turkmath.org

On the 28th of June 2013, an important event happened in the mathematical community: A. Marcus, D.A. Spielman, and N. Srivastava posted a manuscript on arXiv that contained a proof of the Kadison-Singer Problem, a famous and very important problem in operator algebras that was posed in 1959 by R. Kadison and I. Singer. The importance of the Kadison-Singer Problem relies not only on the fact that it clarifies some important aspects in the foundation of Quantum Physics, but also on the fact that, during the 54 years of efforts of proving it, many other problems in operator theory, Banach space theory, harmonic analysis, and signal processing proved to be equivalent with it. In this seminar talk we will explain what the Kadison-Singer problem is and where is it coming from, and then present some of its reductions and the main result of Marcus-Spielman-Srivastava that finally proved it.