Introduction to compact Riemann surfaces

• Grant number: 24/07094-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2024
• End date: August 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Henrique Nogueira de Sá Earp
• Grantee: Lucca Severino Delboni
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 21/04065-6 - BRIDGES: Brazil-France interplays in Gauge Theory, extremal structures and stability, AP.TEM

Abstract

The project aims to develop an extensive introduction to the theory of compact Riemann surfaces through the study of three fundamental theorems: the Teichmüller Theorem, the Uniformization Theorem, and the Riemann-Roch Theorem. Using Jürgen Jost's book as a reference, Lucca will engage in proving theorems and solving exercises, preparing him for future academic investigations in complex differential geometry. The work plan is divided into four stages focused on different theoretical and practical aspects essential for understanding the topics. Additionally, Lucca will participate in an elective course on Riemann surfaces, consolidating his learning and strengthening his foundation for graduate projects.