Applications of Topology to Analysis/Equations and Computation Results

• Grant number: 25/21211-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2026
• End date: January 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: João Vitor da Silva
• Grantee: Isadora Dagostini Lunelli
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this proposal, we will develop a project in the area of topology and metric spaces. In this context, we first present the main definitions and results within topology and metric spaces, as well as the powerful tool of the Banach Fixed Point Theorem. Next, we develop in detail three applications to Mathematical Analysis and Computation: the Existence and Uniqueness Theorem of ODEs, Integral Equations, and finally, as a computational application, we demonstrate the mathematical model of the Google search engine and its effectiveness. (AU)