An introduction to Ricci flow on surfaces

• Grant number: 20/06383-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2020
• End date: July 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Carlos Henrique Grossi Ferreira
• Grantee: Gabriel dos Reis Trindade
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The main goal of the project is to introduce the normalized Ricci flow on compact surfaces. In particular, we expect the student to become acquainted with the technique of evolving metrics on smooth manifolds through partial differential equations and to appreciate the strength of such method (which is a central one in modern geometry). As a final result, the student should present a proof of the Uniformization Theorem for compact surfaces using the Ricci flow (at least in the cases when the average scalar curvature is nonpositive).