Probability, statistics and combinatorics: Homogeneous structures and generalized stability theory

  • Date:
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Vera Koponen
  • Contact person: Fiona Skerman
  • Seminarium

Abstract: 

Here a 'structure' means a set together with finitely many "basic" relations on it (e.g. edges or hyperedges), so (di)graphs and hypergraphs are particular examples of structures. The class of (finite or infinite) countable homogeneous structures have interesting properties from a combinatorial perspective as well as from a model theoretic one (where 'model theory' refers to a branch of mathematical logic). They have also found applications within a number of areas such as Ramsey theory, contraint satisfaction problems, permutation groups and topological groups. In this talk I will explain some of the basics of homogeneous structures and also present some recent results concerning homogenous structures with "nice" stability theoretic properties, where 'stability theory' and its generalizations is an important collection of notions, methods and results in model theory. The precise statement of these results (and notions involved) would require rather much technical knowledge from this area, but I will do my best to give the listeners an intuitive idea of what is going on.