Herbert Edelsbrunner is Professor of Mathematics and Computer Science at IST Austria and co-founder of Geomagic. He works in the field of computational geometry and topology as well as its applications in science and engineering. He is author and co-author of four textbooks in the wider area.
Talk: "Controlling topology by counting and measuring holes"
Abstract: An aspect of simplifying structural geographic information is the change of its topology, which is necessary to avoid severe limitation. We argue that this is best done by counting and measuring holes, globally or locally. The art of defining and counting holes has been perfected during the last century, and we will review homology as a particular algebraic framework, which maps holes to dimensions of certain abelian groups, which in some instantiations are vector spaces over a field. Importantly, homology has recently been extended to measuring persistence, which in a nutshell gives information about the range of scales over which a hole exists. This concept connects holes with the scale hierarchy in much the same way we envision simplification to modify structural information. We will sketch the concept of persistent homology, some of its properties, and its algorithms.