Geometry of algebraic curvature operators

• Grant number: 24/14883-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2024
• End date: November 30, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Gorodski
• Grantee: Fabricio Valencia Quintero
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 22/16097-2 - Modern methods in differential geometry and geometric analysis, AP.TEM

Abstract

This project aims at studying the geometry underlying the space of algebraic curvature operators by describing properties of the critical point orbits of the corresponding curvature potential. The case of the curvature operators of symmetric spaces of inner type is of special interest. We plan to explicitly determine curvature cones defining Ricci flow invariant curvature conditions which can be associated to special geometries. This will allow us to bring new perspectives of classical geometries, offering plenty of new examples, techniques, and applications in both geometry and algebra.