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Notes

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.

dan 2021-09-032021-09-03 Notes, Poplular Maths Articles No Comments Read more

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.

dan 2019-02-282020-06-17 Notes No Comments Read more

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

dan 2019-02-282020-06-17 Notes No Comments Read more

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.

dan 2019-02-052020-06-17 Notes No Comments Read more

From Liouville geometry to contact geometry

The standard contact structure on R^3.

(Technical) We’re going to take Liouville structures and move them into 3 dimensions, to obtain contact structures.

dan 2019-02-032020-06-21 Notes, Poplular Maths Articles No Comments Read more

Lovely Liouville geometry

Lovely Liouville geometry

(Technical) I’d like to show you some very nice geometry, involving some vector fields and differential forms.

dan 2019-02-012020-09-21 Notes, Poplular Maths Articles 2 Comments Read more

Complex vector spaces, duals, and duels

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

dan 2007-12-302020-06-23 Notes No Comments Read more

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

Basic results and the power of convex surfaces.

dan 2007-03-142020-06-23 Notes No Comments Read more

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.

dan 2007-03-062020-06-23 Notes No Comments Read more

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

My attempt to flesh out a few of the details.

dan 2007-03-062020-06-23 Notes No Comments Read more
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Recent research notes

  • Summarise your maths research in one slide, Dan
  • Uniqueness of contact structures and tomography
  • Convex surfaces and tomography
  • Liouville structures and convex surfaces
  • From Liouville geometry to contact geometry
  • Lovely Liouville geometry
  • Complex vector spaces, duals, and duels
  • Notes on Giroux’s 1991 paper, “Convexite en topologie de contact”
  • Notes on Eliashberg’s 1992 paper, “Contact 3-manifolds twenty years since J. Martinet’s work”
  • Notes on Eliashberg’s 1989 paper, “Classification of overtwisted contact structures on 3-manifolds”
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