Word
maps and stability of representations

Erwin Schrödinger International
Institute, Vienna

April 11-12-13, 2013

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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)

Hyperlinear groups

Random groups

Ulam stable and strongly Ulam stable groups

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

Local organizer: Goulnara Arzhantseva (Vienna)

The workshop is a part of an Austrian-Swiss research network on Sofic groups of Goulnara Arzhantseva (Vienna), Nicolas Monod (Lausanne), Alain Valette (Neuchatel), grant CRSI22-130435 of the Swiss National Science Foundation.

If you are interested in participation, please contact the organizers. For tourist information, please visit the ESI’s website on that topic.

List of participants