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Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC) (Institutional affiliation for the last research proposal) Birthplace: Argélia
Farid Tari in research grants and scholarships supported by FAPESP.
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Singularity theory deals with the study of singular varieties and mappings. It is a well established theory and gained wide interestdue to its applications to various areas of science and its interaction with several areas of mathematics. It has applications to, among others, optics, robotics and computer vision. The project has four central research directions: one deals with problems in…
The research project contains problems which are connected with singularity theory, ordinary differential equations, differential geometry, and control theory. There is an interest in studying manifolds with singular metrics both in mathematics and in physics. In our research project, we concentrate on mathematical aspects of singular metrics, in particular, on singularities of geodesic f…
Singularity theory has wide applications to various areas of mathematics and in particular to differential geometry and qualitative theory of differential equations. These branches of mathematics feedback, in turn, into and enrich singularity theory. The aim of this project is to develop methods of classification of real and complex singularities with special attention to invariants and e…
For generic surface M with a generic singular metric, the locus of degeneracy of the metric is a smooth curve on M called the parabolic curve. At each point on the parabolic curve there is a unique isotropic direction (or lightlike direction). Alexey Remizov established the generic behaviour of the geodesic on M at parabolic points where the unique isotropic direction is transverse to the…
(Only some records are available in English at this moment)
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 curv…
The study of the singularities of plane curves (real in our case) is a classic subject. The plane can be endowed with a metric, for example the Euclidean or Minkowski metric. Thus, when deforming the curve, it expected that the geometry concentrated at the singularity (vertices, inflections, bi-tangencies, self-intersections, light-like points in the case of curves in the Minkowski plane…
This project is embedded in a major proposal that includes applications to graph theory to coupled dynamical systems. It provides an introduction to the algebraic theory of graphs applied to dynamical systems, a topic that is rapidly expanding in results and applications during the last twenty years. The studies are directed to the recognition of graphs as a tool in the investigation of n…
(Only some records are available in English at this moment)
Our aim is to initiate the study of discretedifferential geometry of plane curves from a singularity theory viewpoint.
The project has two lines of research in applications of singularity theory to differential geometry and to algebraic geometry. In the first line of research, our purpose is to investigate the Minkowski Symmetry Sets of surfaces in the Minkowski 3-space and to seek Minkowski analogues of Damon's results on skeletal structure. Challenges arise at the locus of points on the surface where th…
The project is about the problem of the existence of a versal deformation theory for germs of curves that take into consideration the deformation of the singularity of the curve as well as the deformation in its geometry (inflections, vertices and lightlike points). The project will also consider invariants associated to the singularity of the curve as well as its geometry and seek relati…
(Only some records are available in English at this moment)
The aim of the project is to seek a theory of deformations of germs of singular varieties which takes into consideration the singularities of the deformed variety together with its extrinsic differential geometry in the Euclidean space where it is embed. (AU)
| 1 / 1 | Ongoing research grants |
| 7 / 7 | Completed research grants |
| 4 / 4 | Ongoing scholarships in Brazil |
| 10 / 7 | Completed scholarships in Brazil |
| 1 / 1 | Completed scholarships abroad |
| 23 / 20 | All research grants and scholarships |
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