Composing and Decomposing Surfaces in R^n

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.

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