graduation at Bacharelado em Matemática from Universidade de São Paulo (2002) and doctorate at Mathematics from Universidade de São Paulo (2007). Has experience in Mathematics, acting on the following subjects: teoria das singularidades, singularity theory, euler obstruction of f, topologia and matemática. (Source: Lattes Curriculum)
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.…
In this project we will work with Professor Gaffney two distinct lines of work. One addressing Lipschitz geometry and the other the study of invariants defined in determinantal varieties. (AU)
This project has two strands. In the first one, we propose to investigate the calculation of invariants related to the study of characteristic classes such as the Euler obstruction and Brasselet number (in global and local configurations).In addition to this, the second one proposes to investigate the topology of a differentiable variety through the critical set of applications defined on…
(Only some records are available in English at this moment)
The study of characteristic classes of singular varieties is a current theme and has been widely used in various areas of Science. The purpose of this project is to study Schwartz-MacPherson classes through the means of the Classical Singularity Theory. The central approach of the project is the use of Thom's polynomials, which will provide an appropriate set of tools for the development …
The project aims to introduce the applicant to the topics of Obstruction Theory and its connectios to the theory of Characteristic Classes, as well as to study some applications of these ideas in Singularity Theory and Mathematical Physics. (AU)
The study of characteristic classes of singular varieties is a current theme and has been widely used in several areas of Science. The aim of this project is to study Schwartz-MacPherson strands through the classical Singularity Theory bias. The central approach of the project is the use of Thom's polynomials, which will provide an appropriate tool for the development of issues that gener…
The project aims to present to the candidate the main basic concepts of Algebraic Topology in order to prepare him for the study of Intersection Homology. (AU)
The study of characteristic classes of singular varieties is a current theme and has been widely used in various areas of science. The purpose of this project is to study Schwartz-MacPherson classes through the means of the Classical Singularity Theory. The central approach of the project is the use of Thom's polynomials, which will provide an appropriate set of tools for the development …
The goal of this project is to introduce the applicant to the study of characteristic classes: an important set of invariants used in the study and classification of fibre bundles and smooth manifolds.
(Only some records are available in English at this moment)
The Euler obstruction, defined by MacPherson, is an invariant rised as a tool in the study of characteristic class of singular varieties. Brasselet, Massey, Parameswaran and Seade presented a generalization of this concept, associated with a function with isolated singularity, defined on a singular variety, called the Euler obstruction of f. More recently, Dutertre and Grulha gave another…
In this project we study the topology of analytic map germs. Such germs give rise to a fibration known as Milnor fibration. We will study the topology of Milnor fiber and the link of the singularity, analyzing the cases in which the germ has isolated singularity or not. (AU)
The goal of this projetc is to use the theory of integral closure of modules and multiplicity of pair of modules in the study of equisingularities problems of sets and applications.
