Negative curvature and the Gromov, Lawson, and Thurston conjecture

• Grant number: 16/05444-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2016
• End date: April 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Carlos Henrique Grossi Ferreira
• Grantee: Gabriel Nogueira Malta
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

We expect the student to dedicate himself to the study of hyperbolic geometry in its various facets, from metric spaces of non-positive curvature (à la Alexandrov) to Hadamard manifolds and riemannian manifolds of negative curvature (pinched or not). To avoid a dangerous and unmotivated 'study by itself,' the project is surrounded by a known and concrete problem in real hyperbolic geometry, the Gromov, Lawson, and Thurston conjecture.