My research areas are geometry (differential geometry, Riemannian manifolds, and minimal submanifolds), analysis (geometric flows and systolic inequalities), and algebra (homogeneous spaces), and they are deeply interconnected. Moreover, my research focuses on $G_2$-structures, with an emphasis on topics such as harmonic structures, the Laplacian coflow on homogeneous spaces and contact Calabi-Yau manifolds, and the modified Laplacian coflow, as detailed in 4 papers and 1 preprint. Additionally, I have worked on the Riemannian geometry of $G_2$-type real flag manifolds, even more the Ricci flow using analyses of dynamical systems, with a related preprint. My project covers various aspects of differential geometry and geometric analysis, including the existence and uniqueness of the Laplacian coflow, constant scalar curvature of $CR$-structures, and short-time existence of some flows.
Previously I obtained my PhD in Mathematics from Campinas univerity. I wrote my thesis under the joint supervision of Henrique Sa Earp.
Orcid: 0000-0002-5227-0219
Email: julieth.p.saavedra@gmail.com