This volume flows from the activity Dynamics: Topology and Numbers, held
at the Max Planck Institute for Mathematics (MPIM) in Bonn in July 2018. The
activity brought together about 90 researchers from 25 different countries, along
with many of the long-term visitors at the MPIM. This was the fourth conference at
the MPIM on the theme of dynamical systems and its relationships with the diverse
fields of number theory, geometry, topology, ergodic theory, and combinatorics.