Renato Ferreira de Velloso Vianna
Mathematics
Mathematician Renato Ferreira Vianna always says that a good night’s sleep is the best editor of his ideas and an endless source of insights. He completed his undergraduate studies at the University of Brasilia. He later pursued his master’s and Ph.D. in mathematics at the Institute of Pure and Applied Mathematics and the University of California, Berkeley, respectively. He embarked on post-doctoral fellowships at two esteemed institutions, the Mathematical Sciences Research Institute (MSRI) in the United States and the University of Cambridge, England.
Currently a professor at the Federal University of Rio de Janeiro, Renato is researching simple geometry. A Corinthian soccer team supporter at heart, he also enjoys yoga, meditation, and skiing whenever he gets the opportunity to travel. He shares his life and home with his partner Aline and their two cats, Podrick and Brandon.
Projects
Symplectic geometry is rooted in the physical theory known as Hamiltonian mechanics. This relationship with physics has led to the mathematical concept of mirror symmetry, influenced by physical concepts in string theory. This concept bridges two distinct mathematical fields: algebraic geometry and symplectic geometry. Within this relationship, Lagrangian subvarieties serve as the core objects in the structure on the symplectic aspect. Weinstein’s credo that “everything is a Lagrangian subvariety,” underscores their significance, suggesting that all objects and constructions in symplectic geometry should be expressed as Lagrangian subvarieties.” Our project aims to explore the behavior of these Lagrangians in families, known as Lagrangian fibrations, their connections with Gromov-Witten theory, and the ambitious task of classifying them within a specific space.
