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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
Principal Investigator:Farid Tari
Grantee:Farid Tari
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Co-Principal Investigators: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 ; Luciana de Fátima Martins ; Luis Fernando de Osório Mello ; Marcelo Escudeiro Hernandes ; Maria Elenice Rodrigues Hernandes ; Míriam Garcia Manoel ; Mostafa Salarinoghabi ; Ronaldo Alves Garcia


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)