Cantor Minimal Systems (SoSe 2022)

Veranstaltungszeitplan

Hinweis

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Beschreibung

In this seminar, we will study Cantor minimal systems (i.e. minimal homeomorphisms of the Cantor set) following the homonymous book by Ian F. Putnam. Cantor minimal systems are a particularly simple class of dynamical systems and can be classified up to orbit equivalence (i.e. up to homeomorphisms of the space mapping orbits to orbits) by a simple algebraic invariant. Along the way, we will study fascinating interactions between AF-equivalence relations, Bratteli diagrams, and dimension groups. The motivation for this theory comes from the classification of C*-algebras by K-theory. Although the book does not mention C*-algebras or K-theory, we plan to take a detour and learn all the relevant tools to classify AF-algebras and crossed products of Cantor minimal systems. We will discuss these applications in the last talk.  The required prerequisites are basic knowledge in point-set topology, elementary algebra, and elementary measure theory. The seminar is aimed mainly at Master- and PhD students. However, it should also be accessible to Bachelor students who have attended courses such as Introduction to Algebra and Analysis, Topology and Geometry, or Functional Analysis.

Literatur

Dozenten

• Dr. Julian Kranz (verantwortlich)