Efficient Partition Computations for Kadison-Singer Equivalent Problems.

In their seminal work in 2013, Marcus, Spielman and Srivastava showed the existence of the generalized weaver partition (GWP). Their work immediately implies that the Kadison-Singer conjecture is true, but leaves the question of computing the GWP unanswered. In this talk, we develop efficient algorithms for computing the GWP and for solving a number of other equivalent Kadison-Singer problems. Our numerical experimental results suggest that the partitions computed by our algorithms are close to optimal.