On 20 September 2022 I gave a zoom talk in the Topology seminar at Tsinghua University, Beijing, entitled “A symplectic approach to 3-manifold triangulations and hyperbolic structures”.
Monash topology talk on Symplectic approach to 3-manifold Triangulations, September 2022
On 14 September 2022 I gave a talk (in person!) in the Monash Topology seminar, entitled “A symplectic approach to 3-manifold triangulations and hyperbolic structures”.
“There is always room for a new theory in mathematics”: Maryna Viazovska and her mathematics
In August 2022 I gave a talk about recent Fields medallist Prof Maryna Viazovska and some of her mathematical work. This was a Monash LunchMaths seminar.
A symplectic basis for 3-manifold triangulations
In the 1980s, Neumann and Zagier introduced a symplectic vector space associated to an ideal triangulation of a cusped 3-manifold, such as a knot complement. We give a geometric interpretation for this symplectic structure in terms of the topology of the 3-manifold, via intersections of certain curves on a Heegaard surface. We also give an algorithm to construct curves forming a symplectic basis.
Talk at Knots in Washington 49.75
On 22 April 2022 I gave a (virtual) talk at the 49.75th (!) Knots in Washington conference.
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.
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.
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.
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.
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.