Lecture notes : The local regularity of soap films after Jean Taylor

The following text is a minor modification of the transparencies that were used in the conference; please excuse the often telegraphic style. The main goal of the series of lectures is a presentation (with some proofs) of Jean Taylor’s celebrated theorem on the regularity of almost minimal sets of dimension 2 in R3, and a few more recent extensions or perspectives. Some of the results presented below are work of, or with T. De Pauw, V. Feuvrier A. Lemenant, and T. Toro. The main references for these lectures are [D4] and [D5] (for the proofs), [D3] (for some of the questions), and the theses [Feu] and [Le].