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Some applications of algebraic topology

Grant number: 16/00326-1
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): April 01, 2016
Effective date (End): December 31, 2016
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Alice Kimie Miwa Libardi
Grantee:Marco Antonio de Freitas Contessoto
Home 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.