**The Distribution of Primes** (Tuesday 27th October 2009 - Windsor Auditorium, 6pm)

"The primes are the atoms of arithmetic, the building blocks from which all other numbers are constructed. Yet there are still many fundamental questions about the distribution of the primes that we cannot answer. For example, we know that there are infinitely many primes, but we do not know whether there are a finite or infinite number of pairs of primes differing by two (or by any other even number); and one of the central problems in modern mathematics - the Riemann Hypothesis (whose 150th anniversary we mark this year) - concerns the number of primes in large intervals. Interestingly, there are probabilistic models of the primes for which these fundamental questions can be resolved. I shall review some things that we know and many things that we do not know about the primes and these probabilistic pseudoprimes."

**Jon Keating **is Professor of Mathematical Physics at the University of Bristol, where he is also currently the Dean of Science. He did his PhD under the supervision of Professor Sir Michael Berry in the late 1980s. He held an EPSRC Senior Research Fellowship from 2004 until 2009 and was elected a Fellow of the Royal Society in 2009. His research interests centre on the quantum mechanics of chaotic systems, random matrices, and number theory.