The current list of proposed themes for working groups:

• Mitja Mastnak and Heydar Radjavi: Local to global properties of collections of matrices
  
  Let X be a collection of n-by-n matrices with structure (e.g., a semigroup, group, or a linear space). Suppose we know that every sub-collection that is in some sense "small" (e.g., size one, two, finite) satisfies some interesting property. Does this imply some significant global property for X? One of the first results of this nature is the following observation: if every element of a group of matrices is unipotent (i.e., 1 is the only eigenvalue), then the group is simultaneusly triangularizable. One known generalization is the following: suppose that tr(ABC)=tr(BAC) for all A,B,C in a semigroup, then it also follows that the semigroup is simultaneously trianguarizable. Not all results are necessarily about triangularizability. For example: if for all A,B in an irreducible semigroup we have that the spectrum of AB-BA is real, then the semigroup is simultaneously similar to a semigroup of real matrices.
  
  The aim of this working group is to study some open problems in the area and perhaps also come up with new open problems.
  
  
• Konrad Schmüdgen and Aljaž Zalar: Moment problems, positive polynomials and applications
  
  The moment problem (MP) is a classical question in analysis that has been studied since the end of the 19th century (Stieltjes, 1894). A general version of the moment problem is the following: Let E be a real vector space of continuous functions on a locally compact Hausdorff space X. When is a linear functional on E an integral with respect to some positive measure on X supported by a given closed set of X? One may ask for characterizations of the existence, uniqueness and the set of representing measures.
  
  In the past various versions of the MP appeared in the literature. In the most interesting cases E consists of multivariate polynomials on X=ℝⁿ. Then positive polynomials play a crucial role and there is a close interaction of the moment problem and real algebraic geometry. When the degree of the polynomials is bounded, we have the truncated MP. When the number of variables is infinite, the problem is usually called an infinite dimensional MP. When E is some unital commutative real algebra A and X the set of all characters of A, we obtain an abstract formulation of the MP. When E is replaced by a vector space of matrix/operator polynomials or when the functional is replaced by the operator which maps into matrices, we have non-commutative versions of the MP.
  
  Nowadays, MPs find their applications in many fields such as real algebraic geometry, polynomial optimization, operator theory, probability and statistics, the theory of differential equations, statistical physics and others.
  
  This working group will consist of talks, followed by discussions on open problems in the area, presented by participants.
  
  
• Chi-Kwong Li: Preserver problems
  
  Preserver problems concern the study of maps ɸ on matrices or operators with some special properties such as ɸ(S)⊆S for a given set S, f(ɸ(A))=f(A) for given function f, or ɸ(A)~ɸ(B) whenever A~B for a given relation ~. The study has attracted many researchers because the subject has connections with many pure and applied areas. In particular, many preservers results have implications to other subjects, and many techniques from other subjects could be used to study preserver problems.
  
  In this working group, we would like to bring (experienced or new) researchers interested in the topic to share results, experience, problems, and explore further connections of the topic to other areas.