Post-docs and StudentsI am currently working with three post-doctoral fellows. Chao Chen graduated in 2009 from the Computer Science Department at the Rensselaer Polytechnic Institute. He works on topological algorithms, including optimal cycle structures and applications to computer vision. Michael Kerber graduated in 2009 from the Computer Science Department at the Saarland University. He is interested in fast algorithms for topology and images. Olga Symonova received her doctorate from the University of Trento and was postdoc at Georgia Tech working on biologically motivated shape modeling questions. She continues her work on the growth modeling of agricultural root systems. I am advising four graduate students at various stages of their program. Brittany Fasy looks at curves in three and higher dimensions as well as the heat equation through the lense of persistence diagrams and vineyards. Ying Zheng works on algorithm for symmetry in images and shapes.
ResearchIn the year 2005, we started two DARPA funded projects. The first is on tda, short for ``algebraic topological tools for high dimensional data analysis and the study of families of shapes''. Under its umbrella we develop algorithms for homology groups, persistence, Morse complexes and more. The second is on funbio, short for ``microstates to macrodynamics: a new mathematics of biology''. It aims at deepening our understanding of broad biological questions through the use of novel mathematical methods. Data analysis with algebraic topology is one of the new methods. I am also involved in biology projects lead by Philip Benfey. In particular, an NSF funded project on identifying genes for root system architecture traits and an NIH funded center for systems biology.
TeachingDuring the Fall and Winter of 2010/11, I co-teach a course on Computational Topology with Paul Bendich at IST Austria.
SoftwareThe Alpha Shapes software is designed to analyze point data in three dimensions. It specializes on molecular conformations, where a molecule is given as a set of atoms and each atom is a sphere given by its center (a point) and radius. For surface reconstruction I recommend Geomagic Wrap instead. I used that software to create the 180 wrapped tubes, which you can download in .stl format and print if you have a layered technology machine.
PublicationsI list my publications in reverse chronological order.
Herbert Edelsbrunner Duke University Computer Science Department Box 90129 Durham, NC 27708