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”.
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.
“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.
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”.
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, and it was known to the ancient Babylonians. But it’s
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 wondeful 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.