(Only some records are available in English at this moment)
| 1 / 1 | Ongoing research grants |
| 9 / 8 | Completed research grants |
| 3 / 3 | Ongoing scholarships in Brazil |
| 17 / 13 | Completed scholarships in Brazil |
| 4 / 4 | Completed scholarships abroad |
| 34 / 29 | 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 | 12 |
| Citations | 28 |
| Cit./Article | 2.3 |
| Data from Web of Science | |
BRASSELET, J. -P.; GRULHA, JR., N. G.; RUAS, M. A. S.. The Euler obstruction and the Chern obstruction. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, v. 42, n. 6, p. 1035-1043, DEC 2010. Web of Science Citations: 2. (09/08774-0)
CISNEROS-MOLINA, JOSE LUIS; SEADE, JOSE; GRULHA, JR., NIVALDO G.. On the topology of real analytic maps. INTERNATIONAL JOURNAL OF MATHEMATICS, v. 25, n. 7, JUN 2014. Web of Science Citations: 4. (11/03185-6, 13/11258-9, 09/08774-0)
DA SILVA, THIAGO F.; GRULHA, JR., NIVALDO G.; PEREIRA, MIRIAM S.. The Bi-Lipschitz Equisingularity of Essentially Isolated Determinantal Singularities. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 49, n. 3, p. 637-645, SEP 2018. Web of Science Citations: 0. (13/22411-2, 17/09620-2)
SANTANA, HELLEN. Brasselet Number and Function-Germs with a One-Dimensional Critical Set. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 52, n. 2, JUN 2020. Web of Science Citations: 0. (15/25191-9, 17/18543-1)
DALBELO, T. M.; GRULHA, JR., N. G.. The Euler obstruction and torus action. Geometriae Dedicata, v. 175, n. 1, p. 373-383, APR 2015. Web of Science Citations: 2. (13/11258-9)
BARBOSA, G. F.; GRULHA, JR., N. G.; SAIA, M. J.. Minimal Whitney stratification and Euler obstruction of discriminants. Geometriae Dedicata, v. 186, n. 1, p. 173-180, FEB 2017. Web of Science Citations: 1. (13/11258-9, 14/00304-2, 15/16746-7)
BONOTTO, EVERALDO M.; GRULHA, JR., NIVALDO G.. LYAPUNOV STABILITY OF CLOSED SETS IN IMPULSIVE SEMIDYNAMICAL SYSTEMS. Electronic Journal of Differential Equations, JUN 8 2010. Web of Science Citations: 0.
GRULHA, JR., NIVALDO DE GOES. THE EULER OBSTRUCTION AND BRUCE-ROBERTS' MILNOR NUMBER. QUARTERLY JOURNAL OF MATHEMATICS, v. 60, n. 3, p. 291-302, SEP 2009. Web of Science Citations: 10.
AGUILAR-CABRERA, HAYDEE. Open-book decompositions of S-5 and real singularities. INTERNATIONAL JOURNAL OF MATHEMATICS, v. 25, n. 9, AUG 2014. Web of Science Citations: 1. (13/10176-9)
DUTERTRE, NICOLAS; GRULHA, JR., NIVALDO G.. Le-Greuel type formula for the Euler obstruction and applications. ADVANCES IN MATHEMATICS, v. 251, p. 127-146, JAN 30 2014. Web of Science Citations: 7. (13/11258-9, 09/08774-0)
GRULHA JR, N. G.; MARTINS, R. S.. Results on Milnor Fibrations for Mixed Polynomials with Non-isolated Singularities. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 52, n. 2, MAR 2020. Web of Science Citations: 1. (13/22718-0, 17/09620-2, 15/19721-5)
GAFFNEY, TERENCE; GRULHA, JR., NIVALDO G.; RUAS, MARIA A. S.. The local Euler obstruction and topology of the stabilization of associated determinantal varieties. MATHEMATISCHE ZEITSCHRIFT, v. 291, n. 3-4, p. 905-930, APR 2019. Web of Science Citations: 0. (14/00304-2, 17/09620-2, 15/16746-7)
(References retrieved automatically from State of São Paulo Research Institutions)
SILVA, Thiago Filipe da. Geometria Bi-Lipschitz invariante. Tese (Doutorado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (13/22411-2)
MARTINS, Rafaella de Souza. Sobre a topologia das fibrações de Milnor. Tese (Doutorado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (13/22718-0)
AMENT, Daiane Alice Henrique. A obstrução de Euler de uma função. Dissertação (Mestrado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (11/02851-2)
RUIZ, Camila Mariana. Do número de Milnor ao número de Milnor de Lê. Dissertação (Mestrado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (09/12266-0)
JÚNIOR, Nivaldo de Góes Grulha. Obstrução de Euler de aplicações analíticas. Tese (Doutorado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (03/13929-6)
DALBELO, Thais Maria. O índice de Poincaré-Hopf e generalizações no caso singular. Dissertação (Mestrado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (09/03201-1)
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