Publications
Preprints
Fock space: A bridge between Fredholm index and the quantum Hall effect (with J. Xia)
Index of Bargmann-Fock space and Landau levels
Quantization of conductance and the coarse cohomology of partitions (with M. Ludewig)
Refereed Journal Articles
Topological edge states of 1D chains and index theory.
J. Math. Phys. 64 061901 (2023)
Bulk-interface correspondences for one dimensional topological materials with inversion symmetry. (With H. Zhang)
Proc. R. Soc. A 479 20220675 (2023)
Topology in shallow-waver waves: A spectral flow perspective. (With C. Tauber)
Ann. Henri Poincaré 24 107-132 (2023)
Delocalized spectra of Landau operators on helical surfaces. (With M. Ludewig and Y. Kubota)
Commun. Math. Phys. 395(3) 1121-1242 (2022)
Large-scale geometry obstructs localization. (With M. Ludewig)
J. Math. Phys. 63 091902 (2022)
Special Collection on the Proceedings on Mathematical Aspects of Topological Phases, <strong>63</strong> <a arXiv:2204.12895
Cobordism invariance of topological edge-following states. (With M. Ludewig)
Adv. Theor. Math. Phys. 26(3) 673-701 (2022)
'Real' Fermi gerbes and Dirac cones of topological insulators. (With K. Gomi)
Commun. Math. Phys. 388(3) 1507--1555 (2021)
Twisted crystallographic T-duality via the Baum-Connes isomorphism. (With K. Gomi, Y. Kubota)
Int. J. Math. 32(10) 2150078 (2021)
The Fermi gerbe of Weyl semimetals. (With A. Carey)
Lett. Math. Phys. 111(3) 72 (2021)
Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry. (With M. Ludewig)
Commun. Math. Phys. 386(1) 87-106 (2021)
On Spectral Flow and Fermi Arcs.
Commun. Math. Phys. 385(1) 465-493 (2021)
Edge-following Topological States.
J. Geom. Phys. 156 103796 (2020)
Good Wannier bases in Hilbert modules associated to topological insulators. (With M. Ludewig)
J. Math. Phys. 16 061902 (2020)
Topological phases on the hyperbolic plane: fractional bulk-boundary correpondence. (With V. Mathai)
Adv. Theor. Math. Phys. 23(3) 803-840 (2019)
Topological characterization of classical waves: the topological origin of magnetostatic surface spin waves. (With K. Yamamoto, G.C. Thiang, P. Pirro, K.-W. Kim, K. Everschor-Sitte, E. Saitoh)
Phys. Rev. Lett. 122 217201 (2019)
Crystallographic T-duality. (With K. Gomi)
J. Geom. Phys. 139 50-77 (2019)
Crystallographic bulk-edge correspondence: glide reflections and twisted mod 2 indices. (With K. Gomi)
Lett. Math. Phys. 109(4) 857-904 (2019)
T-duality simplifies bulk-boundary correspondence: the noncommutative case. (With K.C. Hannabuss, V. Mathai)
Lett. Math. Phys. 108(5) 1163-1201 (2018)
Fu-Kane-Mele monopoles in semimetals. (With K. Sato and K. Gomi)
Nucl. Phys. B 923 107-125 (2017)
Differential topology of semimetals. (With V. Mathai)
Commun. Math. Phys. 355(2) 561-602 (2017)
Global topology of Weyl semimetals and Fermi arcs. (With V. Mathai)
J. Phys. A: Math. Theor. (Letter) 50(11) 11LT01 (2017), Publicity at JPhys+
T-duality simplifies bulk-boundary correspondence: the parametrised case. (With K.C. Hannabuss, V. Mathai)
Adv. Theor. Math. Phys. 20(5) 1193-1226 (2016)
T-duality simplifies bulk-boundary correspondence: some higher dimensional cases. (With V. Mathai)
Ann. Henri Poincaré 17(12) 3399-3424 (2016)
T-duality simplifies bulk-boundary correspondence. (With V. Mathai)
Commun. Math. Phys. 345(2) 675-701 (2016)
On the K-theoretic classification of topological phases of matter.
Ann. Henri Poincaré 17(4) 757-794 (2016)
T-duality of Topological Insulators. (With V. Mathai)
J. Phys. A: Math. Theor. 48 42FT02 (2015)
Topological phases: isomorphism, homotopy and K-theory.
Int. J. Geom. Methods Mod. Phys. 12 1550098 (2015)
Degree of Separability of Bipartite Quantum States.
Phys. Rev. A 82(1) 012332 (2010)
Optimal Lewenstein--Sanpera Decomposition for two-qubit states using Semidefinite Programming. (With P. Raynal, B.-G. Englert)
Phys. Rev. A 80(5) 052313 (2009)
Refereed Conference Proceedings
T-duality and K-theory: a view from condensed matter physics.
In: Noncommutative Geometry and Physics IV, proceedings for TFC thematic year 2015 on "Strings, Black Holes and Quantum Information" (2017)
On the K-theoretic classification of topological phases of matter (conspectus)
In: Proceedings of Frontiers of Fundamental Physics 14 (2014)
Edited Volume
V. Mathai, G.C. Thiang, P. Hekmati, H. Bursztyn, P. Bouwknegt, D. Baraglia,
String geometries, dualities and topological matter.
J. Geom. Phys. 138 (2019)