LIU QIHOU

Qihou Liu works on low-dimensional topology and its links with quantum field theory. He took his PhD at Yale University in 2008, and has since taught at the Central University of Finance and Economics in Beijing, at Xi'an Jiaotong-Liverpool University, and at the International IT University in Almaty.

As a graduate student Qihou Liu studied 3-dimensional topology and knot theory. The volume conjecture, which relates Chern–Simons gauge theory to hyperbolic volume, is the central theme of his thesis, in which he settled two special cases. The first of the two preprints below was later quoted and extended by H. Murakami and A. T. Tran in Kashaev invariants of twice-iterated torus knots, Topology and its Applications 290 (2021).

His interests since then have centred on the relation between topology and quantum field theory. Algebraic constraints often suggest the shape of a quantum theory in the way that symmetry principles do in quantum physics, sparing the hard analysis. While visiting the Institute of Advanced Study at Tsinghua in 2010 he organised a seminar on vertex operator algebras and tensor categories with Liang Kong, Hao Zheng and Yinghua Ai.

From 2014 to 2018 he visited Dezhuan Han at Chongqing University each summer, working on topological effects in optics and on topological insulators, and contributing tensor decomposition calculations to their joint work.

PhD in Mathematics — Yale University, USA (2004–2008).

M.Sc. and M.Phil. in Mathematics — Yale University, USA (2001–2004).

B.Sc. in Mathematics — Peking University, China (1997–2001).

1. 2024–2025 — Associate Professor, Department of Mathematical and Computer Modeling, International IT University, Almaty.
2. 2015–2024 — Lecturer, Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, China.
3. 2008–2015 — Assistant Professor, China Economics and Management Academy, Central University of Finance and Economics, Beijing.
4. 2010 — Visiting Scholar, Institute of Advanced Study, Tsinghua University (September to November).

1. X. Yang, Q. Liu, D. Zhang and X. Gu, A unified approach to the topological origin of Wigner–Seitz cells, Chinese Physics B (to appear). doi
2. L. Liu, L. Ge, P. Hu, H. Xiang, W. Yang, Q. Liu and D. Han, Toroidal dipolar response in plasmonic nanoparticle clusters, Journal of Physics D: Applied Physics 51 (2018). doi
3. Q. Liu, On the cable expansion formula, preprint (2008). arXiv:0810.1697
4. Q. Liu, On the colored Jones polynomials of certain cable of the torus knots, preprint (2008). arXiv:0807.4780

Teaching has been the main part of his duties since 2008, in courses spanning elementary and advanced mathematics.

1. International IT University, Almaty (2024–2025) — Algebra and Geometry; Discrete Mathematics and Mathematical Logic; Probability Theory and Mathematical Statistics; Mathematical Analysis.
2. Xi'an Jiaotong-Liverpool University (2015–2024) — Calculus; Mathematical Analysis; Linear Algebra; Mathematics for Engineering; An Introduction to Mathematical Statistics.
3. Central University of Finance and Economics (2008–2015) — Introduction to Topology; Stochastic Processes, undergraduate and graduate; Introduction to Probability Theory; Advanced Probability Theory; Functions of Real Variables; Mathematical Analysis.