This week John and I have been at the annual meeting of the Australian Mathematical Society at the University of Queensland in Brisbane. The conference seems to be getting bigger and better every year with 11 plenaries and over 320 participants this year. The conference also included a teachers afternoon which had at least an additional 60 participants. Congratulations to the organisers for organizing a great 4 days.

John was one of the organisers of the Combinatorics special session. I spent my time jumping between those talks and the Algebra and Number Theory special session. I also made one trip to the Mathematical physics session.

Highlights included

• Michael Hopkins’s plenary lecture on his recent result with Hall and Ravenel determining that a smooth, stably framed manifold with Kervaire invariant 1 has dimension 2,6,14,30,62 or 126. Apparently it had previously been believed that any dimension of the form ${2^n-2}$ was possible. This is related to the existence of manifolds that are homeomorphic but not diffeomorphic to an ${n}$-sphere, so called `exotic spheres’. Despite the fact that I know very little algebraic topology I felt that I was able to follow what was going on for most of the talk, which is exactly want you want from a plenary.
• Ben Green’s plenary talk on approximate groups. This was another good plenary lecture. Approximate groups (like quantum groups) are not groups. A ${k}$– approximate group is a finite subset ${A}$ of some ambient group such that ${A^2}$ is covered by ${k}$ translates of ${A}$. It is believed that any approximate group is “roughly equivalent” to some approximate group B contained in some subgroup ${N_1}$ of ${G}$ and containing some normal subgroup ${N_2}$ of ${N_1}$ such that ${N_1/N_2}$ is nilpotent.
• Kate Smith-Miles from Monash gave a very good overview of her work in her acceptance talk for the AustMS medal.
• Jon Borwein gave a very good public lecture on The life of ${\pi}$, that looked at its history and the many attempts at calculating ${\pi}$ to more and more decimal places.
• James Borger’s plenary outlining the links between arithmetic and algebraic geometry as well as ${\Lambda}$-structures on absolute varieties.

John and I both speak in the Combinatorics special session this afternoon with my talk being the very last one of the session. I will speak on our work on regular groups of automorphisms of generalised quadrangles and you can find the slides here.