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.

Uniqueness of contact structures and tomography

In the previous episode, we asked: if you have a family of foliations on a surface, do they arise as the movie of characteristic foliations of a contact structure? In this episode, we ask how unique these contact structures are.

Convex surfaces and tomography

We’ve seen that convex surfaces have wonderful foliations. We’re now going to consider the relationship between these foliations on surfaces, and contact structures

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.

Complex vector spaces, duals, and duels

Fun with a number, or two, or four. An interesting complex complexity.

Notes on Giroux’s 1991 paper, “Convexite en topologie de contact”

Basic results and the power of convex surfaces.

Notes on Eliashberg’s 1992 paper, “Contact 3-manifolds twenty years since J. Martinet’s work”

Details on the significance of the paper, overtwisted discs, characteristic foliations, and contact structures.

Notes on Eliashberg’s 1989 paper, “Classification of overtwisted contact structures on 3-manifolds”

My attempt to flesh out a few of the details.