BIRS Workshop Lecture Videos
Combining sub-level and level-set persistence Catanzaro, Michael
Theoretical methods in persistent homology have traditionally considered one of two viewpoints: R-indexed/sub-level set persistence, or zig-zag/level-set persistence. Even in the case of a single variable real-valued function, there is still much to be understood by combining these two forms of persistence together. This version of multiparameter persistence naturally lends itself to analysis of families of functions on smooth manifolds, as well as generalized versions of Reeb graphs and Merge trees. In this talk, I will show what we hope to learn by mixing these two together through a variety of examples, ranging from manifolds to Arnold's Calculus of Snakes. This ongoing work is joint with Peter Bubenik.
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