On the geometry of singular surfaces

• Grant number: 22/10370-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2022
• End date: September 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Farid Tari
• Grantee: Samuel Paulino dos Santos
• 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 project is within singularity theory and its applications to differential geometry. The main goal of the project is to study the geometry of singular surfaces in the Euclidian and Minkowski spaces. We intend to study local properties of singular surfaces which appears as bifurcation sets of versal unfoldings, as focal surfaces and those invariants under screw motions. Amongst the problems proposed in this project are the study of parameterized singular surfaces via the geometry of their sections by parallel planes and the study of surfaces with $D_4^\pm$ singularities in the three dimensional Minkowski space.