We re-prove the classification of flexible octahedra, obtained by Bricard at beginning XX century, means combinatorial objects satisfying some elementary rules. The explanations these rules rely on use a well-known creation modern algebraic geometry, moduli space stable rational curves with marked points, for description configurations graphs sphere. Once one accepts and rules, becomes (though ...

We study two conjectures in additive combinatorics. The first is the polynomial Freiman-Ruzsa conjecture, which relates to the structure of sets with small doubling. The second is the inverse Gowers conjecture for U3, which relates to functions which locally look like quadratics. In both cases a weak form, with exponential decay of parameters is known, and a strong form with only a polynomial l...

The purpose of this note is to showcase a certain line of research that connects harmonic analysis, specifically restriction theory, to other areas of mathematics such as PDE, geometric measure theory, combinatorics, and number theory. There are many excellent in-depth presentations of the various areas of research that we will discuss, see e.g. the references below. The emphasis here will be o...

Chang’s Lemma is a widely employed result in additive combinatorics. It gives optimal bounds on the dimension of the large spectrum of probability distributions on nite abelian groups. In this note, we show how Chang’s Lemma and a powerful variant due to Bloom both follow easily from an approximation theorem for probability measures in terms of generalized Riesz products. The latter result invo...

The Steering Committee decided to approach the Editors of the Australasian Journal of Combinatorics with a proposal to publish selected refereed papers from the conference. We were delighted when the proposal was accepted, and the Australasian Journal of Combinatorics joined other journals such as Advances in Applied Mathematics, Annals of Combinatorics, Electronic Journal of Combinatorics, Jou...