The Drunkard's Walk and UHF Algebra - From Hilbert Spaces to Supernatural Numbers

Explore the intricacies of UHF algebra in this 1-hour 9-minute lecture delivered by Bhishan Jacelon from the Czech Academy of Sciences in Prague. Delve into a comprehensive overview of key concepts, starting with an introduction to helmet spaces and Hilbert spaces. Examine the fundamentals of UHF algebra, star homomorphisms, and compact operators. Investigate the inductive limit and universal property of UHF algebras. Discover the fascinating concept of supernatural numbers and their relevance to the field. Follow along as Jacelon presents a detailed proof and concludes with an exploration of the drunkard's walk in relation to UHF algebra. Gain valuable insights into this advanced mathematical topic through clear explanations and examples provided throughout the lecture.

Introduction
Helmet Spaces
Hilbert Spaces
UHF Algebra
Star Homomorphisms
Examples
Compact Operators
Inductive Limit
Universal Property
UHF
Supernatural Number
Proof
The Supernatural Number
Drunkard Walk