I don’t know that I would have anything to say that’s not a platitude, but here are some thoughts.

## Summarise your maths research in one slide, Dan

As part of an upcoming workshop participants were asked to introduce themselves with a one-page slide. I took it as an extreme form of concision: summarise your maths research in one slide, Dan.

## One line Euler line

A fun fact from Euclidean geometry that I thought was a wonderful enough gem to share. It’s standard, but it’s nowhere near any curriculum. I’ll try not to get too snarky about the curriculum.

## I got problems – congruence problems

On 7 December 2020 I gave a (virtual) lecture at the Australian Mathematical Olympiad Committee’s School of Excellence on congruences.

## From Here to Hensel

Here’s a nice maths problem, which I thought it would be fun to discuss. The question doesn’t involve any advanced concepts, but it leads on to a very nice result called Hensel’s lemma.

## Sitting out the math wars

Very few professional mathematicians have been involved in the “math wars”, and when they have, they have not always inspired confidence. I wondered why.

## Liouville structures and convex surfaces

Starting from a Liouville 1-form on a surface, we have been led to 3-dimensional contact geometry, and convex surfaces. We now go in the other direction.

## From Liouville geometry to contact geometry

(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.

## 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.