Dr. Dmitriy Morozov, Postdoctoral Scholar in the Computational Research Division
Lawrence Berkeley National Laboratory
In the last decade, persistent homology emerged as a particularly active topic within the young field of computational topology. Homology is a topological invariant that counts the number of cycles in the space: components, loops, voids, and their higher-dimensional analogs. Persistence keeps track of the evolution of such cycles and quantifies their longevity. By encoding physical phenomena as real-valued functions, one can use persistence to identify their significant features.
This talk is an introduction to the subject, discussing the settings in which persistence is effective as well as the methods it employs. As examples, we consider problems of scalar field simplification and non-linear dimensionality reduction. The talk will sketch the budding field of topological data analysis and its future directions.