What is the most efficient arrangement of spheres in various dimensions?
Science / Mathematics
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.
