Talk Title: Dualities in Persistent (co)Homology(Part I and II)

Event: Graduate Student Geometry and Topology Seminar

Where: Department of Mathematics, Michigan State University

Date: January 17 and 24, 2018

Abstract: For a filtered topological space, its persistent homology is a multi-set of half open real intervals known as barcode. Each bar represents the lifespan of a homology class. A fundamental principle is that the length of such a bar determines the significance of the corresponding class. In 2011, V. de Silva et al studied the relationships between (persistent) absolute homology, absolute cohomology, relative homology and relative cohomology. This talk will be a theoretical overview of that study.