Barcodes: the persistent topology of data

• Grant number: 16/08852-4
• Support Opportunities: Scholarships abroad - Research Internship - Scientific Initiation
• Start date: June 15, 2016
• End date: August 14, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alice Kimie Miwa Libardi
• Grantee: Marco Antonio de Freitas Contessoto
• Supervisor: Roberto Facundo Memoli Techera
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
• Institution abroad: Ohio State University, Columbus, United States
• Associated to the scholarship: 16/00326-1 - Some applications of algebraic topology, BP.IC

Abstract

In the paper "Barcodes: the persistent topology data" is presented the primary mathematical tool considered in a homology theory for point- cloud data sets (persistent homology) and a novel representation of this algebraic characterization (barcodes) and in "Persistent Homology - a survey" is given a short history of persistent homology and present its basic concepts. (AU)