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Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC) (Institutional affiliation for the last research proposal) Birthplace: Argélia
Farid Tari in research grants and scholarships supported by FAPESP.
Singularity theory deals with the study of singular varieties and mappings. It is a well established theory and gained wide interestdue to its applications to various areas of science and its interaction with several areas of mathematics. It has applications to, among others, optics, robotics and computer vision. The project has four central research directions: one deals with problems in…
The research project contains problems which are connected with singularity theory, ordinary differential equations, differential geometry, and control theory. There is an interest in studying manifolds with singular metrics both in mathematics and in physics. In our research project, we concentrate on mathematical aspects of singular metrics, in particular, on singularities of geodesic f…
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…
For generic surface M with a generic singular metric, the locus of degeneracy of the metric is a smooth curve on M called the parabolic curve. At each point on the parabolic curve there is a unique isotropic direction (or lightlike direction). Alexey Remizov established the generic behaviour of the geodesic on M at parabolic points where the unique isotropic direction is transverse to the…
(Only some records are available in English at this moment)
The project has two lines of research in applications of singularity theory to differential geometry and to algebraic geometry. In the first line of research, our purpose is to investigate the Minkowski Symmetry Sets of surfaces in the Minkowski 3-space and to seek Minkowski analogues of Damon's results on skeletal structure. Challenges arise at the locus of points on the surface where th…
The project is about the problem of the existence of a versal deformation theory for germs of curves that take into consideration the deformation of the singularity of the curve as well as the deformation in its geometry (inflections, vertices and lightlike points). The project will also consider invariants associated to the singularity of the curve as well as its geometry and seek relati…
The candidate is a student in Electrical Engineering. Functions in complex variables play a key role in modelling and solving problems in engineering. The aim of the project is to help the student understand the basic concepts in complex analysis. The project also contains a more advanced part on hyperbolic polynomials.
(Only some records are available in English at this moment)
The aim of the project is to seek a theory of deformations of germs of singular varieties which takes into consideration the singularities of the deformed variety together with its extrinsic differential geometry in the Euclidean space where it is embed. (AU)
| 1 / 1 | Ongoing research grants |
| 7 / 7 | Completed research grants |
| 9 / 6 | Completed scholarships in Brazil |
| 1 / 1 | Completed scholarships abroad |
| 18 / 15 | 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 | 20 |
| Citations | 39 |
| Cit./Article | 1.9 |
| Data from Web of Science | |
SINHA, RAUL OSET; TARI, FARID. Projections of surfaces in R-4 to R-3 and the geometry of their singular images. REVISTA MATEMATICA IBEROAMERICANA, v. 31, n. 1, p. 33-50, 2015. Web of Science Citations: 9. (10/01501-5, 11/21240-4)
REMIZOV, A. O.. On the local and global properties of geodesics in pseudo-Riemannian metrics. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 39, p. 36-58, APR 2015. Web of Science Citations: 3. (12/03960-2)
CHERTOVSKIH, R. A.; REMIZOV, A. O.. On Pleated Singular Points of First-Order Implicit Differential Equations. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, v. 20, n. 2, p. 197-206, APR 2014. Web of Science Citations: 0. (12/03960-2)
HASEGAWA, MASARU; HONDA, ATSUFUMI; NAOKAWA, KOSUKE; SAJI, KENTARO; UMEHARA, MASAAKI; YAMADA, KOTARO. Intrinsic properties of surfaces with singularities. INTERNATIONAL JOURNAL OF MATHEMATICS, v. 26, n. 4, MAR 2015. Web of Science Citations: 11. (13/02543-1)
