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A Symplectic Basis for 3-manifold Triangulations, AustMS 2021

On 8 December 2021 I gave a (virtual) talk in the Topology session of the 2021 meeting of the Australian Mathematical Society.

dan 2021-12-082021-12-28 Research Talks No Comments Read more

General tips for studying mathematics

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

dan 2021-10-092021-10-09 Etc., Poplular Maths Articles No Comments Read more

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

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.

dan 2021-06-142021-06-14 Poplular Maths Articles No Comments Read more

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.

dan 2020-12-072020-12-09 Popular Maths Talks No Comments Read more

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.

dan 2020-12-052020-12-05 Poplular Maths Articles No Comments Read more

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.

dan 2020-08-232020-08-23 Etc., Poplular Maths Articles 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
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Recent

  • A Symplectic Basis for 3-manifold Triangulations, AustMS 2021
  • Five-minute surrealist antiwar exposition of topological data analysis
  • General tips for studying mathematics
  • Summarise your maths research in one slide, Dan
  • One line Euler line
  • 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
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