# The Mathematics of Ageing

## Dr David Steinsaltz

Why do humans and many (but not all!) other organisms build up elaborate bodies over the course of months or years or even decades, but are then incapable of maintaining what they have built up, so that they gradually (or in some organisms very rapidly) become weaker and more susceptible to disease and death as they age?

In the half century since evolutionary biologist George Williams formulated this question, there has been quite a lot of progress toward answering this question. Biologists and medical scientists have played an important role, of course, but so have mathematicians and statisticians.

The talk will present a few examples of how this biological question gets transformed into mathematical and statistical questions, and how very concrete questions about the natural world force us to address questions of very abstract mathematics, in areas such as:

- Dynamical systems on general metric spaces
- Dynamic programming
- Asymptotics of products of random matrices
- Eigenvalues of self-adjoint differential operators

It is not assumed that any of these topics are already familiar to the audience.