A Shannon-Kneser-Poulsen Theorem for Geometric Information Theory

Explore a mathematical lecture examining the relationship between geometric principles and information theory through the lens of the Kneser-Poulsen conjecture and its applications to communication channels. Delve into two fundamental questions: whether the volume of unified balls decreases when centers move closer together, and if communication quality diminishes over an additive white Gaussian noise channel when transmitters are brought closer. Learn how the speaker frames and proves an entropic formulation of the Kneser-Poulsen conjecture, leveraging analogies between convex geometry and information theory. Discover how this theoretical framework provides definitive insights into communication channel behavior while the original geometric conjecture remains an open question. Based on collaborative research with Dongbin Li, this 48-minute presentation from the Hausdorff Center for Mathematics bridges abstract mathematical concepts with practical applications in information transmission.