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Singularity theory and its applications to differential geometry, differential equations and computer vision

Grant number: 19/07316-0
Support type:Research Projects - Thematic Grants
Duration: August 01, 2019 - July 31, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Farid Tari
Grantee:Farid Tari
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Pesquisadores principais:
João Do Espirito Santo Batista Neto ; João Nivaldo Tomazella ; Moacir Antonelli Ponti
Assoc. researchers:Ana Claudia Nabarro ; Antonio Castelo Filho ; Bruna Orefice Okamoto ; Daiane Alice Henrique Ament ; Débora Lopes da Silva ; Douglas Hilário da Cruz ; Fabio Scalco Dias ; Francisco Braun ; James William Bruce ; Jaume Llibre Salo ; Jorge Luiz Deolindo Silva ; Leandro Nery de Oliveira ; Luciana de Fátima Martins ; Luis Fernando de Osório Mello ; Marcelo Escudeiro Hernandes ; Maria Elenice Rodrigues Hernandes ; Míriam Garcia Manoel ; Mostafa Salarinoghabi ; Ronaldo Alves Garcia
Associated scholarship(s):22/10370-9 - On the geometry of singular surfaces, BP.PD
22/10661-3 - Discrete differential geometry from a singularity theory view point, BP.IC
22/06325-8 - Geometric deformations of singularities, BP.PD
+ associated scholarships 22/00133-0 - Geometric bifurcations of singular plane curves, BP.MS
22/01501-2 - Algebraic theory of graphs and neural networks, BP.IC
21/08895-3 - Qualitative theory of differential equations in the plane: topological classification results, BP.MS
21/02932-4 - On k-folding map-germs and hidden symmetries of curves in the Euclidean plane, BP.MS
21/03830-0 - Deep multi-domain representations for analyzing social media posts, BP.IC
21/02923-5 - Discrete differential geometry of plane curves from a singularity theory viewpoint, BP.IC
20/16475-1 - Mapping representations between different domains and subspaces using geometric deep learning, BP.IC
20/10888-2 - Equisingularity of families of surfaces with non-isolated singularities, BP.PD
20/07224-5 - Image curves reconstruction by means of robust features, BP.IC
20/04143-4 - Dynamics of piecewise smooth functions on the interval, BP.IC
19/19714-0 - Apparent contour of surfaces in R3 and extensions of Koenderink's formula, BP.MS - associated scholarships

Abstract

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 singularity theory proper, and the other three consider applications of this theory to differential geometry, differential equations, computer vision and image analysis. The project will continue the work of the team in these area of research and will start two new lines of research on the study of vector fields from an infinitesimal point of view and recognition of images using a geometric approach. The problems are challenging, ambitious and innovative, both from a theoretical point of view and applications. The team, formed by internationally renowned researchers and with its extensive and varied experience, is well prepared to face the challenges of the project. It is worth emphasising that a part of the project is multi-disciplinary an envolves mathematicians as well as computer scientists. In addition to the expected scientific results, the team will contribute to the training of human resources through the supervision of undergraduate, doctoral and post-doctoral students, and dissemination of scientific knowledge. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (11)
(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)
DIAS, FABIO FELIX; PONTI, MOACIR ANTONELLI; MINGHIM, ROSANE. classification and quantification approach to generate features in soundscape ecology using neural network. NEURAL COMPUTING & APPLICATIONS, v. 34, n. 3, SI, . (19/07316-0)
CASTELO, SONIA; PONTI, MOACIR; MINGHIM, ROSANE. A Visual Mining Approach to Improved Multiple- Instance Learning. ALGORITHMS, v. 14, n. 12, . (19/07316-0, 13/25055-2)
OLIVEIRA DE RESENDE, DAMARES CRYSTINA; PONTI, MOACIR ANTONELLI. obust image features for classification and zero-shot tasks by merging visual and semantic attribute. NEURAL COMPUTING & APPLICATIONS, v. 34, n. 6, . (18/22482-0, 19/07316-0)
DIAS, FABIO SCALCO; MELLO, LUIS FERNANDO. Polynomial Vector Fields on Algebraic Surfaces of Revolution. Results in Mathematics, v. 76, n. 1, . (19/07316-0)
DIAS, FABIO SCALCO; RIBEIRO, RONISIO MOISES; VALLS, CLAUDIA. Global Phase Portraits for the Kukles Systems of Degree 3 with Z(2)-Reversible Symmetries. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 31, n. 06, . (19/07316-0)
BRAUN, FRANCISCO; GONCALVES DIAS, LUIS RENATO; SANTOS, JEAN VENATO. ON GLOBAL INVERTIBILITY OF SEMI-ALGEBRAIC LOCAL DIFFEOMORPHISMS. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 58, n. 2, p. 713-730, . (17/00136-0, 19/07316-0)
MANOEL, MIRIAM; OLIVEIRA, LEANDRO N.. EQUIVARIANT MAPPINGS AND INVARIANT SETS ON MINKOWSKI SPACE. Colloquium Mathematicum, v. 167, n. 1, . (19/07316-0)
IZUMIYA, SHYUICHI; NABARRO, ANA CLAUDIA; SACRAMENTO, ANDREA DE JESUS. CURVES IN A SPACELIKE HYPERSURFACE IN MINKOWSKI SPACE-TIME. OSAKA JOURNAL OF MATHEMATICS, v. 58, n. 4, p. 947-966, . (19/07316-0, 16/19139-7)
LIMA-PEREIRA, B. K.; NUNO-BALLESTEROS, J. J.; OREFICE-OKAMOTO, B.; TOMAZELLA, J. N.. THE RELATIVE BRUCE-ROBERTS NUMBER OF A FUNCTION ON A HYPERSURFACE. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 64, n. 3, p. 662-674, . (19/07316-0)
CASTELO, ANTONIO; BUENO, LUCAS MOUTINHO; GAMEIRO, MARCIO. A combinatorial marching hypercubes algorithm. COMPUTERS & GRAPHICS-UK, v. 102, p. 67-77, . (13/07375-0, 19/06249-7, 19/07316-0, 17/25631-4)
DOS SANTOS, FERNANDO P.; ZOR, CEMRE; KITTLER, JOSEF; PONTI, MOACIR A.. Learning image features with fewer labels using a semi-supervised deep convolutional network. NEURAL NETWORKS, v. 132, p. 131-143, . (19/07316-0, 18/22482-0)

Please report errors in scientific publications list by writing to: cdi@fapesp.br.