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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

Return of the Euler-Fermat theorem

A long long time ago, in a galaxy far away, I wrote up an account of the Euler-Fermat theorem for school students.

dan 2020-12-022020-12-02 Poplular Maths Articles No Comments Read more

Topology: The shape of space

Monash Open Day in 2020 was a purely online affair, thanks to COVID. I recorded a video talking about Topology: The Shape of Space.

dan 2020-08-302020-11-30 Popular Maths Talks 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

Not human, but inhabited by humans: writing mathematics

Mathematics can be written in many ways. One approach, very popular with professional pure mathematicians, is to write as little as possible. But there should also be others.

dan 2020-08-172020-08-17 Poplular Maths Articles No Comments Read more

“I liked doing what I wasn’t supposed to do”: the life and mathematics of Karen Uhlenbeck

In September 2019 I gave a talk about the life and some of the mathematics of Karen Uhlenbeck, the great mathematician and first woman to win an Abel Prize. This was a Monash LunchMaths seminar.

dan 2019-09-112020-06-17 Popular Maths Talks No Comments Read more

Breakthroughs in primary school arithmetic

Humans have known how to multiply natural numbers for a long time. In primary school you learn how to multiply numbers using an algorithm which is often called long multiplication, but it’s called “long” for a reason! Recently, a new paper purports to give an algorithm to multiply faster.

dan 2019-05-052020-06-17 Poplular Maths Articles 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

  • 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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