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Daniel Mathews

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symplectic

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

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.

dan 2019-01-272020-06-17 Poplular Maths Articles No Comments Read more

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Recent

  • Ptolemy vs Thurston in Hyperbolic Geometry and Topology, AustMS 2020
  • I got problems – congruence problems
  • From Here to Hensel
  • Return of the Euler-Fermat theorem
  • Topology: The shape of space
  • University forever
  • Sitting out the math wars
  • Not human, but inhabited by humans: writing mathematics
  • A-polynomials, Ptolemy varieties, and Dehn filling, Melbourne June 2020
  • Monash topology talk on Circle packings, Lagrangian Grassmannians, and Scattering Diagrams, April 2020
  • A-polynomials, Ptolemy varieties and Dehn filling
  • AustMS 2019 talk on geometry and physics of circle packings
  • The sensitivity conjecture, induced subgraphs of cubes, and Clifford algebras
  • Talk in Monash discrete mathematics seminar, September 2019
  • “I liked doing what I wasn’t supposed to do”: the life and mathematics of Karen Uhlenbeck
  • Monash topology talk on sensitivity conjecture and Clifford algebras, July 2019
  • Breakthroughs in primary school arithmetic
  • Uniqueness of contact structures and tomography
  • Convex surfaces and tomography
  • Liouville structures and convex surfaces
  • From Liouville geometry to contact geometry
  • Lovely Liouville geometry
  • Emmy had a theorem (mathematical nursery rhyme #2)
  • Golay Golay Golay (Top of the autocorrelation world)
  • The “Australia day” category error
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