# 2013-2014 Baylor Lecture Series in Mathematics

## Jon Keating

Professor Jon Keating, the Henry Overton Wills Professor of Mathematics and Dean of Science at Bristol University(England), was the seventh speaker in the annual Baylor Lecture Series in Mathematics when he visited Baylor University from October 30-November 2.

Dr. Keating, a Fellow of the Royal Society, gave two lectures during his visit. His public lecture, suitable for a general audience, was given on Thursday, October 31 at 4:00 pm in BSB D10; the title of this lecture was "*Primes, Quantum Mechanics, Random Matrices and the Riemann Hypothesis*". His second lecture was given in SR 344; the title of this lecture was "*Primes, Polynomials and Random Matrices*".

Jon earned First Class Honours in obtaining his B.S. degree in Physics from Oxford in 1985. Subsequently, he earned his Ph.D. in Physics from Bristol University in 1989 under the supervision of Sir Michael Berry. He has been at Bristol University since 1995 and was made a Professor of Mathematical Physics there in 1997. He was Head of the department from 2001-2004; more recently, he has been Dean of Science at Bristol since 2009.

Dr. Keating has earned several honors throughout his professional career, including being named a Hewlett-Packard BRIMS Research Fellow (1995-2001) and an EPSRC Senior Research Fellow (2004-2009). He was made a Fellow of the Royal Society in 2009 and won the Frölich Prize in 2010. He is an editor of several mathematics and physics journals and is co Editor-in-Chief of the journal *Nonlinearity*. In addition, he has given several plenary lectures at major mathematical physics conferences throughout the world.

The titles, and abstracts, for his two lectures are:

*Thursday, October 31, 2013 at 4:00 pm - D109 (Baylor Sciences Building)*

### The Primes, Quantum Mechanics, Random Matrices and the Riemann Hypothesis

**Abstract**: I will discuss one of the central problems in mathematics - the Riemann Hypothesis - which is related to the distribution of the prime numbers. In particular, I will describe highly speculative ideas which relate this problem to quantum mechanics. This has led to several new insights concerning long-standing statistical questions that arise in the theory of the primes, where mathematical physics plays a surprising role.

*Friday, November 1, 2013 at 4:00 pm - MMSci 301*

### Primes, Polynomials and Random Matrices

**Abstract**: The Prime Number Theorem tells us roughly how many primes lie in a given long interval. We have much less knowledge of how many primes lie in short intervals, and this is the subject of a deep conjecture due to Goldston and Montgomery. Likewise, we also have much less knowledge of how many primes lie in different arithmetic progressions. This is the subject of an important conjecture due to Hooley. I will discuss the analogues of these conjectures for polynomials defined over function fields and explain how they can be proved using the theory of random matrices.