北京雁栖湖应用数学研究院 北京雁栖湖应用数学研究院

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关于我们
院长致辞
理事会
协作机构
参观来访
人员
管理层
科研人员
博士后
来访学者
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学术研究
研究团队
公开课
讨论班
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教研人员
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住宿
交通
配套设施
周边旅游
新闻
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通知公告
资料下载
清华大学 "求真书院"
清华大学丘成桐数学科学中心
清华三亚国际数学论坛
上海数学与交叉学科研究院
BIMSA > 陈群皓

陈群皓

     博士后    
博士后 陈群皓

团队: 数学物理

办公室: A3-3-101

邮箱: chunhaochen@bimsa.cn

研究方向: 数学物理

个人主页: http://bimsa.net/people/HankChen/

CV

研究兴趣


  • Quantum algebras and representations
  • Topological quantum field theory
  • Integrable field theory and lattice systems
  • Category theory

教育经历


  • 2012 - 2017      Simon Fraser University      Mathematical Physics Honours      B.Sc.      Concentration: quantum Hall effects in graphene      (Supervisor: Malcolm Kennett)
  • 2017 - 2019      McMaster University      Physics and Astronomy      M.Sc.      Concentration: chiral superconductivity      (Supervisor: Catherine Kallin)
  • 2020 - 2024      University of Waterloo      Applied Mathematics      Ph.D      Concentration: quantum algebras and categorification      (Supervisor: Florian Girelli)

荣誉与奖项


  • 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

出版物


  • [1] Hank Chen, Combinatorial quantization of 4d 2-Chern-Simons theory I: the Hopf category of higher-graph states (2025)
  • [2] Hank Chen, Categorical quantum symmetries and ribbon tensor 2-categories (2025)
  • [3] Hank Chen, Joaquin Liniado, Higher Gauge Theory and Integrability, 110(086017) (2024)
  • [4] Hank Chen, Florian Girelli, Integrability from categorification and the 2-Kac-Moody algebra (2024)
  • [5] Hank Chen, Drinfel'd double symmetry of the 4d Kitaev model, JHEP, 2023, 141 (2023)
  • [6] Hank Chen, Florian Girelli, Categorical Quantum Groups and Braided Monoidal 2-Categories (2023)
  • [7] Hank Chen, Florian Girelli, Categorified Drinfel’d double and BF theory: 2-groups in 4D, PRD, 106, 105017 (2022)
  • [8] Hank Chen, Florian Girelli, Gauging the Gauge and Anomaly Resolution (2022)
  • [9] Hank Chen, Lieb–Schultz–Mattis theorem and the filling constraint, 111, 139 (2021)
  • [10] 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. 

 

更新时间: 2025-05-20 15:34:26


北京雁栖湖应用数学研究院
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北京雁栖湖应用数学研究院 101408

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