(Technical) We’re going to take Liouville structures and move them into 3 dimensions, to obtain contact structures.

## Lovely Liouville geometry

(Technical) I’d like to show you some very nice geometry, involving some vector fields and differential forms.

## Emmy had a theorem (mathematical nursery rhyme #2)

In the spirit of previous work in abstract algebra, I have, erm, adapted another nursery rhyme. To the tune of “Mary had a little lamb”, a discussion of Noether’s theorem.

## Golay Golay Golay (Top of the autocorrelation world)

In 1949, Marcel Golay was thinking about spectrometry. Here’s what happened next…

## Topological entropy: information in the limit of perfect eyesight

Entropy means many different things in different contexts, but there is a wonderful notion of entropy which is purely topological. It only requires a space, and a map on it. It is independent of geometry, or any other arbitrary features — it is a purely intrinsic concept. This notion is known as topological entropy.

## Abstract algebra nursery rhyme

In the spirit of hilariously advanced baby books like Chris Ferrie’s Quantum Physics for Babies, I have taken to incorporating absurdly sophisticated concepts into nursery rhymes.

## Limitless as that space too narrow for its inspirations

In which I recall, via neurologist Oliver Sacks, some musings of Sylvester from 1877 on the limitlessness of mathematics.

## The beauty of mathematics shows itself to patient followers

In September 2018 I gave a talk on the life and mathematics of Maryam Mirzakhani in the School of Physical and Mathematical Sciences colloquium at NTU in Singapore.

## The Brain makes Contact with Contact Geometry

It’s always nice, intellectually, when two apparently unrelated areas collide. I had an experience of this sort recently with an area of mathematics — one very familiar to me — and an ostensibly completely distinct area of science.

## “The beauty of mathematics shows itself to patient followers” — The work of Maryam Mirzakhani

The recent passing of Maryam Mirzakhani came as a shock to many of us in the world of mathematics. Together with Norman Do, we attempt to share something about Mirzakhani’s work.