Homogeneous Structures (15w5100)
Claude Laflamme (University of Calgary)
Lionel Nguyen Van Thé (University of Aix-Marseille)
Stevo Todorcevic (University of Toronto)
Robert Woodrow (University of Calgary)
Our principal objective is to promote close interactions between different fields of mathematics affected by these recent developments, 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:
• Universal objects Examples include the Fraïssé theory in logic and generalizations in model theory, universal graphs in combinatorics, the universal Urysohn space in topology, universality in algebraic geometry.
• Homogeneous structures Automorphism groups of homogeneous structures, Polish groups and topological dynamics, structural Ramsey theory, constraint satisfaction, omega-categoricity and amalgamation constructions, metric homogeneous structures, and classification results.
Universal objects are central to Mathematics in a sense that they may reflect properties and non-properties of a given class of structures. They are typically very homogeneous, and hence the deep connection between these areas. Recent applications across the above themes and disciplines provide a unique opportunity to gather experts with knowledge from various mathematical angles, from model theorists who provide techniques for constructing such objects, to permutation group theorists who can provide insight into the automorphism groups of these rich structures.
In addition to tackling central problems, the workshop will contain a substantial training component.
This is also an opportunity to celebrate Professor Sauer’s 70th birthday and his contributions to the subject over 45 years.