| Speaker: Nicholas Witte Affiliation: Massey University Time: 3:00 pm Friday, 9 June, 2017 Location: PLT1/303-G20 |
| The mystery surrounding the distribution of prime numbers has profoundly deepened through empirical discoveries which have revealed an intimate connection with models possessing a random character - in particular random unitary matrices. This connection has been so successful, one can use these models to accurately conjecture and predict the behaviour of a central object in analytic number theory - the Riemann zeta function. The zeta function is relevant here because it encodes the prime numbers and thus information about their distribution. Number theory is just one of the many applications of these random models and the theory behind them draws many sub-disciplines of mathematics together. Examples include: the combinatorics of random permutations and random growth models; the analysis of integrable, nonlinear differential equations using inverse scattering method tools; the appearance of novel, non-Gaussian universal distributions in statistics incorporating correlations; energy minimising configurations of electro-static charges; and approximation theory. However, all of the number theory results remain conjectures, yet the hope is that in revealing more of the mathematical details behind the theory, we might expect to gain insight into a deeper explanation of why the models work so well. |