Tag - Analysis

Jean Bourgain: Decoupling in harmonic analysis and the Vinogradov mean value theorem

17th December, 2015

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).

Keith Ball: Where Is a Convex Set?

19th September, 2015

This video is of the London Mathematical Society and European Mathematical Society‘s Joint Mathematical Weekend in 2015.

Daniel Spielman: The solution of the Kadison-Singer problem

5th November, 2014

We will explain our recent solution of the Kadison-Singer Problem and the equivalent Bourgain-Tzafriri and Paving Conjectures. We will begin by introducing the method of interlacing families of polynomials and use of barrier function arguments to bound the roots of polynomials. To prove the Paving Conjecture, we introduce the Mixed Characteristic Polynomial of a collection of matrices, and use the theory of Real Stable polynomials and multivariate generalizations of the barrier function arguments to bound their roots.