Research Interests:
I am interested in physics, mathematics and natural philosophy and have published research papers in both physics journals
and mathematics journals. Although I was often regarded by my colleagues as a mathematician, all my works are motivated by fundamental questions in physics or natural philosophy.
My long term goals are to develop a new calculus for quantum many-body theory or quantum field theory
(including a new paradigm of phase transitions) and to gain a deeper understanding of the origin of space and time.
A summary of my past research can be found here: Liang Kong’s Research. I provide a list of topics that I am interested in.
- Physics: topological/conformal/quantum field theories, quantum phases in condensed matter physics (including topological orders, SPT/SET orders, spontaneous symmetry-breaking orders, quantum liquids), phase transitions and quantum gravity.
- Mathematics: vertex operator algebras and their representations, conformal/topological nets, operator algebras, higher categories, higher algebras, higher representations, factorization homology, higher homotopy theory and geometric Langlands correspondence.
Publications:
See most of my arXiv articles here: http://arxiv.org/a/kong_l_1.html. I will keep the latest updates of a few arXiv papers below.
- The latest version of the paper Higher Condensation Theory (03/21/2026,
a minor revision of the third arXiv version arXiv:2403.07813.)
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The latest version of “An invitation to topological orders and category theory”:
(04/28/2025, a minor revision of arXiv:2205.05565)
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In the latest version, we corrected some mistakes in citations about modular tensor categories in the earlier versions.
We also rewrote the introduction section and added some references on generalized/non-invertible/topological symmetries.
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We are planing a major version of this paper. In particular, we plan to rewrite the microscopic definition of an anyon.
Ideally, we would like to provide a short review of all known approaches towards a rigorous definition of an anyon,
including the approach based on the superselection sectors of the net of local operator algebras
and the entanglement bootstrap approach. We plan to add a lot of new topics, including (anyon) condensation theory,
G-crossed braided fusion categories, (de)-equivariantizations, enriched fusion categories,
topological Wick rotations, Ising chain, etc. What is really amazing is that one can see the emergence of
all these rich mathematical structures and deep physical principles within the toric code model.
