Assistant Professor
Beijing International Center for Mathematical Research
Peking University
[email: guochuanthiang (at) bicmr (dot) pku (dot) edu (dot) cn ]
[Office: 81-105]
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
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.
Topological edge states of 1D chains and index theory. J. Math. Phys. 64 061901 (2023) arXiv:2303.09505
Bulk-interface correspondences for one dimensional topological materials with inversion symmetry. (With H. Zhang) Proc. R. Soc. A 479 20220675 (2023) arXiv:2209.03111
Topology in shallow-waver waves: A spectral flow perspective. (With C. Tauber) Ann. Henri Poincaré 24 107-132 (2023) arXiv:2110.04097
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
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
Cobordism invariance of topological edge-following states. (With M. Ludewig) Adv. Theor. Math. Phys. 26(3) 673-710 (2022) arXiv:2001.08339
'Real' Fermi gerbes and Dirac cones of topological insulators. (With K. Gomi) Commun. Math. Phys. 388(3) 1507-1555 (2021) arXiv:2103.05350
Twisted crystallographic T-duality via the Baum-Connes isomorphism. (With K. Gomi, Y. Kubota) Int. J. Math. 32(10) 2150078 (2021) arXiv:2102.00393
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
The Fermi gerbe of Weyl semimetals. (With A. Carey) Lett. Math. Phys. 111(3) 72 (2021) arXiv:2009.02064
On Spectral Flow and Fermi Arcs. Commun. Math. Phys. 385(1) 465-493 (2021) arXiv:2007.06193
Edge-following Topological States. J. Geom. Phys. 156 103796 (2020) arXiv:1908.09559
Good Wannier bases in Hilbert modules associated to topological insulators. (With M. Ludewig) J. Math. Phys. 61 061902 (2020) arXiv:1904.13051
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
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
Crystallographic T-duality. (With K. Gomi) J. Geom. Phys. 139 50-77 (2019) arXiv:1806.11385
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
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
Fu-Kane-Mele monopoles in semimetals. (With K. Sato and K. Gomi) Nucl. Phys. B 923 107-125 (2017) arXiv:1705/06657
Differential topology of semimetals. (With V. Mathai) Commun. Math. Phys. 355(2) 561-602 (2017) arXiv:1611.08961
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
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
T-duality simplifies bulk-boundary correspondence: some higher dimensional cases. (With V. Mathai) Ann. Henri Poincaré 17(12) 3399-3424 (2016) arXiv:1506.04492
T-duality simplifies bulk-boundary correspondence. (With V. Mathai) Commun. Math. Phys. 345(2) 675-701 (2016) arXiv:1505.05250
On the K-theoretic classification of topological phases of matter. Ann. Henri Poincaré 17(4) 757-794 (2016) arXiv:1406.7366
T-duality of Topological Insulators. (With V. Mathai) J. Phys. A: Math. Theor. 48 42FT02 (2015) arXiv:1503.01206
Topological phases: isomorphism, homotopy and K-theory. Int. J. Geom. Methods Mod. Phys. 12 1550098 (2015) arXiv:1412.4191
Degree of Separability of Bipartite Quantum States. Phys. Rev. A 82(1) 012332 (2010) arXiv:1005.3675
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