This is the second Number Theory seminar on this date.  Please note the special time.  Based on a new decoupling inequality for curves in R^d, we obtain the essentially optimal form of Vinogradov's mean value theorem in all dimensions (the case d=3 is due to T. Wooley). Various consequences will be mentioned and we will also indicate the main elements in the proof (joint work with C. Demeter and L. Guth).