Disorder-generated multifractals and random matrices: freezing phenomena and extremes

I will start with discussing the relation between a class of disorder-generated multifractals and logarithmically-correlated random fields and processes. An important example of the latter is provided by the so-called "1/f noise" which, in particular, emerges naturally in studies of characteristic polynomials of CUE matrices. Extending the consideration to GUE setting reveals more processes of that type, in particular a special singular limit of the Fractional Brownian Motion. In the rest of the talk I will attempt to show how to use heuristic insights from Statistical Mechanics of disordered systems to arrive to detailed conjectures about distributions of high and extreme values of logarithmically correlated processes and multifractals, including the absolute maximum of the Riemann zeta-function in intervals of the critical line.