Topics in singularity theory

• Grant number: 19/18820-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2019
• End date: October 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ana Claudia Nabarro
• Grantee: Amanda Dias Falqueto
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project aims to introduce some important topics of Singularity Theory to complement the student's knowledge, using as a book the classic text: "Curves and Singularities", by J.W.Bruce and P.J.Giblin. In this project we will study discriminants, unfoldings and applications, as well as some of the theory needed to classify functions of various variables, consequences and examples. The student will also solve exercises proposed in the book cited. Supporting software may be used. (AU)