GIBLIN, PETER; REEVE, GRAHAM. CENTRE SYMMETRY SETS OF FAMILIES OF PLANE CURVES. DEMONSTRATIO MATHEMATICA, v. 48, n. 2, SI, p. 167-192, JUN 2015. Web of Science Citations: 2. (12/05326-9)
FUKUI, TOSHIZUMI; HASEGAWA, MASARU; NAKAGAWA, KOUICHI. Contact of a regular surface in Euclidean 3-space with cylinders and cubic binary differential equations. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, v. 69, n. 2, p. 819-847, APR 2017. Web of Science Citations: 0. (13/02543-1)
IZUMIYA, SHYUICHI; TARI, FARID. Apparent contours in Minkowski 3-space and first order ordinary differential equations. Nonlinearity, v. 26, n. 4, p. 911-932, APR 2013. Web of Science Citations: 4. (11/21240-4)
BRANDER, DAVID; TARI, FARID. Families of spherical surfaces and harmonic maps. Geometriae Dedicata, v. 201, n. 1, p. 203-225, AUG 2019. Web of Science Citations: 0. (16/02701-4, 14/00304-2)
GUERVILLE-BALLE, BENOIT; VIU-SOS, JUAN. Configurations of points and topology of real line arrangements. MATHEMATISCHE ANNALEN, v. 374, n. 1-2, p. 1-35, JUN 2019. Web of Science Citations: 1. (17/15369-0, 16/14580-7)
DEOLINDO-SILVA, JORGE LUIZ. Cross-Ratio Invariants for Surfaces in 4-Space. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, JUL 2020. Web of Science Citations: 0. (12/00066-9)
DEOLINDO-SILVA, JORGE LUIZ. Cross-Ratio Invariants for Surfaces in 4-Space. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, JUL 2020. Web of Science Citations: 0. (12/00066-9)
DIAS, FABIO SCALCO; TARI, FARID. ON THE GEOMETRY OF THE CROSS-CAP IN MINKOWSKI 3-SPACE AND BINARY DIFFERENTIAL EQUATIONS. TOHOKU MATHEMATICAL JOURNAL, v. 68, n. 2, p. 293-328, JUN 2016. Web of Science Citations: 1. (11/21240-4, 11/01946-0, 14/00304-2)
HASEGAWA, MASARU; HONDA, ATSUFUMI; NAOKAWA, KOSUKE; SAJI, KENTARO; UMEHARA, MASAAKI; YAMADA, KOTARO. Intrinsic properties of surfaces with singularities. INTERNATIONAL JOURNAL OF MATHEMATICS, v. 26, n. 4, MAR 2015. Web of Science Citations: 11. (13/02543-1)
CHERTOVSKIH, R. A.; REMIZOV, A. O.. On Pleated Singular Points of First-Order Implicit Differential Equations. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, v. 20, n. 2, p. 197-206, APR 2014. Web of Science Citations: 0. (12/03960-2)
SINHA, RAUL OSET; TARI, FARID. Projections of surfaces in R-4 to R-3 and the geometry of their singular images. REVISTA MATEMATICA IBEROAMERICANA, v. 31, n. 1, p. 33-50, 2015. Web of Science Citations: 9. (11/21240-4, 10/01501-5)
REMIZOV, A. O.. On the local and global properties of geodesics in pseudo-Riemannian metrics. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 39, p. 36-58, APR 2015. Web of Science Citations: 3. (12/03960-2)
IZUMIYA, SHYUICHI; TARI, FARID. Apparent contours in Minkowski 3-space and first order ordinary differential equations. Nonlinearity, v. 26, n. 4, p. 911-932, APR 2013. Web of Science Citations: 4. (11/21240-4)
HASEGAWA, MASARU; TARI, FARID. On Umbilic Points on Newly Born Surfaces. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 48, n. 4, p. 679-696, DEC 2017. Web of Science Citations: 0. (16/02701-4, 14/00304-2, 13/02543-1)
DIAS, FABIO SCALCO; MELLO, LUIS FERNANDO. Polynomial Vector Fields on Algebraic Surfaces of Revolution. Results in Mathematics, v. 76, n. 1, MAR 2021. Web of Science Citations: 0. (19/07316-0)
REEVE, GRAHAM MARK; TARI, FARID. MINKOWSKI SYMMETRY SETS OF PLANE CURVES. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 60, n. 2, p. 461-480, MAY 2017. Web of Science Citations: 0. (14/00304-2, 12/05326-9)
(References retrieved automatically from State of São Paulo Research Institutions)
NABARRO, Ana Claudia. Sobre a geometria local de hipersuperfícies em R4. Tese (Doutorado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (96/11954-8)
OLIVEIRA, Regilene Delazari dos Santos. Sobre pares de folheações em variedades de dimensão 2. Tese (Doutorado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (97/11735-7)
SILVA, Jorge Luiz Deolindo. Cr-invariantes para superfícies em R^4. Tese (Doutorado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (12/00066-9)