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: Brazil
Undergraduate degree at Bachelor in Mathematics from Universidade Federal da Bahia (1996), Master degree at Mathematics from Universidade Federal do Ceará (1999), Ph.D. at Mathematics from Universidade de São Paulo (2002) and Associate Professor from Universidade de São Paulo (2011). He has experience in Mathematics focusing on pure Mathematics, acting on the following subjects: real and complex milnor fibrations, stratification theory, geometry and topology of singularities, differential and algebraic topology, algebraic geometry. (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.…
Singularity Theory is a branch of mathematics that studies sets, mappings, and the relationship among them. Roughly speaking, singularists are concerned with studying those points in a set where, in a certain sense, a mathematical model does not behave as ``expected". Due to its fundamental importance in characterizing the behavior of sets, basic notions of singularities are already taug…
This project contains two main directions which are connected with each other and will be developed simultaneously, using techniques and tools from differential topology, algebraic topology and singularity theory; to now, the existence of fibered structures in the presence of singularities, and a classification of real algebraic sets according to the Akbulut-King program} introduced in th…
(Only some records are available in English at this moment)
The aim of this project is to develop an algebraic-geometric studies on the structures of complex numbers, hypercomplex numbers, e use their main techniques to model and solve classical problems of Plane Euclidean geometry, spacial geometry, and on higher dimensional spaces involving some symmetries.
A'Campo introduced the family of divide links and showed that all (complex) algebraic links are divide links, and all divide links are fibered. As it is well known, however, that not all fibered links aredivide links, for instance, the figure-eight knot is not a dividelink. It is not known yet how big the set of divide links is inside the set of fibered links. On the other hand, the Bened…
In this project we intend to develop a geometric study of the quaternary numbers aiming to develop their main relationships with matrix groups of rotations and their applications in symmetry problems in R^3 and rotations problems of 3D-images.
In this project we will develop a study of differential forms and its main applications in the geometric/topological studies of differentiable manifolds based on the references "From Calculus to Cohomology" by Madsen and Tornehave, and "Differential Forms and Applications "by Manfredo P. do Carmo. In these references the authors have introduced the main techniques and theorems in aelement…
In this project we study the bifurcation locus of a polinomial function f:R^2 -- R and other phenomena at infinity as polar curves, bifurcation locus in families of curves, fibration structures at infinity, curvature of the fibres at infinity, Gauss-Bonnet defect and Poincaré-Hopf type formula. (AU)
In this project we aim to introduce the student on basics tools of algebraic geometry throughout the studies of singular curves in the complex affine and projective spaces. Even though the project is focused in the complex case, we will be using examples from real setting to contrast with the complex ones. (AU)
(Only some records are available in English at this moment)
In this project we study the bifurcation locus of a polinomial function $ f : R^2 \to R$ and other phenomena at infinity as polar curves, bifurcation locus in families of curves, fibrations structures at infinity, curvature of fibres of polynomials, Gauss-Bonnet defect and Poincaré-Hopf type formula. (AU)
In this Ph.D project the candidate/fellow will be introduced to Geometric/Topological studies of real and complex Singularities through the interraction between Singularity and Knot Theories.
Taking as starting point some works by J. Milnor, Lê D. Trang, H. Hamm, E. Looijenga, Alexandru Dimca and A. Jacquemard developed during '60, '70, '80 and '90, and more recents works by S. Akbulut ([AK]) and H. King ([HK]) on the topology of real algebraic sets, we intend to introduce a new viewpoint that allow us to find topological invariants associated to real singularities, aiming to…
| 1 / 1 | Ongoing grants |
| 9 / 9 | Completed research grants |
| 3 / 3 | Ongoing scholarships in Brazil |
| 8 / 7 | Completed scholarships in Brazil |
| 4 / 3 | Completed scholarships abroad |
| 25 / 23 | All research grants and scholarships |
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