11:00 to 11:45 C Hughes ([AIM])Mollified \& amplified moments: Some new theorems \& conjecturesSession: Matrix Ensembles and L-Functions Two of the most important areas in analytic number theory concern counting the number of zeros of zeta functions on and off the line, and in beating subconvexity bounds. Both types of results can be obtained from knowing moments of the zeta function multiplied by a Dirichlet polynomial. In this talk we present an asymptotic formula for the fourth moment of the zeta function multiplied by a Dirichlet polynomial, and conjecture a formula for general moments. INI 1 12:00 to 12:30 H Montgomery ([Michigan])Primes \& pair correlation of zerosSession: Matrix Ensembles and L-Functions After a review of older work on this topic, some new results obtained jointly with Soundararajan will be described. These concern higher moments of the error term for the number of primes in a short interval. INI 1 14:30 to 15:00 A Ivic ([Belgrade])On the moments of Hecke series at central pointsSession: Matrix Ensembles and L-Functions INI 1 15:00 to 15:30 M Jutila ([Turku])The twelth moment of central values of Hecke seriesSession: Matrix Ensembles and L-Functions INI 1 16:00 to 16:45 P Diaconis ([Stanford])Testing random matrix theory vs the zeta zerosSession: Matrix Ensembles and L-Functions I will give a tutorial on methods of testing predictions of random matrix theory on data. There is some nice math (symmetric function theory) and some subtlety (the level repulsions lead to correlated data and need cutting edge tools such as the block bootstrap). This is joint work with Marc Coram. INI 1 17:00 to 17:30 D Bump ([Stanford])Automorphic summation formulae and moments of zetaSession: Matrix Ensembles and L-Functions The strong parallel between conjectural asymptotics of the 2n-th moment of zeta (Conrey, Farmer, Keating, Rubinstein and Snaith) with a constant term'' of an Eisenstein series on GL(2n) will be reviewed. For the second moment, the parallel is explained by the Voronoi-Oppenheim summation formula. For larger n, divisor functions of lattices will be defined and a pleasant new Voronoi-type summation formula will be proved for the lattice divisor functions, making use of Bessel functions associated with the Shalika-Kirillov model of a degenerate principal series representation of GL(2n,R). INI 1 17:30 to 18:00 I Smolyarenko ([Cambridge])Parametric RMT, discrete symmetries, \& cross-correlations between zeros of L-functionsSession: Matrix Ensembles and L-Functions I will describe numerical and analytical results on cross-correlations between zeros of different L-functions. By analogy with parametric spectral correlations in random matrix theory and in dynamical systems, these cross-correlations can be used to establish the concept of a "distance" in the space of (conjectural) generalised Riemann operators, and to gain some insight into their overall structure. INI 1 18:45 to 19:30 Dinner at Wolfson Court (Residents Only)