Embedding and Non-Embedding into the Heisenberg Group

 I'll give a new proof, using Brezis and Nguyen's "distributional Jacobian" of Gromov's non-embedding result for Holder mappings into the Heisenberg Group.  I'll also provide our latest numerical evidence, that a stronger conjecture of Gromov is (probably) false.  The results are from a forthcoming paper with Hajlasz and Schikorra.