Title: Topological invariants

Abstract: Recent advances in condensed matter physics have brought forth integer and Z/2 valued topological charges, the most famous being the integer quantum Hall effect. Mathematically this can be understood from topology as a so-called Chern-class.
Such classes appear in many contexts, such as fiber bundles, curvature of connections and C*-algebras and are at their heart K-theory invariants. The Z/2 invariants are more mysterious and have been mathematically matched to a real version of this theory. We will give an introduction to the different perspectives followed by new developments.