Explore the intricacies of surface composition and decomposition in R^n through this 44-minute lecture by Robert J Young for the International Mathematical Union. Delve into Lipschitz functions, quantitative nonorientability, and cellular cycles. Discover how to measure and bound nonorientability, and examine the proof for decomposing surfaces in R^n. Investigate the nonembeddability of the Heisenberg group and explore applications with Naor. Gain insights into advanced mathematical concepts and their practical implications in this comprehensive presentation.
Overview
Syllabus
Intro
Motivation
Warm-up Lipschitz functions
How do you decompose a Lipschitz function?
How can we measure nonorientability?
Quantitative nonorientability for cellular cycles
What's the most nonorientable surface?
Nonorientability is bounded by area
Proof: Decomposing surfaces in Rº
Proof: Conclusion
Nonembeddability of the Heisenberg group
Applications with Naor
Taught by
International Mathematical Union
