Topology has emerged as an important concept for characterizing quantum matter. Together with symmetry it gives rise to a plethora of new and exotic phases. At the interface between topologically distinct phases, seemingly impossible phenomena become reality, such as charge fractionalization, chiral currents or single Dirac cones. Because topological phenomena give rise to extremely precise quantization and robustness against disorder, they hold promise for game-changing applications ranging from metrology to quantum computation. Topological effects are at the focus of current research, with new concepts and new topological materials being discovered at an amazing pace.

The interplay of topology and strong interactions is one of the most vibrant and challenging problems in condensed-matter physics, and quantum simulators of topological systems have gained increasing attention. Ultracold atoms in optical lattices have emerged as a versatile platform for combining strong artificial gauge fields and topological bandstructures with tunable interactions.

The aim of this school is to train a new generation of young researchers on the subject of topology and interactions in optical lattices.

Topics

• Engineering artificial gauge fields in ultracold quantum gases
• Topological insulators and band structures
• Topological order in strongly correlated systems
• Experimental platforms from solids to quantum simulators
• Floquet engineering
• Driving and interaction in synthetic topological quantum matter
• Numerical methods for simulating strongly correlated systems

(Online Summer School)