Introductory Study in Ergodic Theory: Formalism and Method in Mathematical Research

• Grant number: 25/08278-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2025
• End date: July 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Cláudia Buttarello Gentile Moussa
• Grantee: João Pedro Rocha Dias
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

This project proposes an introductory path to mathematical research, with an emphasis on conceptual and methodological development through the systematic study of elements from Ergodic Theory. The work will gradually introduce fundamental concepts in real analysis, measure theory, topology, and aspects of dynamical systems, integrating reading, discussion, and mathematical writing. The proposal aims not only to provide the student with a solid mathematical foundation but also to facilitate the transition of an engineering student into the realm of scientific research in mathematics, focusing on a contemporary and stimulating theme with potential for dialogue with various interdisciplinary applications. (AU)