A New Paradigm for Mathematics and Physics - Diffusion Symmetry

Explore a new paradigm for understanding symmetry in mathematics and physics through the lens of diffusion symmetry. Delve into a 48-minute lecture that challenges the traditional group theory approach by examining the diffusion of gas in an empty room. Discover how this alternative perspective unifies concepts from character theory, strongly regular graphs, von Neumann algebras, Hecke algebras, Lie group representation theory, cyclotomy, and conformal field theory. Learn about hypergroups and fusion rule algebra, and how they offer a rich alternative to the usual "transformational" approach. Gain insights into the interplay between diffusion symmetry and group theory, particularly in relation to duality and character tables. Explore how this new paradigm simplifies non-commutative harmonic analysis into commutative harmonic analysis in certain situations. Follow along as the lecture progresses through topics such as types of symmetries, gas diffusion experiments, historical context, initial examples, multiset of neighbors, fusion rule algebra, probabilistic variants, and character tables of alternating groups and hypergroups.

Intro
Overview
Two Types of Symmetries
Though Experiment: Gas Diffusion
History of the Subject
An Initial Example
The Multiset of Neighbors
Fusion Rule Algebra
The Probabilistic Variant
Character Table of an Alternating Group
Character Table of a Hypergroup