## Breadcrumb

## Number theory

Commonly referred to as the queen of mathematics, number theory is an ancient branch of pure mathematics that deals with properties of the integers. Bringing together tools from analysis, geometry and algebra, the work that takes place in Bristol centres largely upon Diophantine equations and prime numbers.

Despite its blue-sky nature, number theory research has fundamental application in modern life and the group collaborates closely with other disciplines, such as quantum physics and computational science. As an example of this, the subject of algorithmic number theory is closely linked to cryptography, the basis of secure e-commerce and internet communications.

The number theory group shares a seminar programme with the Heilbronn institute (named after the famous number theorist Hans Heilbronn who was a professor at Bristol), and organises a number of advanced lecture courses throughout the year. See the Events section for further details.

#### Research Highlight on Random Matrix theory

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 predicting all of the moments of the Riemann zeta function.