Publications

Preprints

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. 63 091902 (2022)

Special Collection on the Proceedings on Mathematical Aspects of Topological Phases, <strong>63</strong> <a arXiv:2204.12895

6. Cobordism invariance of topological edge-following states. (With M. Ludewig)

Adv. Theor. Math. Phys. 26(3) 673-701 (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. The Fermi gerbe of Weyl semimetals. (With A. Carey)

Lett. Math. Phys. 111(3) 72 (2021)

arXiv:2009.02064

10. 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

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. 16 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, G.C. Thiang, 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

Refereed Conference Proceedings

1. 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)

2. On the K-theoretic classification of topological phases of matter (conspectus)

In: Proceedings of Frontiers of Fundamental Physics 14 (2014)

Edited Volume

1. V. Mathai, G.C. Thiang, P. Hekmati, H. Bursztyn, P. Bouwknegt, D. Baraglia,

String geometries, dualities and topological matter.

J. Geom. Phys. 138 (2019)