Morse Theory

• Grant number: 20/04871-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2020
• End date: April 30, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ivan Struchiner
• Grantee: Pietro Mesquita Piccione
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project, the student will study Morse Theory, as natural extension of the courses in geometry and topology that he took during last semesters. The project will start from elementary theory of Differential Topology, to acquire the knowledge for the study of Morse theory, culminating in the Morse index theorem in Riemannian geometry, and its applications. Such applications include, for example, results that relate geometry to topology.