CV Lattes
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Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC) (Institutional affiliation from the last research proposal) Birthplace: Argélia
graduation at Diplome d'Etudes Superieures from Universidade de Bab-Ezouar, Argel (1986) and doctorate at Teoria de Singularidades from Universidade de Liverpool (1990). He is currently full professor at Universidade de São Paulo. Has experience in Mathematics, focusing on Theory of the Singularities and Theory of the Catastrophes, acting on the following subjects: differential equations, singularities, singularidades, pairs of foliations and multiplicities. (Source: Lattes Curriculum)
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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 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 …
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 prob…
Our aim is to initiate research on the discrete differential geometry of curves from a singularity theory viewpoint.(AU)
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)…
(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)
| 2 / 2 | Ongoing grants |
| 7 / 7 | Completed research grants |
| 2 / 2 | Ongoing scholarships in Brazil |
| 15 / 12 | Completed scholarships in Brazil |
| 1 / 1 | Completed scholarships abroad |
| 27 / 24 | All research grants and scholarships |
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