# Research

**Research Interests**: conformal field theories, topological field theories, factorization algebras, factorization homology, category theory and their applications in physics.

- Nearly all my works are motivated by my own program on “Quantum Gravity” or “Quantum Geometry”, which was briefly outlined in the following publication:
*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]

- In the last ten years, nearly all my works are trying to develop and to understand the mathematical theory of the boundary-bulk duality in both 2d rational conformal field theories and topological orders in any dimensions, because this duality, which can be viewed as some kind of holographic principle, plays the role of “general principle of relativity” in my program of quantum gravity.

**Publications**: see all my publications here: http://arxiv.org/a/kong_l_1.html

**Works in progress**:

- Vertex operator algebras and tensor categories, Liang Kong, Hao Zheng.
- Finite modular Grothendieck-Verdier categories, 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

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