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BIRS Workshop Lecture Videos

Topology as a tool for obtaining global from local information Sazdanovic, Radmila


Data can often be encoded by a graph or a point cloud. Homology groups of associated simplicial complex, and other tools of Topological Data Analysis (TDA) can be used to compare data sets and detect properties and patterns in the data. We focus on the theoretical results that can be used to address computational challenges caused by the complexity and size of the data. For example, we show that the (local) bottleneck distance between zig-zag persistence modules restricted to an interval provides a lower bound on the bottleneck distance and analyze persistence of metric wedge sums and metric gluings. This is joint work with Henry Adams, Michael Adamaszek, Ellen Gasparovic, Maria Gommel, Emilie Purvine, Bei Wang, Yusu Wang, and Lori Ziegelmeier.

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