Abstract: In the last 15 years, persistent homology emerged as a particularly active topic within the young field of computational topology. Persistence tracks the evolution of homology classes and quantifies their longevity. By encoding physical phenomena as real-valued functions, one can use persistence to identify their significant features. This talk will introduce persistence, discussing the settings in which it is effective as well as the methods it employs. It will also describe two extensions to persistent homology, zigzag persistent homology and well groups, and how all three relate to each other, through a Mayer--Vietoris pyramid, when the input data is a real-valued function.
Dmitriy Morozov is a research scientist in the Computational Research Division of the Lawrence Berkeley National Laboratory (LBNL). After completing his PhD in computer science at Duke University, he was a postdoctoral scholar in the Departments of Computer Science and Mathematics at Stanford University and later LBNL. Dmitriy’s work is concerned with geometric and topological data analysis, especially with the development of efficient algorithms and software in this field.