Random matrix theory
Random matrices arise whenever complex systems are described by linear equations. For example, they are central to the mathematical description of complex quantum systems, such as molecular and nano-electrical networks, telecommunications in complex environments, large computer networks, and string theory.
Bristol has an internationally leading research group developing the fundamentals of random matrix theory and exploring significant new applications, for example to number theory and quantum information theory.
Random matrix and Riemann
Research at Bristol on random matrix theory has provided significant new insights into the behaviour of the Riemann zeta function and other L-functions, which are central to some of pure mathematics' most important unsolved problems – the Riemann Hypothesis, which relates to the distribution of the primes, and the Birch-Swinnerton-Dyer conjecture, which relates to the theory of elliptic curves.
Jon Keating and Nina Snaith at Bristol describe the energy levels in quantum systems with random matrix theory. Using RMT methods they produced a formula for calculating all of the moments of the Riemann zeta function.