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: Methods of Modern Mathematical Physics (Noncommutative geometry, K-theory, operator algebras) (Course webpage)

Summer 2024: ECNU Lectures on Geometry and Physics. [ Notes ]

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

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.

 

Research

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 fractional 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.

 

Supervision

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 ]

Preprints

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

Refereed Journal Articles

  1. Fractional index of Bargmann-Fock space and Landau levels. J. Geom. Phys. (to appear) (2025) arXiv:2401.06660

  2. Topological semimetals. Encyclopedia of Math. Phys. (Second Edition), Vol. 1, 66-77 (2025) arXiv:2407.12692

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

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

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

  6. 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

  7. 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

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

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

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

  11. 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

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

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

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

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

  16. 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

  17. 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

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

  19. 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

  20. 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

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

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

  23. 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

  24. 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 

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

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

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

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

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

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

  31. 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