Applications of Algebraic Topology to Combinatorics

• Grant number: 22/13930-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2022
• Status: Discontinued
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Guilherme Oliveira Mota
• Grantee: Victor Manuel Dias Saliba
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This is an undergraduate research project for Victor Manuel Dias Saliba to be carried out under the supervision of Guilherme O. Mota and Y. Kohayakawa at the Institute of Mathematics and Statistics of the U. of São Paulo, from 15 August 2022 to 30 June 2024 (24 months). The main goal of this project is an in-depth study, at undergraduate level, of techniques and problems in different areas of mathematics, especially topology, algebra and combinatorics. This work will involve the study of a mixture of topics from these areas, focusing on applications of algebraic topology to graph theory and combinatorics. At the end of this project, which we plan to extend to the end of the student's undergraduate programme, the student will have had a deeper contact with current lines of research in mathematics, not covered in undergraduate courses, and thus he will be able to start his graduate studies with a strong background.