Topology and matter

The theory of topological properties of materials or condensed matter systems has
become increasingly sophisticated. The most prominent has been Kitaev's "periodic table"
for topological insulators. The main idea is that there are topological invariants, which
dictate the behavior of the system. The tools include Chern-classes and K-theory in
various flavors. We will give an overview of these tools and explain how they can be
used in concrete situations.