5 problems

Let $G$ (or $G_f$) be a spatial symmetry group with given additional symmetry data, and let $G^{\text{eff}}$ (or $G_f^{\text{eff}}$) be the corresponding effective internal symmetr…

Cohomological classification conjecture. The topological action is largely classified by $H^{d+1}(BG_s,U(1)_r)$. This proposes a cohomological description of crystalline SPT phases…

Twisted crystalline equivalence principle. In interacting fermionic systems, the crystalline equivalence principle should be applied in a twisted way: spinless (spin-$1/2$) fermion…

Let $n\in\{2,3,4,6\}$, and consider two-band, insulating, $\mathrm{P}n$-symmetric Hamiltonians with trivial Chern class. Their topological invariants include the Hopf invariant and…

Let point-group or space-group symmetry act on an interacting fermionic system, and impose the crystalline principle and the relevant spin-statistics relations. Crystalline extensi…