# Word maps and stability of representations

The goal of this workshop is to bring together specialists both in mathematics and in mathematical physics working on topics related to Ulam's stability of representations and a general "almost implies near" phenomenon. An elementary example of a result of interest is as follows: almost commuting matrices are near matrices which commute. The word-map in this example is taking the commutator word of group elements. More general words can be considered and the results go beyond just complex matrices and the operator norm (which is used to quantify "almost").

We aim also to explore a relation to metric approximations of discrete groups. In particular, this concerns concepts of soficity and hyperlinearity which can be viewed as the existence of such an "almost" object (in the same example: the existence of a metric approximation of group elements by almost commuting matrices).Themes include, but are not limited to, geometric, analytic, combinatorial, algorithmic, and computational aspects of the following major classes of infinite groups:

We aim also to explore a relation to metric approximations of discrete groups. In particular, this concerns concepts of soficity and hyperlinearity which can be viewed as the existence of such an "almost" object (in the same example: the existence of a metric approximation of group elements by almost commuting matrices).Themes include, but are not limited to, geometric, analytic, combinatorial, algorithmic, and computational aspects of the following major classes of infinite groups:

Sofic and linear sofic groups

Hyperlinear groups

Random groups

Ulam stable and strongly Ulam stable groups

Weakly amenable groups and groups with Kazhdan's property (T)