Research

Research Interests:

  1. Mathematics: vertex operator algebras, category theory, representation theory, … etc.
  2. Physics: quantum field theories and topological orders in condensed matter physics.

Publications:  (http://arxiv.org/a/kong_l_1.html)

  1. The functoriality of the centre of an algebra, Alexei Davydov, Liang Kong, Ingo Runkel, Adv. Math. 285 (2015) 811-876 [arXiv:1307.5956]
  2. Anyon condensation and tensor categories, Liang Kong, Nucl. Phys. B 886 (2014) 436-482 [arXiv:1307.8244]
  3. Cardy algebras and sewing constraints, II, Liang Kong, Qin Li, Ingo Runkel, Adv. Math. 262 (2014) 604-681  [arXiv:1310.1875]
  4. Some universal properties of Levin-Wen models, Liang Kong, XVIITH International Congress of Mathematical Physics, World Scientific 444-455 (2014) [arXiv:1211.4644]
  5. Electric-magnetic duality and topological order on the lattice, Oliver Buerschaper, Matthias Christandl, Liang Kong, Miguel Aguado, Nucl. Phys. B. 876 [FS] (2013) 619-636 [arXiv:1006.5823]
  6. Models for gapped boundaries and domain walls, Alexei Kitaev, Liang Kong, Commun. Math. Phys. 313 (2012) 351-373 [arXiv:1104.5047]
  7. Invertible defects and isomorphisms of rational CFTs, Alexei Davydov, Liang Kong, Ingo Runkel, Adv. Theor. Math. Phys., 15, (2011) 43–69 [arXiv:1004.4725]
  8. Conformal field theory and a new geometry, Liang Kong, Mathematical Foundations of Quantum Field and Perturbative String Theory, Hisham Sati, Urs Schreiber (eds.), Proceedings of Symposia in Pure Mathematics, AMS, Vol. 83 (2011) 199–244 [arXiv:1107.3649]
  9. Field theories with defects and the centre functor, Alexei Davydov, Liang Kong, Ingo Runkel, Mathematical Foundations of Quantum Field and Perturbative String Theory, Hisham Sati, Urs Schreiber (eds.), Proceedings of Symposia in Pure Mathematics, AMS Vol. 83 (2011) 71–128 [arXiv:1107.0495]
  10. Algebraic structures in Euclidean and Minkowskian two-dimensional conformal field theory, Liang Kong, Ingo Runkel, Noncommutative structures in Mathematics and Physics, 217–238, K. Vlaam. Acad. Belgie Wet. Kunsten (KVAB), Brussels, 2010, [arXiv:0902.3829]
  11. Cardy algebras and sewing constraints, I, Liang Kong, Ingo Runkel, Comm. Math. Phys. 292, 871–912 (2009) [arXiv:0807.3356]
  12. Morita classes of algebras in modular tensor categories, Liang Kong, Ingo Runkel, Adv. Math. 219, 1548–1576 (2008) [arXiv:0708.1897]
  13. Cardy condition for open-closed field algebras, Liang Kong, Comm. Math. Phys., 283, 25–92 (2008) [arXiv:math/0612255]
  14. Open-closed field algebras, Liang Kong, Comm. Math. Phys., 280, 207-261 (2008) [arXiv:math.QA/0610293]
  15. Modular invariance for conformal full field algebras, Yi-Zhi Huang, Liang Kong, Trans. Amer. Math. Soc. 362 (2010) 3027–3067, [arXiv:math.QA/0609570]
  16. Full field algebras, operads and tensor categories, Liang Kong, Adv. Math. 213 (2007) 271–340, [arXiv:math/0603065]
  17. Full field algebras, Yi-Zhi Huang, Liang Kong, Comm. Math. Phys. 272 (2007) 345–396, [arXiv:math/0511328]
  18. Open-string vertex algebras, categories and operads, Yi-Zhi Huang, Liang Kong, Comm. Math. Phys. 250 (2004) 433–471, [arXiv:math/0308248]

Preprints:

  1. Braided fusion categories, gravitational anomalies and the mathematical framework for topological orders in any dimensions, Liang Kong, Xiao-Gang Wen, [arXiv:1405.5858]
  2. Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers, Liang Kong, Xiao-Gang Wen, Hao Zheng, [arXiv:1502.01690]
  3. The center functor is fully faithful, Liang Kong, Hao Zheng, [arXiv:1507.00503]
  4. A theory of 2+1D fermionic topological orders and fermionic/bosonic topological orders with symmetries, Tian Lan, Liang Kong, Xiao-Gang Wen, [arXiv:1507.04673]
  5. Modular extensions of unitary braided fusion categories and 2+1D topological/SPT orders with symmetries, Tian Lan, Liang Kong, Xiao-Gang Wen, [arXiv:1602.05936]
  6. Classification of 2+1D topological orders and SPT orders for bosonic and fermionic systems with on-site symmetries, Tian Lan, Liang Kong, Xiao-Gang Wen, [arXiv:1602.05946]

Works in progress:

  1. Vertex operator algebras and tensor categories, Liang Kong, Hao Zheng.
  2. Topological orders and topological chiral homology, Yihuan Ai, Liang Kong, Hao Zheng

Book co-edited

  • “Conformal Field Theories and Tensor Categories”, edited by C.M. Bai, J. Fuchs, Y.-Z. Huang, L. Kong, I. Runkel, C. Schweiger, Proceedings of a Workshop Held at Beijing International Center for Mathematical Research, 2013, Springer