Over the past 15 years, we have learned that topological phases of matter are not rare or esoteric, but in fact appear in some form in more than half of all known solid-state materials.  However, the most frequently occurring topological phases in real 3D materials are complicated, symmetry-protected topological crystalline insulator (TCI) states that, unlike more familiar quantum Hall states, have unknown smoking-gun experimental signatures, and hence practical applications. 

In his starting ERC TopoRosetta, Dr. Wieder has outlined several paths to translating theoretical models of TCIs to real-material experiments, including fundamental research into the robustness of TCI states leveraging techniques based on interacting quantum field theory, and novel numerical techniques for analyzing TCIs in density-functional-theory-based material simulations. 

The unifying thread for his investigations is the mathematical language of symmetry group theory, which provides fundamental constraints on topological phases in crystalline materials.  In TopoRosetta, Dr. Wieder will introduce a "Rosetta Stone" based in group theory to translate between the currently disconnected languages of solid-state topology and system-independent physical observables, with the hope of uncovering new experimental platforms for spintronics and quantum information science. 

Congratulations to Ben on his remarkable success!