CV Lattes
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Universidade Federal de São Carlos (UFSCAR). Centro de Ciências Exatas e de Tecnologia (CCET) (Institutional affiliation from the last research proposal) Birthplace: Brazil
graduation at Matemática São Carlos from Universidade de São Paulo (1979), master's at Matemática São Carlos from Universidade de São Paulo (1983) and doctorate at Matemática São Carlos from Universidade de São Paulo (1991). Retired as Full Professor at ICMC-USP, São Carlos. Visiting professor at the Federal University of São Carlos from 2021 to 2023. Currently is a Full Professor in the Mathematics Department at IGCE-São Paulo State University, Rio Claro.His main subject of research is Theory of Singularities and Theory of Catastrophes, acting on the following topics: Singularities of real and complexes germs of maps, topological and geometric invariants, triviality and equisingularity, Sufficiency of jets. Topology of maps defined on manifolds with singularities, isolated or not. Integral closure of ideals and modules, Newton's polyhedra and Newton non-degenerate sets. (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.…
The main theme addressed in the research projects that Professor Jean-Paul has developed with several researchers in the area of Singularities in Brazil is the description of topological and geometric properties of applications between varieties. One of the most used methods to understand these properties is the determination of numeric, algebraic and topological invariants associated wit…
(Only some records are available in English at this moment)
One of the main goals of this project is to present the basic concepts of the theory of Toric Varieties, studying the necessary elements to understand the construction of such varieties, using convex geometry, aiming to understand the combinatory present in these objects. As an application of this theory, we intend to study monomial parameterized surfaces in C^4. (AU)
One of the main goals of this project is to present an important tool of differential topology, which has been deeply used in several areas of mathematics: the topological degree theory. First, we will study some analytical results on $\mathbb{R}^n$, and then we will study the theory of manifolds. Next, we will study the concept of degree, its properties and some of its applications, such…
One of the main goals of this project is to present the basic concepts of Vector Fields theory on Manifolds, studying the necessary elements to understand the definition of the index of a singularity as well as the important results related to this invariant. In particular, we intend to present the Poincaré-Hopf Theorem and approach how such a result connects topological elements to geome…
(Only some records are available in English at this moment)
Kouchnirenko in 1976 shows a formula to compute the Milnor number of isolated singularity germs of functions in terms of the Newton polyhedron of the germ. Bivia-Ausina, Fukui and Saia in 2002 characerized a class of finite codimension ideals in the ring of formal power series which satisfy a Newton non degeneracy condition, moreover they showed how to compute the Hilbert Samuel multiplic…
We study the geometry of immersed surfaces in the 4-affine space, we will characterize these from singularities which appear in the contact of the surfaces with hyperplanes obtained from the height function, since these are affine invariants. Mochida, Romero-Fuster and Ruas described this problem in the Euclidean case and obtained results of the geometry of a surface. We intend to develop…
| 1 / 1 | Ongoing grants |
| 22 / 16 | Completed research grants |
| 21 / 10 | Completed scholarships in Brazil |
| 3 / 2 | Completed scholarships abroad |
| 47 / 29 | All research grants and scholarships |
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