• 2024      Ontario graduate scholarship      UWaterloo
• 2024      President’s graduate scholarship      UWaterloo
• 2023      QEII-GSST      UWaterloo
• 2023      Ontario graduate scholarship      UWaterloo
• 2023      President’s graduate scholarship      UWaterloo

• [1] Hank Chen, Florian Girelli, Integrability from categorification and the 2-Kac-Moody algebra, submitted to Comm. Math. Phys. (2024)
• [2] Hank Chen, Joaquin Liniado, Higher Gauge Theory and Integrability (2024)
• [3] Hank Chen, Drinfel'd double symmetry of the 4d Kitaev model, JHEP, 2023, 141 (2023)
• [4] Hank Chen, Florian Girelli, Categorical Quantum Groups and Braided Monoidal 2-Categories (2023)
• [5] Hank Chen, Florian Girelli, Categorified Drinfel’d double and BF theory: 2-groups in 4D, PRD, 106, 105017 (2022)
• [6] Hank Chen, Florian Girelli, Gauging the Gauge and Anomaly Resolution (2022)
• [7] Hank Chen, Lieb–Schultz–Mattis theorem and the filling constraint, 111, 139 (2021)
• [8] Hank Chen, Matthew R. C. Fitzpatrick, Sujit Narayanan, Bitan Roy, Malcolm P. Kennett, Interacting quantum Hall states in a finite graphene flake and at finite temperature, PRB, 102, 205401 (2020)

My research interests concerns the interplay between physics, algebra and geoemtric topology exemplified by the following closely related phenomena:

1. as observed by Witten, the Wilson lines in 3d topological quantum field theories (TQFTs), such as Chern-Simons theories at integral level, form braided tensor categories,
2. as observed by Jones, the observables in 2d integrable quantum spin systems/field theories (IFTs) produce knot invariants.

These results turn out to be very closely related through properties of the quantum group Hopf algebras underlying the TQFTs and IFTs. As such, such structures play very central roles in my research. 

Specifically, I am currently working on a categoification of the above phenomena to 4-dimensions, which is summarized by the following diagram.

My approach is based on a categorification of Hopf algebras that allows one to produce 4d TQFTs (such as higher-Chern-Simons theories and Poisson AKSZ models) and 3d IFTs, and whose modules are briaded monoidal higher categories. The goal is to construct novel 4d topological invariants from such theories, and to relate these to knot categorification.