Packing Points in Projective Spaces

Explore the fascinating world of packing points in projective spaces in this 47-minute seminar presented by Dustin Mixon for the Society for Industrial and Applied Mathematics. Delve into a fundamental problem in metric geometry, examining how to arrange a given number of points to maximize minimum distance in compact metric spaces. Trace the historical roots of this question from Newton and Gregory's 1694 dispute to its modern applications in error correction for digital communication. Investigate the state-of-the-art techniques in real and complex projective spaces, including Welsh bounds, orthonormal bases, and semidefinite programming. Discover key open problems and cutting-edge concepts such as the Jasper Prize, Tarski-Seidenberg theorem, and singular tight frames. Gain insights into the Game of Sloanes, contact graphs, and the intriguing connections to Schrödinger's work and emergent features in this comprehensive exploration of applied geometry and algebra.