Topology is a field of mathematics which classifies properties of mathematical structures which are robust under deformations. This field has recently emerged as a powerful paradigm to discover, classify, and investigate quantum properties of materials. The international workshop, attended by 90 participants, has focussed on two classes of such topological quantum materials. First, in Dirac matter topological properties are often intrinsically linked to the relativistic Dirac equation. Second in spin systems geometry and spin-orbit coupling can suppress magnetic ordering and give rise to novel topological spin liquid states. The workshop brought together experimental and theoretical physicists working in the two fields. It gave an overview on the tremendous scientific development especially in the last one or two years focussing on synergies of the two fields, on experimental realizations of topological concepts and on future research directions shaping the field.

The experimental and theoretical investigation of new topological quantum materials was not only the main topic of the inspiring colloquium talk by S. Nakatsuji but also central to many key contributions to the workshop (Y. Ando, C. Felser, P. Gegenwart, Z. Hasan, Y.-B. Kim, O. Rader, K. Ross, M. Sato, H. Takagi, R. Valenti). Topological insulators, topological superconductors, and magnetic materials with strong spin-orbit interactions and frustration were some of the most discussed material classes. The classification of interacting topological states, which have not yet been realized experimentally, and routes towards their realization were also a major theme (e.g., in presentations of L. Balents, M. Daghofer, O. Erten, M. Hermanns, G. Jackeli, L. Savary, or T. Senthil). I. Bloch showed how experiments in ultracold atoms can be used to map topological Berry phases and gave a perspective of how concepts from solid state physics find their application in quantum optics experiments.

The latest development on magnetic skyrmion materials (C. Pfleiderer, K. von Bergmann), including their controlled creation and destruction by electric fields, the quest for experimental signature of Majorana fermions in spin liquids in neutron scattering (S. Nagler, L. Balents), the observation of the topologically quantized electromagnetic response of topological insulators (P. Armitage), magnetic quantum oscillations without Fermi surfaces (J. Knolle) and anomalous magnetotransport (R. Arita, L. Balicas, Y. Ando) were presented in inspiring talks.

Overall, the workshop was characterized by lively and intensive discussions until late in the night. In particular the poster sessions offered a wealth of fresh experimental results and theoretical insights and highlighted the passion of young scientists for the field. A brainstorming session on the most important future research directions in topological quantum matter showed that this field is still at its infancy. Interacting topological states, experiments probing projective symmetries, strange metals and the experimental realization of emergent gauge fields were only some of the research areas where the participants expect major advances in the near future.

Besides the generous support by the Max Planck Society, the workshop was also supported by the TOPONET program of the Institute for Solid State Physics (University of Tokyo) and the profile area ”Quantum Matter and Materials“ of the University of Cologne.