Multigap Topological Insulators: Non-Abelian Bands, Riemannian Geometry, Quantised Optical Responses

Explore a comprehensive seminar by Wojciech Jankowski from the University of Cambridge discussing the fascinating world of multigap topological insulators that extend beyond conventional K-theory classifications. Delve into the homotopy classification of multigap topological phases with bulk topological invariants defined under PT symmetry, and discover the cohomological characterization of non-Abelian bands with special focus on non-Abelian Hopf insulators featuring quaternion algebra-based invariants. Learn about momentum-space Riemannian geometry of quantum states in multigap Bloch bundles and their physical manifestations in optical responses. Understand how three-dimensional multigap topological insulators can exhibit quantized integrated non-linear shift photoconductivities, with explanations of how this quantization emerges from momentum-space torsion tensors, their connections to real Chern-Simons forms, and virtual multiband optical transition amplitudes.