Johannes Kellendonk has worked on the non-commutative topology of tilings, a topic initiated by Alain Connes and Jean Bellissard which is important for the gap-labelling of tight binding Hamilton-operators on quasicrystals. He studied the K-theory of substitution tilings and, in joint work with Alan Forrest and John Hunton, quasiperiodic tilings. He also gave a symbolic description of tilings which is based on inverse semigroups. In joint work with Tim Hoffmann, Nadja Kutz and Nicolai Reshetikhin, Johannes Kellendonk investigated discrete nonlinear Toda lattices -- a discretation of Toda lattices -- using the Poisson-geometry of (complex) Poisson-Lie-groups. These lattices form integrable dynamical systems whose dynamics is given by a factorization relation. Johannes Kellendonk is currently interested in the integer quantum Hall-effect and here more precisely in the relation between the formulation of the Hall-conductivity in the edge current picture and the bulk-picture which expresses the conductivity as a Chern number. Together with Thomas Richter and Hermann Schulz-Baldes he approaches the subject using C*-algebras in order to include the disorder of the Hall-bar.