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December 19, Tuesday
12:00 – 14:00

Topological persistence measures the "persistence" of topological features, such as connected components, tunnels and cavities, within the sublevel sets, ${x: f(x) < c}$, of a scalar field. The topological persistence of a feature is stable under small perturbations of the scalar field. Interval persistence is a generalization of topological persistence which better represents topological features in level sets, ${x: f(x) = c}$, gives a fuller matching of critical values, and is the appropriate setting for a stability theorem for critical points under small perturbations of scalar fields.

I will give an introduction to topological persistence and then discuss interval persistence, its relationship to topological persistence, and stability and matching of critical points under interval persistence. Joint work with Dr. Tamal Dey and Dr. Yusu Wang from The Ohio State University. Dr. Rephael Wenger is an associate professor in the Department of Computer Science and Engineering at The Ohio State University. He works on computational geometry, geometric algorithms and geometric modelling, particularly as they apply to graphics, visualization and biomedical image processing.