Curves and singularities

• Grant number: 22/11895-8
• Support Opportunities: Scholarships in Brazil - Program to Stimulate Scientific Vocations
• Start date: January 03, 2023
• End date: February 22, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Maria Aparecida Soares Ruas
• Grantee: Odete Lara Melo Budtinger
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Classical differential geometry is the object of study of the undergraduate course in Mathematics. The approach of geometry topics in R3 through the singularity theory allows a very rich study of the geometric properties of curves, families of curves and surfaces, which successfully complements the classical approach. On the other hand, the introduction of the theory of singularities in order to study the generic properties of curves and surfaces does not require much prior knowledge and is therefore quitesuitable for undergraduate students. (AU)