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.
The last resort of scoundrels
Patriotism, at least in its usual sense of love of one’s country over others, veneration of the virtue of its people over others, and adoration of its flag, is awful, irrational nonsense.
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 Doors of Crime Perception
Crime is uniquely susceptible to the manipulation of perceptions.
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.
Talk on Counting Curves on Surfaces, September 2018
On 19 September 2018 I gave a talk at the National University of Singapore (NUS) in the Topology and Geometry seminar. The talk was entitled “Counting Curves on Surfaces”.
The algebra and geometry of contact categories, Melbourne July 2018
On Monday July 23 2018 I gave a talk in the Geometry and Topology seminar at the University of Melbourne.
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.