Logarithmically Correlated Fields from Random Matrices

In 2012, Fyodorov, Hiary, and Keating discovered a new connection between random matrices and extremal values of logarithmically correlated fields, such as branching Brownian motion and the 2D Gaussian Free Field.
In particular, they conjectured that extreme statistics of random characteristic polynomials of unitary matrices belong to the universality class of logarithmically correlated fields, which was first identified by Bramson in his seminal work on branching Brownian motion.
I will review several contributions in proving this connection and present some new recent works establishing new connections of characteristic polynomials of non-Hermitian matrices and two- and three-dimensional logarithmically correlated fields.