As a graduate student in pure mathematics, Renato’s main interests are related to global analysis and differential geometry, particularly applications of analysis techniques to study the geometry and topology of Riemannian and semi-Riemannian manifolds. These areas are also closely related to physics, providing a wide range of theoretical frameworks—from general relativity and fluid mechanics to more modern theories, such as supergravities and braneworld cosmology.
Renato earned his bachelor’s degree from the University of Sao Paulo, Brazil, in 2008. For his master’s thesis at that same university, he extended classic generic properties of nondegeneracy for the Riemannian geodesic flow to the semi-Riemannian case, proving a more general version of the Bumpy Metric Theorem, for (possibly noncompact) semi-Riemannian manifolds.
Now at Notre Dame, he says: “The atmosphere on campus is extremely exciting and is helping me realize my academic goals. Just during my first year at Notre Dame, I managed to finish two preprints that were submitted for peer-reviewed publications as well as completing most of the departmental requirements for coursework and qualification exams. With highly qualified faculty and very active research groups, this is a fantastic environment for young people interested in a scientific career.”