On 4 December 2019 I gave a talk in the Topology session of the 2019 Australian Mathematical Society meeting, entitled “Geometry and physics of circle packings”.
The sensitivity conjecture, induced subgraphs of cubes, and Clifford algebras
We give another version of Huang’s proof that an induced subgraph of the n-dimensional cube graph containing over half the vertices has maximal degree at least , which implies the Sensitivity Conjecture. This argument uses Clifford algebras of positive definite signature in a natural way. We also prove a weighted version of the result.
Talk in Monash discrete mathematics seminar, September 2019
On 16 September 2019 I gave a talk in the Monash discrete mathematics seminar. The talk was entitled “The sensitivity conjecture, induced subgraphs of cubes, and Clifford algebras”.
Monash topology talk on sensitivity conjecture and Clifford algebras, July 2019
On 31 July 2019 I gave a talk at Monash University in the topology seminar, entitled “The sensitivity conjecture, induced subgraphs of cubes, and Clifford algebras”.
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.
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
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.
From Liouville geometry to contact geometry
(Technical) We’re going to take Liouville structures and move them into 3 dimensions, to obtain contact structures.
Lovely Liouville geometry
(Technical) I’d like to show you some very nice geometry, involving some vector fields and differential forms.
The beauty of mathematics shows itself to patient followers
In September 2018 I gave a talk on the life and mathematics of Maryam Mirzakhani in the School of Physical and Mathematical Sciences colloquium at NTU in Singapore.