Matteo Cavaleri: A (non-)standard approach to soficity
We introduce some basic facts of non-standard analysis and their fruitful applications to problems related to soficity. We define the universal sofic group and its natural action on the Loeb space.
Moreover, we define two special subgroups of the universal sofic group. The first one can be described as the group of certain generalised automorphisms and the second one as the kernel of the ultralimit of normalised Coxeter lengths. Their quotient contains all countable groups and each sofic representation can be conjugated inside the first subgroup.
