14w5136 Algebraic and Model Theoretical Methods in Constraint Satisfaction

The aim in a constraint satisfaction problem (CSP) is to find an assignment of values to a given set of variables, subject to constraints on the values which can be assigned simultaneously to certain specified subsets of variables. CSPs are used to model a wide variety of computational problems in computer science, discrete mathematics, artificial intelligence, and elsewhere, and they have found numerous applications in those areas. Several very successful approaches to study the complexity and algorithms for constraint satisfaction problems have been developed over the last decade. One of the most fruitful uses universal algebra. So far the bulk of research on the CSP has been done assuming the variables can take only a finite number of values. The infinite CSP, in which this restriction is removed, has much stronger expressive power, but is also much harder to study. Two recent discoveries made it possible to transfer some techniques, in particular the algebraic approach, from the finite to some classes of the infinite CSP. The first one is the expansion of the algebraic approach onto infinite domain CSPs by Bodirsky and Nešetřil. The universal algebraic approach rests on the observation that primitive positive definability in finite structures can be characterized by polymorphisms. The second one is a surprising connection between topological dynamics and Ramsey theory discovered by Kechris, Pestov, and Todorcevic [?]. This is highly relevant in the context of constraint satisfaction, since the universal-algebraic approach is particularly powerful for omega-categorical structures that are definable in ordered Ramsey structures. In contrast to finite domain CSPs the study of infinite domain CSPs through algebra and model theory is still in its infancy, and many directions, problems, and hypotheses are yet to be identified. The workshop therefore focuses on the interaction of three areas of mathematics and computer science: