Stability of Yang-Mills-Higgs fields and the vortex equations in CP^n

• Grant number: 23/07224-3
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate (Direct)
• Start date: January 15, 2024
• End date: May 14, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Henrique Nogueira de Sá Earp
• Grantee: Luiz Henrique Lara dos Santos
• Supervisor: Da Rong Cheng
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of Miami, United States
• Associated to the scholarship: 20/15054-2 - Spectrum of the Laplacian on Hermitian Vector Bundles over Homogeneous Spaces, BP.DD

Abstract

This work intends to generalize a work of Da Rong Cheng, which characterizes the local minimizers of the abelian Yang-Mills-Higgs functional in terms of the so called vortex equations on the 2-sphere and the 2-dimensional torus. Being aware of the existence of a generalization of the vortex equations to Kahler manifolds, our aim is to obtain such a characterization of minimizers when the base manifold is the complex projective space CP^n. (AU)