Sofic groups

Abstract

According to folklore, Gromov conjectures that any statement about all groups is either trivial or false. In this talk I want to introduce a relatively new concept in group theory, that of a sofic group. Soficity is a generalisation of residual finiteness among other things, and to define it we need the Symmetric groups, the Hamming distance from coding theory, and some epsilons. I will try to show that it is non-trivial, and at the time of writing this abstract there is no group known to be non-sofic.