Maximizing the Spread of Symmetric Non-Negative Matrices

The spread of a matrix is defined as the diameter of its spectrum. In this talk, we consider the problem of maximizing the spread of a symmetric non-negative matrix with bounded entries and discuss a number of recent results. This optimization problem is closely related to a pair of conjectures in spectral graph theory made by Gregory, Kirkland, and Hershkowitz in 2001, which were recently resolved by Breen, Riasanovsky, Tait, and Urschel. This talk will give a light overview of the approach used in this work, with a strong focus on ideas, many of which can be abstracted to more general matrix optimization problems.