Guo Chuan Thiang

Assistant Professor

Beijing International Center for Mathematical Research

Peking University

[email: guochuanthiang (at) bicmr (dot) pku (dot) edu (dot) cn ]

[Office: 81-105]


Teaching 2022-2024

Fall 2024: Topics in Mathematical Physics (Planned topics: K-theory, operator algebras, noncommutative geometry)

Spring 2024: Quantum Theory (Functional analysis, gauge theory, and quantum mechanics) (Course webpage and lecture notes)

Spring 2023: Differential Topology (Course webpage)

Fall 2022: Topics in Mathematical Physics (Course Webpage.)

Spring 2022: Differential Topology


Brief biography

Previously, I held postdoctoral and DECRA Research Fellow positions, funded by the Australian Research Council, and was based at the University of Adelaide.

My formal education was in mathematics and physics at the University of Oxford, University of Cambridge, and the National University of Singapore.

I also worked briefly as a Research Assistant at the Centre for Quantum Technologies, NUS.



I am a mathematical physicist. My research interest revolves around K-theory, index theory, noncommutative geometry, operator algebras, and functional analysis, usually in the usually in the physical contexts of quantum systems such as topological-geometric phases of matter.

Currently, I am investigating the role of higher trace formulae in coarse geometry and index theory, for application in rigorously understanding "macroscopically quantized physics" (Lecture slides) , as dramatically manifested in the famous quantized Hall conductivity.

The latter is a profound experimental phenomenon which, since 2019, gives humanity the modern mass standard via macroscopic and robust access to Planck's constant.

See the Essay by the discoverer of the quantum Hall effect himself.



Feel free to contact me if you wish to discuss research projects involving geometry, topology, analysis and physics.

BICMR has openings for doctoral and postdoctoral positions.


Notes for recent talks

  1. Quantum kilogram, large-scale index, quantum Hall effect [ Notes ]


  1. Fock space: A bridge between Fredholm index and the quantum Hall effect (with J. Xia) arXiv:2401.07449
  2. Index of Bargmann-Fock space and Landau levels arXiv:2401.06660
  3. Quantization of conductance and the coarse cohomology of partitions (with M. Ludewig) arXiv:2308.02819 [ Slides ]

Refereed Journal Articles

  1. Topological edge states of 1D chains and index theory. J. Math. Phys. 64 061901 (2023) arXiv:2303.09505

  2. Bulk-interface correspondences for one dimensional topological materials with inversion symmetry. (With H. Zhang) Proc. R. Soc. A 479 20220675 (2023) arXiv:2209.03111

  3. Topology in shallow-waver waves: A spectral flow perspective. (With C. Tauber) Ann. Henri Poincaré 24 107-132 (2023) arXiv:2110.04097

  4. Delocalized spectra of Landau operators on helical surfaces. (With M. Ludewig and Y. Kubota) Commun. Math. Phys. 395(3) 1121-1242 (2022) arXiv:2201.05416

  5. Large-scale geometry obstructs localization. (With M. Ludewig) J. Math. Phys. Special Collection on the Proceedings on Mathematical Aspects of Topological Phases, 63 091902 (2022) arXiv:2204.12895

  6. Cobordism invariance of topological edge-following states. (With M. Ludewig) Adv. Theor. Math. Phys. 26(3) 673-710 (2022) arXiv:2001.08339

  7. 'Real' Fermi gerbes and Dirac cones of topological insulators. (With K. Gomi) Commun. Math. Phys. 388(3) 1507-1555 (2021) arXiv:2103.05350

  8. Twisted crystallographic T-duality via the Baum-Connes isomorphism. (With K. Gomi, Y. Kubota) Int. J. Math. 32(10) 2150078 (2021) arXiv:2102.00393

  9. Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry. (With M. Ludewig) Commun. Math. Phys. 386(1) 87-106 (2021) arXiv:2009.07688

  10. The Fermi gerbe of Weyl semimetals. (With A. Carey) Lett. Math. Phys. 111(3) 72 (2021) arXiv:2009.02064

  11. On Spectral Flow and Fermi Arcs. Commun. Math. Phys. 385(1) 465-493 (2021) arXiv:2007.06193

  12. Edge-following Topological States. J. Geom. Phys. 156 103796 (2020) arXiv:1908.09559

  13. Good Wannier bases in Hilbert modules associated to topological insulators. (With M. Ludewig) J. Math. Phys. 61 061902 (2020) arXiv:1904.13051

  14. Topological phases on the hyperbolic plane: fractional bulk-boundary correpondence. (With V. Mathai) Adv. Theor. Math. Phys. 23(3) 803-840 (2019) arXiv:1712.02952

  15. Topological characterization of classical waves: the topological origin of magnetostatic surface spin waves. (With K. Yamamoto, P. Pirro, K.-W. Kim, K. Everschor-Sitte, E. Saitoh) Phys. Rev. Lett. 122 217201 (2019) arXiv:1905.07907

  16. Crystallographic T-duality. (With K. Gomi) J. Geom. Phys. 139 50-77 (2019) arXiv:1806.11385

  17. Crystallographic bulk-edge correspondence: glide reflections and twisted mod 2 indices. (With K. Gomi) Lett. Math. Phys. 109(4) 857-904 (2019) arXiv:1804.03945

  18. T-duality simplifies bulk-boundary correspondence: the noncommutative case. (With K.C. Hannabuss, V. Mathai) Lett. Math. Phys. 108(5) 1163-1201 (2018) arXiv:1603.00116

  19. Fu-Kane-Mele monopoles in semimetals. (With K. Sato and K. Gomi) Nucl. Phys. B 923 107-125 (2017) arXiv:1705/06657

  20. Differential topology of semimetals. (With V. Mathai) Commun. Math. Phys. 355(2) 561-602 (2017) arXiv:1611.08961

  21. Global topology of Weyl semimetals and Fermi arcs. (With V. Mathai) J. Phys. A: Math. Theor. (Letter) 50(11) 11LT01 (2017), Publicity at JPhys+ arXiv:1607.02242

  22. T-duality simplifies bulk-boundary correspondence: the parametrised case. (With K.C. Hannabuss, V. Mathai) Adv. Theor. Math. Phys. 20(5) 1193-1226 (2016) arXiv:1510.04785 

  23. T-duality simplifies bulk-boundary correspondence: some higher dimensional cases. (With V. Mathai) Ann. Henri Poincaré 17(12) 3399-3424 (2016) arXiv:1506.04492

  24. T-duality simplifies bulk-boundary correspondence. (With V. Mathai) Commun. Math. Phys. 345(2) 675-701 (2016) arXiv:1505.05250

  25. On the K-theoretic classification of topological phases of matter. Ann. Henri Poincaré 17(4) 757-794 (2016) arXiv:1406.7366

  26. T-duality of Topological Insulators. (With V. Mathai) J. Phys. A: Math. Theor. 48 42FT02 (2015) arXiv:1503.01206 

  27. Topological phases: isomorphism, homotopy and K-theory. Int. J. Geom. Methods Mod. Phys. 12 1550098 (2015) arXiv:1412.4191

  28. Degree of Separability of Bipartite Quantum States. Phys. Rev. A 82(1) 012332 (2010) arXiv:1005.3675

  29. Optimal Lewenstein--Sanpera Decomposition for two-qubit states using Semidefinite Programming. (With P. Raynal, B.-G. Englert) Phys. Rev. A 80(5) 052313 (2009) arXiv:0909.4599