Explore isoperimetric inequalities on the Hamming cube near and at the critical exponent 1/2, as well as closely related L1 Poincaré inequalities in this one-hour lecture. Delve into joint research conducted with P. Durcik and P. Ivanisvili, focusing on mathematical concepts and their applications in the context of the Hamming cube. Gain insights into advanced mathematical theories and their implications for isoperimetric and Poincaré inequalities.