Construction of the moduli space of instantons

• Grant number: 14/18855-5
• Support Opportunities: Scholarships in Brazil - Master
• Start date: January 01, 2015
• End date: February 29, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Alcides de Carvalho Júnior
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Gauge Theory emerged as an important area of mathematicas in the 1980s, after the work of Michael F. Atiyah, Simon K. Donaldson e Nigel J. Hitchin, among others. Since then, it has becaome an important tool for more traditional areas, like differential topology, complex geometry and algebraic geometry. This project will serve as an introduction to research in this area. The student will study the basic concepts and tools in the theory, like connectins and curvature on principal and vector bundles, and some of the main equations considered, like Yang--Mills and Hitchins equations. The final goal will be the understanding the onstruction of the moduli space of instantons on four-dimensional manifolds, including functorial aspects of this construction.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

CARVALHO JÚNIOR, Alcides de. The Seiberg-Witten equations. 2016. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.