Geometric graphs and Li-Yorke systems

• Grant number: 24/04155-3
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Effective date (Start): August 01, 2024
• Effective date (End): July 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Leandro Fiorini Aurichi
• Grantee: Michel Fernandes Gaspar
• Supervisor: Paul Larson
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Research place: Miami University, United States
• Associated to the scholarship: 22/13561-0 - Consistence and independence in definable graph combinatorics, BP.PD

Abstract

The main objective of this research stay is to answer set-theoretic questions about Borel and measurable colorings of graphs relevant to geometry and dynamical systems. The main technique that we may employ is iterated forcing of notions that satisfy Axiom A. If the objectives are achieved, we will have contributed to expanding the frontiers of set theory.