|Support type:||Scholarships in Brazil - Master|
|Effective date (Start):||January 01, 2015|
|Effective date (End):||February 29, 2016|
|Field of knowledge:||Physical Sciences and Mathematics - Mathematics - Geometry and Topology|
|Principal researcher:||Marcos Benevenuto Jardim|
|Grantee:||Alcides de Carvalho Júnior|
|Home Institution:||Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil|
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.