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A counterexample to the periodic tiling conjecture
Rachel Greenfeld, Terence Tao
The periodic tiling conjecture asserts that any finite subset of a lattice which tiles that lattice by translations, in fact tiles periodically. In this work we disp…
A counterexample to the periodic tiling conjecture (announcement)
Rachel Greenfeld, Terence Tao
The periodic tiling conjecture asserts that any finite subset of a lattice which tiles that lattice by translations, in fact tiles periodically. We announce here a d…
The inverse theorem for the Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches
Asgar Jamneshan, Terence Tao
We state and prove a quantitative inverse theorem for the Gowers uniformity norm on an arbitrary finite abelian group ; the cases when was of odd order or a vector…
Undecidable translational tilings with only two tiles, or one nonabelian tile
Rachel Greenfeld, Terence Tao
We construct an example of a group for a finite abelian group , a subset of , and two finite subsets of , such that it is u…
Zarankiewicz's problem for semilinear hypergraphs
Abdul Basit, Artem Chernikov, Sergei Starchenko +2
A bipartite graph with is semilinear if for some and the edge relation consists of th…
An inverse theorem for an inequality of Kneser
Terence Tao
Let be a compact connected abelian group, and let denote its probability Haar measure. A theorem of Kneser (generalising previous results of Macbeath and Raikov)…