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.

## 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.