Jiankang Huang is a PhD student at Fudan University working on the mathematical theory of topological orders. Her first project studies cohomological invariants of Lieb–Schultz–Mattis (LSM) anomalies in 2D and 3D quantum spin systems with diverse space groups and internal symmetries. Building on the crystalline equivalence principle, she connects the unified cocycle description of LSM anomalies with the real-space construction approach, yielding their spatial distribution. This work has also trained her in homological algebra and algebraic topology, especially spectral sequences and resolutions. Jiankang's second project develops the boundary theory of n‑dimensional 𝐺‑symmetry‑enriched topological (𝐺‑SET) orders. They construct a general framework for gapped domain walls between distinct 𝐺‑SETs, analysing obstructions to symmetric condensations. Looking ahead, they aim to classify gapless walls via topological holography and vertex operator algebras, potentially illuminating orbifold theories of VOAs