Ruediger Urbvanke Spatial-coupling: An Algorithm and a Proof Technique Abstract: Spatial coupling is an idea that has its root in physics. The key words there are nucleation, crystallization, and metabstability. If we apply this idea to locally-tree like structures, together with low-complexity message-passing algorithms, the resulting systems show optimal performance. I will talk about two applications. First, error correcting codes such as those that you find in your cell phones. (called LDPC codes or turbo codes). Second, how we can apply this idea not only algorithmically, but also as a proof technique to determine the location of thresholds.