Multi-local singularities of k-folding maps on curves and surfaces.

• Grant number: 23/11669-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: January 01, 2024
• End date: February 28, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Farid Tari
• Grantee: Amanda Dias Falqueto
• 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 aim of this work is to study the multi-local singularities of k-folding maps on plane curves and surfaces in Euclidean space and the related geometry. Our study will generalize the notion of Symmetrical Set of curves and surfaces. We also intend to study the bifurcations of local and multi-local singularities in families of k-folding maps parameterised by the Grassmanian of planes in R3 in the case of surfaces and of lines in R2 in the case of plane curves.