April 26, 2012. Yan V. Fyodorov (Queen Mary, University of London). Freezing Transition: from 1/f landscapes to Characteristic Polynomials of Random Matrices and the Riemann zeta-function.

In the talk (based on a joint work with G.Hiary and J.Keating; arXiv:1202.4713) I will argue that the freezing transition scenario, previously conjectured to take place in the statistical mechanics of 1/f-noise random energy models, governs, after reinterpretation, the value distribution of the maximum of the modulus of the characteristic polynomials of large random unitary (CUE) matrices. I then conjecture that the results extend to the large values taken by the Riemann zeta-function over stretches of the critical line s=1/2+it of constant length, and present the results of numerical computations of the large values of ζ(1/2+it). The main purpose is to draw attention to possible connections between the statistical mechanics of random energy landscapes, random matrix theory, and the theory of the Riemann zeta function.

List of talks at previous sessions of the seminar.