Some applications of algebraic topology

• Grant number: 16/00326-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2016
• End date: December 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alice Kimie Miwa Libardi
• Grantee: Marco Antonio de Freitas Contessoto
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
• Associated scholarship(s): 16/08852-4 - Barcodes: the persistent topology of data, BE.EP.IC

Abstract

This project aims to give an overview of applications of Algebraic Topology. Simple examples of applications of the following topics will be presented: Manifolds, Euler Characteristic, Homology and Cohomology, Morse Theory and Conley Index. All topics, except for Morse theory, have been developed formally by the student previously. The student will learn new concepts with the reading of a survey on persistent homology and barcodes. The student intends to do an internship at Ohio State University, under the supervision of Roberto Facundo Mémoli Techera from June,15 until July, 15.