Persistent Homology and Its Extensions

Geometry/Topology Seminar, Math Department, UC Davis

Lecture

October 13, 2016
2:00pm to 3:00pm
UC Davis

Event Website

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.

Speaker(s)

Dmitriy Morozov

Alumni - BIDS Data Science Fellow

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.