Description: This project aims to advance the frontiers of knowledge in singularity theory through the development of fundamental topics in the field. Notable areas include the recognition of the topology and geometry of real and complex singularities, the characterization of families of singular sets satisfying certain equisingularity conditions, and the Lipschitz geometry of singularities. Invariants will be investigated in their various forms—geometric, algebraic, or topological. Special classes of singularities, such as matrix singularities and determinantal and toric varieties, will also be studied. Recent pioneering results motivate new research directions in this area.
The central theme of the proposal is the study of real and complex singularities of sets, mappings, differential equations, and vector fields. The driving question is the investigation of the structure of various classes of singular objects and their generic perturbations through the development of classification methods and algorithms for singularity recognition. The study of singularity invariants and the topology of associated fibrations is a fundamental part of the proposal, which also aims at applications of the theory, particularly in geometry and dynamical systems.
The Brazilian team is specialized in this research area and has made substantial and pioneering contributions to the study of invariants, applications of singularity theory to the geometry and topology of subvarieties, as well as the qualitative theory of ODEs and bifurcations.
The main goal of the project is to foster interaction between the singularity research activities of the São Carlos team and other centers in Brazil and abroad, promoting the development of the following topics: Classification, Equisingularity, and Invariants; Geometry, Topology of Varieties, and Singular Varieties; Singularities in Differential Geometry; Singularities of Vector Fields. The researchers involved have extensive experience in these areas, and their previous collaborations have already produced fundamental advances in singularity theory and its applications. Interaction among researchers from the various centers is evidenced by the team’s publications.
Grant Period: 2023 – Present
Principal Investigator: Regilene D. S. Oliveira
Funding Agency: CNPq
Key Personnel: Míriam Manoel, Maria Aparecida Soares Ruas, Patrícia Hernandes Baptistelli, Regilene de Lazari Oliveira, Carles Bivià-Ausina, Maria Elenice Rodrigues Hernandes
