# Maths and beyond - abstracts for speakers

**10:00--11:00**

**Caroline Series, Indra's Pearls: Geometry and Symmetry**

**ABSTRACT**

This talk is based on the book of the same title by David Mumford, Caroline Series and David Wright, published by Cambridge University Press. Here is an extract from the book jacket:

Felix Klein, one of the great nineteenth-century geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbours, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeating reflections, each simple in itself, but whose interactions produce fractals on the edge of chaos. In the 1980's, the authors embarked on the first computer exploration of Klein's vision, and in doing so, found further extraordinary images of their own.

Illustrated with many pictures, this talk will be an introduction to the mathematics and algorithms behind the fractal pictures explained in the book.

**11:30--12:30
Ian Stewart FRS, All the world's a network**

**ABSTRACT**

Networks are all the rage in today's science. Food webs in ecology, gene transcription networks in biology, the Internet, Google, the London Underground, even the solar system---they all can be viewed as networks.

Recent advances include the idea of a 'small world' network, which explains the famous 'six degrees of separation' between any two people on the planet, and can be seen in the Kevin Bacon game and the mathematicians' Erdos Number.

At Warwick we have studied the dynamics of networks, with special emphasis on the effects of symmetry. Applications include the human visual system, animal movement, and the formation of new species---all included in the talk.

This is an illustrated talk with no formulas and no technical maths. It does include a pig.

Oh, and it does tell you what a network is, too.

**2:00--3:00
Samir Siksek, Beyond Fermat's Last Theorem**

**ABSTRACT**

Wiles' proof of Fermat's Last Theorem is one of the happiest memories of the 20th century. Adaptations of Wiles' ideas enable us to solve not only Fermat's Last Theorem, but many other problems that have fascinated and baffled generations of mathematicians (both professionals and amateurs alike). We take a look at three of these:

(i) Perfect powers in Pascal's triangle.

(ii) Perfect powers in the Fibonacci sequence.

(iii) An equation due to the Indian genius Srinivasa Ramanujan.

**4:00--5:00
David Rand, Systems biology and its mathematical challenges**

**ABSTRACT**

In my lecture I will introduce Systems Biology and discuss some of the problems it is being used to tackle. Then I will discuss some of the mathematical challenges that it poses.