Differential topology and topological methods for the study of differential equations on manifolds

• Grant number: 16/19227-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2016
• End date: November 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Pierluigi Benevieri
• Grantee: Rodrigo Lima Dias
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The project deals with the study of the basic concepts in differential topology and their connections with the classical topological methods in nonlinear analysis, as the topological degree theory and the notion of degree of a tangent vector field to a differentiable manifold. These methods will be applied to the study of some differential equations, of first and second order, on manifolds. Classical topological results, as Brouwer and Schauder fixed point theorems will be tackled. (AU)