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Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME) (Institutional affiliation from the last research proposal) Birthplace: Colômbia
Fabricio Valencia Quintero in research grants and scholarships supported by FAPESP.
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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…
In this project we propose a generalization of classical Morse theory to the setting of Lie groupoids. This offers a unified approach to study equivariant Morse theory and Morse theory on orbifolds. As applications, we will investigate the existence of closed geodesics on Riemannian stacks and cohomological properties of symplectic reductions of Hamiltonian Lie 2-group actions on étale sy…
In this project we propose to start the study of the problem concerning the existence of closed geodesics on a Riemannian stack. For that purpose we plan to study the properties of the energy functional defined over stacky curves as well as a proper notion of Jacobi field along stacky geodesics on the Riemannian stack. This proposal is framed in the Fapesp project "Morse theory on Lie gro…
| 1 / 1 | Ongoing scholarships in Brazil |
| 1 / 1 | Completed scholarships in Brazil |
| 1 / 1 | Completed scholarships abroad |
| 3 / 3 | All Scholarships |
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