(Technical) We’re going to take Liouville structures and move them into 3 dimensions, to obtain contact structures.
From Liouville geometry to contact geometry
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, not surprisingly, 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 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. On the
“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.
Tutte meets Homfly
I’ll tell you about some extremely clever methods to tell graphs and knots apart, involving polynomials: the Tutte and HOMFLY polynomials. And they’re closely related.