The goal of this STEaLTH Workshop is to provide an exposition on coarse compression and bi-Lipschitz distortion estimates when embedding Heisenberg group into super-reflexive Banach spaces. The material is taken from the paper ``Sharp quantitative nonembeddability of the Heisenberg group into superreflexive Banach spaces'' (Groups Geom. Dyn. 7 (2013), 497–522) by T. Austin, A. Naor, and R. Tessera. Only a very basic knowledge of functional analysis is required to be able to follow the workshop. The proof will be broken into several stand-alone vignette-talks given by Audrey Fovelle (Universidad de Granada), Alain Valette (Université de Neuchâtel), and Florent Baudier (Texas A&M University)