Colloquium Math Dept ULB : Stefaan Vaes (KUL) : The Kadison-Singer problem

Friday 9 Dec 2016, 16:30 → 17:30 Europe/Brussels

NO Building, 5th floor, Campus Plaine (ULB-Salle Solvay)

The Kadison-Singer problem originally is a question about maximal abelian subalgebras of $B(H)$, the bounded operators on a Hilbert space. It turned out to be equivalent to several famous questions throughout mathematics. A particularly innocent looking equivalent statement is the following one on $n \times n$ matrices $A$ with zeros on the diagonal: can we make a block decomposition of $A$ such that all diagonal blocks have small norm, and with the number of blocks independent of $n$? In 2013, the Kadison-Singer problem was solved by Marcus, Spielman and Srivastava, using totally unexpected methods. I will explain the original problem, some of its reformulations, the solution of Marcus-Spielman-Srivastava, and a much more general conjecture for maximal abelian subalgebras of arbitrary von Neumann algebras, as proposed in a joint work with Sorin Popa.