Study on Sparsification: In Theory and Practice

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, we revisit and study the problem in its original formulation and also explore its transition to a result with wide ranging applications. The objective of this study is to see how the notion of ’sparsification’ transcended various fields and how this notion led to resolution of the problem. Besides, in this study, we also take a look at the impact and implications of the resolution in various scientific fields.