Based on a new decoupling inequality for curves in ℝd, 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).
This video is part of the Institute for Advanced Study‘s Number theory seminar.
