João Carlos Ferreira Costa
CV Lattes
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Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. Instituto de Biociências, Letras e Ciências Exatas (IBILCE) (Institutional affiliation for the last research proposal) Birthplace: Brazil
graduate at Licenciatura em Matemática from Universidade Estadual Paulista Júlio de Mesquita Filho (1999), master's at Mathematics from Universidade Estadual Paulista Júlio de Mesquita Filho (2002) and ph.d. at Mathematics from Universidade de São Paulo (2005). Has experience in Mathematics, acting on the following subject: Singularity Theory (Source: Lattes Curriculum)
- Invariants of real singularities, pairs of germs and classification problems, AP.R
Abstract
The purpose of this work is to study importanttopics of Singularity theory such as nvariants, classification problem, finiteness theorems, stable maps, pairs of map germs (or divergent diagrams), among others. Such topics are interrelated with other areas of research, such as Differential Geometry, Topology, Dynamical System and Graph Theory. To develop this study, from local point of...
- Characteristic classes and intersection homology, AV.EXT
Abstract
The research project is on the characteristic classes and intersection homology theory. The first subject to be investigated concerns Milnor classes. It is curious that, at the moment, there are few (or none) examples and applications of them. Another point on Milnor classes, is that the Prof. Brasselet gave a conjecture formula for duality of these classes in terms of polar varieties. ...
- Bi-Lipschitz contact equivalence of smooth map-germs, AP.R
Abstract
The goal of this work is to study properties and invariants of bi-Lipchitz contact equivalence of smooth map-germs. This equivalence relation is the Lipschitz version of contact equivalence introduced by J. Mather. Few results exist on this subject in literature. (AU)
- Singularities of smooth function germs, BP.IC
Abstract
The main goal of this work is to study the classification problem of singularities until codimension 5, up to R-equivalence. The contents of the project are based in a introductory course of Singularity Theory, which is not given in a regular course of Mathematics.
- The Gauss-Bonnet theorem, the Euler-Poincare characteristic and applications, BP.IC
Abstract
The main goal of this plan is to study aspects from the geometry and the topology of surfaces based in the beautiful Gauss-Bonnet theorem. In fact, the Gauss Bonnet theorem presents a good relationship between the geometry of the surface (the Gaussian curvature) and the topological aspects of the surface (Euler-Poincare characteristic). Some physical applications will be studied based o...
- Some practical applications in the study of curves and singularities, BP.IC
Abstract
Our goal is to study the local theory of curves (in R2 and R3) introducing a relationship between topics of Differential Geometry and Singularity theory. To help us in this task we will use the Mathematica software. Also we will give some practical applications of our study. (AU)
| 1 / 1 | Ongoing research grants |
| 4 / 2 | Completed research grants |
| 6 / 3 | Completed scholarships in Brazil |
| 11 / 6 | All research grants and scholarships |
| Associated processes | |
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
| Publications | 5 |
| Citations | 12 |
| Cit./Article | 2.4 |
| Data from Web of Science | |
BIRBRAIR, LEV; FERREIRA COSTA, JOAO CARLOS; FERNANDES, ALEXANDRE. Finiteness theorem for topological contact equivalence of map germs. HOKKAIDO MATHEMATICAL JOURNAL, v. 38, n. 3, p. 511-517, AUG 2009. Web of Science Citations: 5.
ALVAREZ, SERGIO; BIRBRAIR, LEV; FERREIRA COSTA, JOAO CARLOS; FERNANDES, ALEXANDRE. Topological K-equivalence of analytic function-germs. Central European Journal of Mathematics, v. 8, n. 2, p. 338-345, APR 2010. Web of Science Citations: 3.
BRASSELET, JEAN-PAUL; CHACHAPOYAS, NANCY; RUAS, MARIA A. S.. Generic sections of essentially isolated determinantal singularities. INTERNATIONAL JOURNAL OF MATHEMATICS, v. 28, n. 11, OCT 2017. Web of Science Citations: 3.
BRASSELET, JEAN-PAUL; CORREA, MAURICIO; LOURENCO, FERNANDO. Residues for flags of holomorphic foliations. ADVANCES IN MATHEMATICS, v. 320, p. 1158-1184, NOV 7 2017. Web of Science Citations: 1.
BRASSELET, JEAN-PAUL; MIWA LIBARDI, ALICE KIMIE; RIZZIOLLI, ELIRIS CRISTINA; SAIA, MARCELO JOSE. Cobordism of maps of locally orientable Witt spaces. PUBLICATIONES MATHEMATICAE-DEBRECEN, v. 94, n. 3-4, p. 299-317, 2019. Web of Science Citations: 0.
(References retrieved automatically from State of São Paulo Research Institutions)
COSTA, João Carlos Ferreira. Formulação por caminhos para problemas de bifurcação Z2 + Z2-equivariantes. . 106f. Dissertação (Mestrado) - Instituto de Biociências, Letras e Ciências Exatas. Universidade Estadual Paulista. São José do Rio Preto.
COSTA, João Carlos Ferreira. Equivalências de contato topológica e bi-Lipschitz de germes de aplicações diferenciáveis. 2005. Tese (Doutorado) – Instituto de Ciências Matemáticas e Computação de São Carlos. Universidade de São Paulo (USP). São Carlos.