A mathematical introduction to Yang-Mills theory

• Grant number: 25/09589-4
• 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 - Geometry and Topology
• Principal Investigator: Daniel Gomes Fadel
• Grantee: Victor Luiz Gomes de Oliveira
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 21/04065-6 - BRIDGES: Brazil-France interplays in Gauge Theory, extremal structures and stability, AP.TEM

Abstract

The candidate will study Yang-Mills theory from a mathematically rigorous perspective, with an emphasis on its geometric formulation through the theory of principal bundles and connections. The focus will be on understanding the equations of motion of the theory, culminating in the analysis of explicit solutions known as instantons. This study will also serve as an in-depth introduction to differential geometry and the mathematical structure of gauge theories. (AU)