Notes

Flat bands in multichannel honeycomb scattering networks (2025), pdf
A complete Lieb-Schultz-Mattis theorem for 3D quantum magnets (2025), pdf
Theory of symmetry defects in "quantum orders" (2023), pdf
Sachdev-Ye-Kitaev model: random matrix theory, path integral, and quantum dynamics (2020), pdf

Lattice realization of diheral quantum doubles with all Dijkgraaf-Witten twists (2025), pdf
Towards a complete Lieb-Schultz-Mattis theorem for 3D quantum magnets (2024), pdf
Theory for the magnetic memory effect in the suuperconducting phase of 4Hb-TaS2 (2022), pdf
Projective symmetry group classification of bosonic spinons on the pyrochlore lattice (2017), pdf

On generating functions (to be added), pdf
On lattice gauge theory, tenfold way, Kitaev honeycomb models, and related topics (2016 onward), pdf
On Differential forms in algebraic topology by Bott & Tu (2025), pdf
On Equivariant cohomology by Loring Tu (2025), pdf
On group cohomology calculation (2024), pdf
On semisimple Lie algebra, in Chinese (2018), pdf
On point-set topology, in Chinese (2017), pdf
On statistical mechanics, course taught by Andreas Ludwig at UCSB (2016), pdf
On many-body physics (fermions), course taught by Andreas Ludwig at UCSB (2016), pdf

Mod-2 Cohomology ring of crystallographic space groups, code written in GAP
Explicit cochain functions of the generators (≤ degree 3) of the mod-2 cohomology ring of crystallographic space groups, in this Mathematica notebook