densities dependent on a radius threshold. We generalize the analytic results to weighted Delaunay mosaics and to order-k Delaunay mosaics, and we present experimental result for wrap complexes and for weighted Voronoi tessellations.
Joint work with Anton Nikitenko, Katharina Oelsboeck, and Peter Synak.
Herbert Edelsbrunner is Professor at the Institute of Science and Technology Austria. In 1982, he graduated from the Graz University of Technology, Austria, from 1985 to 1999, he was Assistant, Associate, and Full Professor at the University of Illinois at Urbana-Champaign, and from 1999 to 2012, he was Arts and Sciences Professor at Duke University.
In 1996, he co-founded Geomagic, a software company in the field of Digital Shape Sampling and Processing. It offers innovative software solutions for 3-dimensional reconstruction and manipulation, which are applied in diverse industries, including automotive, aerospace, dentistry, toys, etc.
In 1991, he received the Waterman Award from the NSF in the United States, and in 2018, he received the Wittgenstein Prize from the FWF in Austria. He is member of the American Academy of Arts and Sciences, of the German Academy of Sciences (Leopoldina), and of the Austrian Academy of Sciences. His primary research area is computational geometry and topology.
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