Moments of moments of random matrices and Gaussian multiplicative chaos

There has been a lot of interest in recent years in understanding the multifractality of characteristic polynomials of random matrices. In this talk I shall consider the study of moments of moments from the probabilistic perspective of Gaussian multiplicative chaos, and in particular establish exact asymptotics for the so-called critical-subcritical regime in the context of large Haar-distributed unitary matrices. This is based on a joint work with Jon Keating.