Infinite graphs and applications of set-theory

• Grant number: 23/00595-6
• Support Opportunities: Regular Research Grants
• Start date: April 01, 2023
• End date: March 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Leandro Fiorini Aurichi
• Grantee: Leandro Fiorini Aurichi
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The area of graphs is a central area in combinatorics - mainly in finite combinatorics. In the infinite case, infinite combinatorics often gets mixed with set theory and graphs remain an important part. In general, the problems and techniques used in infinite graphs are inspired by their finite versions, but this does not mean that set theory problems and techniques cannot interact. This is the central point of this project: the study of graphs and related problems, from the point of view of people with majority experience in set theory. This inversion seeks new techniques for solving old problems, as well as the development of new concepts and techniques with different inspiration than usual. (AU)

Scientific publications

(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)

AURICHI, LEANDRO FIORINI; REAL, LUCAS SILVA SINZATO. Unfriendly partitions when avoiding vertices of finite degree. JOURNAL OF LOGIC AND COMPUTATION, v. N/A, p. 8-pg., 2023-11-21. (19/22344-0, 23/00595-6, 21/13373-6)

AURICHI, LEANDRO F.; BONANZINGA, MADDALENA; GIACOPELLO, DAVIDE. On some topological games involving networks. Topology and its Applications, v. 351, p. 10-pg., 2024-05-08. (23/00595-6)