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”.
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.
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”.
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.
We’ve seen that convex surfaces have wondeful foliations. We’re now going to consider the relationship between these foliations on surfaces, and contact structures
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.
(Technical) We’re going to take Liouville structures and move them into 3 dimensions, to obtain contact structures.
(Technical) I’d like to show you some very nice geometry, involving some vector fields and differential forms.
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.
On 19 September 2018 I gave a talk at the National University of Singapore (NUS) in the Topology and Geometry seminar. The talk was entitled “Counting Curves on Surfaces”.