Geometric deformations of singularities

• Grant number: 22/06325-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Effective date (Start): July 01, 2022
• Effective date (End): April 17, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Farid Tari
• Grantee: Marco Antônio do Couto Fernandes
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 19/07316-0 - Singularity theory and its applications to differential geometry, differential equations and computer vision, AP.TEM

Abstract

The research of this project is within singularity theory and its applications to differential geometry and qualitative theory of implicit differential equations. Its aim is to study geometric deformations of singular plane curves and surfaces defined implicitly in the Euclidean and Minkowski spaces, and obtain, in particular, the maximum number of inflection points and vertices (for curves) and umbilic points (for surfaces) that can appear in deformations of such objects. Another aim of the project is to study the generic deformations in the lines of principal curvatures on 1-parameter families of surfaces in Minkowski space. (AU)