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 ; 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): 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; + associated scholarships 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)

Scientific publications

(4)

(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. A classification and quantification approach to generate features in soundscape ecology using neural networks. NEURAL COMPUTING & APPLICATIONS, SEP 2021. Web of Science Citations: 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 MAY 2021. Web of Science Citations: 0.

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.

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, DEC 2020. Web of Science Citations: 0.