We outline the main different questions to be addressed within the three subtopics we identified above

1) Spin-orbit physics and artificial gauge fields:
- What methods do we have and need to develop in order to quantitatively study spin-orbit coupling and gauge fields?
- What is the current status of DMRG?
- Determinant auxiliary-field Monte Carlo methods may work in case of unbroken time-reversal symmetry. What are the latest developments?
- With the recent realization of the Haldane model (ETH Zurich), what novel kind of physics is becoming feasible?
- Can methods such as real-space DMFT be used? What is the difference with cluster DMFT methods in terms of accuracy and computational effort?
- For bosons: what are the prospects for developing cluster algorithms for B-DMFT?
- How to study topological states in the presence of interactions? Can Green functions shed light on this question?
- Cold gas experiments: how to implement artificial gauge fields and at the same time control the density and the interactions.

2) Long-range interactions:
- Can diagrammatic Monte Carlo be employed to study fermionic dipolar interactions? How can one observe nematic phases? How does one deal with IO, memory usage, series convergence issues and vertex corrections?
- What are the next experimental steps in cooling earth-alkaline atoms (Er, Dy, Yb), polar molecules and increasing the number of Rydberg atoms?

3) Out-of equilibrium methods:
- How can DMRG be improved in the study real-time dynamics? Can one go to larger times or higher dimensions?
- When do typical and untypical states thermalize?
- What are the possibilities for diagrammatic methods such as DMFT and cluster variants such as DCA? What is the status of numerically exact solvers (CTQMC, ED)? Can the recently developed DMRG impurity-solvers be used for real-time dynamics?