graduation at Licenciatura Em Matemática from Universidade Estadual Paulista Júlio de Mesquita Filho (1970), master's at Mathematics from Universidade de São Paulo (1974) and doctorate at Mathematics from Universidade de São Paulo (1983). Has experience in Mathematics, focusing on Theory of the Singularities and Theory of the Catastrophes, acting on the following subjects: singularidades, invariantes, trivialidade topologica, equacoes binarias and equivalência bi-lipschitz. (Source: Lattes Curriculum)
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Singularity theory has wide applications to several areas of science such as optics, robotic and computer vision, and interacts with several areas of mathematics, among which we highlight the algebraic geometry and algebraic topology, commutative algebra, differential and affine geometry, the qualitative theory of ordinary differential equations, dynamical systems, and bifurcation theory.…
Prof. David Trotman is Full Professor at the Université Aix Marseille, since 1888. Distinguished research in Stratification Theory, his main contribution is on properties of stratification satisfying regularity conditions. His collaboration with the São Carlos Singularity group started in 1991, and his first visit to São Carlos was in 1998, to attend the V Workshop on Real and Complex Sin…
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…
(Only some records are available in English at this moment)
One of the most interesting problems in geometry is the existence and classification of extensions of mappings, whether they are homeomorphisms or diffeomorphisms. A classic result is Alexander's Trick, which says that two homeomorphisms in Bn that are isotopic on the boundary are isotopic. Such isotopies generally do not preserve differential structures, and interesting examples of this …
In this project, we propose to study the topology of complex functions with isolated singularity defined on subsets of C^n through numerical invariants associated to them. We will discuss alternative ways to compute these invariants, using, in particular, the Software SINGULAR.We will use as a basic reference the book Singular points of complex hypersurfaces, by John Milnor. The student a…
Classical differential geometry is the object of study of the undergraduate course in Mathematics. The approach of geometry topics in R3 through the singularity theory allows a very rich study of the geometric properties of curves, families of curves and surfaces, which successfully complements the classical approach. On the other hand, the introduction of the theory of singularities in o…
In this project, we intend to study relationships between the Milnor number of a function germ and the Bruce-Roberts numbers of the function germ with respect to a hypersurface with non-isolated singularity and to obtain information about the logarithmic characteristic varieties. (AU)
(Only some records are available in English at this moment)
In this project, we intend to prove that the logarithmic characteristic variety and its relative version of a hypersurface with nonisolated singularity are Cohen-Macaulay. (AU)
The project proposes the study of determinantal singularities and of one of the main tools in this area: the Tjurina Transform. This is a way of apply the knowlege of Algebraic and Analytic Geometry obtained earlier. The main reference for this will be the article "On determinantal singularities and Tjurina Transform" by Anne Frühbis-Krüger. (AU)
The idea of the project is to acquaint the student with the concept of index of vector fields and 1-forms defined on singular varieties, seeking to understand the different generalizations of the concept for such objects, based on the of the Poincaré-Hopf Index for vector fields on smooth manifolds. The main goal of the project is the investigation of different versions of the Poincaré-Ho…
(Only some records are available in English at this moment)
| 1 / 1 | Ongoing research grants |
| 17 / 13 | Completed research grants |
| 1 / 1 | Ongoing scholarships in Brazil |
| 43 / 21 | Completed scholarships in Brazil |
| 4 / 4 | Completed scholarships abroad |
| 66 / 40 | All research grants and scholarships |
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CV Lattes
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