Felipe Gonçalves
Mathematics
Felipe Gonçalves faces an intriguing and complex mathematical challenge: stacking spheres to reveal deep insights into the nature of geometry and optimization in abstract spaces. Although this problem may seem like a mere curiosity, it has profound implications for mathematical theory, particularly in areas such as data communication and error correction.
Graduated in mathematics from the Federal University of Rio de Janeiro, the scientist also has a master’s and doctorate in mathematics from the Institute of Pure and Applied Mathematics. During his doctorate, he was at the University of Texas, United States, and has four postdoctoral stints. Two at IMPA, a period at the University of Alberta, Canada and, finally, at the Rheinische Friedrich-Wilhelms-Universität Bonn, Germany.
Projects
My problem of interest is simple: I give you infinite copies of a multidimensional orange and ask you to stack those oranges in a multidimensional supermarket. The market manager orders you to do this as efficiently as possible; otherwise, you will be fired. My project proposes a new method to solve this problem in low dimensions, such as 4, 5, 6 and 7. Maryna Viazovska won the Fields Medal in 2022 for saving everyone’s job in dimensions 8 and 24. The idea is to impose additional geometric constraints and find a “second best” configuration. Then, show that the space of better-than-second-best configurations is reducible to a finite case analysis using optimization methods such as semidefinite programming. High-dimensional sphere packing has several applications in error-correcting codes and information theory.
