Ph. D in Mathematics, Rutgers, the State University of New Jersey (2005)
M.S. in Physics, University of Houston (1997)
B.Sc. in Physics, University of Science and Technology of China (中国科学技术大学）(1994)
Career:
Research Fellow (研究员), International Quantum Academy
Research Fellow (研究员), Southern University of Science and Technology（南方科技大学）
Associate Professor, YMSC, Tsinghua University（丘成桐数学科学中心，清华大学）
Lecturer (讲师), Department of Mathematics, University of New Hampshire
Research Associate, Center of Mathematical Sciences and Applications (CMSA), Harvard University
Associate Member (副研究员), Institute for Advanced Study at Tsinghua University (清华大学高等研究院）
Postdoc, California Institute of Technology, USA
Postdoc, Hausdorff Research Institute for Mathematics, Bonn, Germany
Postdoc, Max Planck Institute for Mathematics, Bonn
Postdoc, IHÉS, France
Postdoc, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Reseach 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 (04/12/2025,
a minor revision of arXiv:2403.07813. More references were added.
We adjusted the margin so that the paper has fewer pages.)
The latest version is significantly longer than the first version on arXiv and is close to be complete.
We will continue to add some interesting small results to the paper.
We post the first and incomplete version of our paper on arXiv in May, 2022 in a hurry because there is a high demand from students and colleagues
even for an incomplete note, a phenomenon which reflects the fact that there is no introductory review on this subject before our paper.
Indeed, some earlier versions of this paper, with a lot of mistakes, typos and missing references, have already circulated long before 2022.
So we decided to post a temporary version on arXiv in 2022 to avoid further delay.
Since 2022, we have witnessed explosive developments of this subject.
These developments demand us to add a lot of new references, remarks and perhaps new subsections.
Meanwhile, we have also collected many feedbacks from some of our readers.
Therefore, an update is absolutely necessary.
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.
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.
Unpublished works:
Vertex operator algebras and tensor categories, Liang Kong, Hao Zheng.
Sept. 13, 2024, “Higher Condensation Theory” (in English), workshop “Applications of Generalized Symmetries and Topological Defects to Quantum Matter”, at Simons Center for Geometry and Physics, September 9 – 13, 2024.
September 7, 2023, “A morphism between two QFT’s” (in English), an online talk given at the workshop “Shenzhen–Nagoya Workshop on Quantum Science 2023”
August. 16, 2023, “A morphism between two QFT’s” (in English), a seminar talk given at the workshop “NORDITA program on Categorical Aspects of Symmetries”, at Nordita, Stockholm, Sweden, August 14–25, 2023.
Sept. 27 & Oct. 4, 2022, “Topological Wick rotation and holographic duality I & II” (in Chinese), BIMSA and Tsinghua "Topological Orders and Category Theory" Seminar Series in Autumn 2022.
April 27, May 11 & May 18, 2022, “Rational Conformal Field Theories I, II & III” (in Chinese), BIMSA and Tsinghua "Topological Orders and Category Theory" Seminar Series in Spring 2022.
Nov. 26, 2021, “Ising chain and enriched fusion category” (in Chinese), BIMSA and Tsinghua "Topological Orders and Category Theory" Seminar Series in Autumn 2021.
June 12, 2020, “On the classification of topological orders with finite internal symmetries” (in English), Harvard "Mathematical Picture Language" Seminar.
