Georgia Institute of Technology College of Sciences

The Liouville quantum gravity measure is a properly normalized exponential of 2d log-correlated fields, such as the Gaussian free field. It is the volume form for the scaling limit of random planar maps and numerous statistical physics models. I will explain how this random measure naturally appears in random matrix theory either in space time from random matrix dynamics, or in space from the characteristic polynomial of random normal matrices. A 3d log-correlated field also naturally emerges in random matrix theory, from dynamics on non-Hermitian matrices.