Beijing International Center for Mathematical Research
[email: guochuanthiang (at) bicmr (dot) pku (dot) edu (dot) cn ]
Fall 2022: Topics in Mathematical Physics
For graduates and advanced undergraduates. Topics: Spin geometry, gauge theory, index theory and K-theory, functional analysis and spectral theory, all from quantum physics point of view.
Contact me by email to discuss prerequisites
(Materials for Differential Topology, Spring 2022)
From 2017-2020, I was a DECRA Research Fellow, funded by the Australian Research Council, and based at the University of Adelaide.
From 2015-2017, I was a Postdoc at the School of Mathematical Sciences, University of Adelaide.
Prior to this, I completed a DPhil in Mathematics at the University of Oxford, a Masters degree (Part III of the Mathematical Tripos) at the University of Cambridge, and studied physics and mathematics at the National University of Singapore. I also had a stint as a Research Assistant at the Centre for Quantum Technologies, NUS.
Here is a more detailed (CV)
I am a mathematical physicist. My research interest revolves around K-theory, algebraic topology, noncommutative geometry, index theory, operator algebras, and functional analysis, usually in the physical contexts of topological phases of matter, quantum theory, and strings.
Currently, I am investigating the role of coarse geometry, gerbes, spectral flows, and dualities in contemporary physics problems.
Recent talk: What is a coarse index, physically? [Slides]
Large-scale geometry obstructs localization. (With M. Ludewig) arXiv:2204.12895
Delocalized spectra of Landau operators on helical surfaces. (With M. Ludewig and Y. Kubota) Commun. Math. Phys. (to appear) arXiv:2201.05416
Topology in shallow-waver waves: A spectral flow perspective. (With C. Tauber) Ann. Henri Poincaré (published online) arXiv:2110.04097
Cobordism invariance of topological edge-following states. (With M. Ludewig) Adv. Theor. Math. Phys. 26(3) (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. 16 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