Daniel Palacin:
On a question of Babai and Sós, a nonstandard approach
Time and place
Wednesday, 24.10.18, 16:30-17:30, Raum 404, Ernst-Zermelo-Str. 1
Abstract
Abstract: In 1985, Babai and Sós asked whether there exists a constant c>0 such that every finite group of order n has a product-free set of size at least cn, where a product-free set of a group is a subset that does not contain three elements x,y and z satisfying xy=z. Gowers showed that the answer is no in the early 2000s, by linking the existence of product-free sets of large density to the existence of low\ndimensional unitary representations.\n\nIn this talk, I will provide an answer to the aforementioned question by model theoretic means. Furthermore, I will relate some of Gowers' results to the existence of nontrivial definable compactifications of nonstandard finite groups.