Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.
We study continuous theories of classes of finite dimensional Hilbert spaces expanded by
a finite family (of a fixed size) of unitary operators.
Infinite dimensional models of these theories are called pseudo finite dimensional dynamical Hilbert spaces.
Our main results connect decidability questions of these theories with the topic of approximations of groups by metric groups.
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 dimensional unitary representations.
In 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.
