Sparsification: In Theory and Practice

Abstract

The Kadison-Singer problem has variants in different branches of the sciences and one of these variants was proved in 2013. Based on the idea of "sparsification" and with its origins in quantum physics, at the sixtieth anniversary of the problem, we revisit the problem in its original formulation and also explore its transition to a result with wide ranging applications. We also describe how the notion of "sparsification" transcended various fields and how this notion led to resolution of the problem.