Homogeneous Structures

A relational first order structure is homogeneous if every isomorphism between finite substructures extends to an automorphism. Familiar examples of such structures include the rational numbers with the usual order relation, the countable random and so called Rado graph, and many others. Countable homogeneous structures arise as Fraı̈ssé limits of amalgamation classes of finite structures, and have connections to model theory, permutation group theory, combinatorics (for example through combinatorial enumeration, and through Ramsey theory), and descriptive set theory. Our principal objective at this workshop was to promote close interactions between different fields of mathematics affected by recent developments related to homogeneous structures, including researchers in the areas of combinatorics, descriptive set theory, dynamical systems, group theory, metric spaces, and model theory. Some of the mainstream recent themes that have emerged include the following.