Proof of the magnetic gap-labelling conjecture for
principal solenoidal tori
(with M. T. Benameur), 9 pages,
[1806.06302]
Witten Genus and Elliptic genera for proper actions,
(with Fei Han), 26 pages,
[1807.0????]
Very recent refereed publications (2014-)
Gap-labelling conjecture with non-zero magnetic field, (with M-T. Benameur)
Advances in Mathematics325, (2018) 116-164, [1508.01064]
T-duality simplifies bulk-boundary correspondence: the noncommutative case
(with K. Hannabuss and G. C. Thiang),
Letters in Mathematical Physics,
108, no. 5 (2018) 1163-1201,[1603.00116]
Positive scalar curvature and Poincaré duality for proper actions,
(with Hao Guo and Hang Wang), Journal of Noncommutative Geometry, (to appear),46 pp
[1609.01404]
Geometry of Pseudodifferential algebra bundles
and Fourier Integral Operators
(with R.B. Melrose), Duke Mathematical Journal166 no.10 (2017) 1859-1922,[1210.0990]
Group dualities, T-dualities, and twisted K-theory, (with J. Rosenberg)
Journal of the London Mathematical Society,
97, no. 1 (2018) 1-23,,
[1603.00969]
T-duality simplifies bulk-boundary correspondence:
some higher dimensional cases
(with G.C. Thiang),
Annales Henri Poincare,
17 no. 12 (2016) 3399–3424,[1506.04492]
T-duality trivializes bulk-boundary correspondence:
the parametrised case
(with K. Hannabuss and G. C. Thiang),
Advances in Theoretical and Mathematical Physics,
20 no. 5 (2016)
1193-1226, [1510.04785]
Higher abelian gauge theory associated to gerbes on noncommutative deformed
M5-branes and S-duality (with H. Sati),
Journal of Geometry and Physics, 92 (2015) 240-251,
[1404.2257]
Spherical T-duality II: An infinity of spherical T-duals for
non-principal SU(2)-bundles
(with P.Bouwknegt and J.Evslin),
Journal of Geometry and Physics,
92 (2015) 46-54
[1409.1296]
Exotic twisted equivariant cohomology of loop spaces, twisted
Bismut-Chern character and T-duality
(with F.Han),
Communications in Mathematical Physics,
337, No. 1, (2015) 127-150.[1405.1320]
T-duality for circle bundles via noncommutative geometry
(with J. Rosenberg),
Advances in Theoretical and Mathematical Physics,
18, no. 6
(2014) 1437-1462,[1306.4198]
Index type invariants for twisted signature complexes and homotopy invariance
(with M-T. Benameur),
Mathematical Proceedings of the Cambridge Philosophical Society,156 no.3 (2014) 473-503,[1202.0272]
Refereed publication list (2008-2013; for ERA 2015)
Conformal invariants of twisted Dirac operators and positive scalar curvature
(with M-T. Benameur), Journal of Geometry and Physics,70 (2013) 39-47,[1210.0301] Erratum, Journal of Geometry and Physics,76 (2014) 263-264.
T-duality of current algebras and their quantization
(with P. Hekmati), Contemporary Mathematics,584 (2012) 17-38,[1203.1709]
Nonassociative strict deformation quantization of C*-algebras and
nonassociative torus bundles
(with K. Hannabuss), Letters in Mathematical Physics,102, No. 1 (2012), 107-123,[1012.2274]
Topology and Flux of T-Dual Manifolds with Circle Actions
(with S. Wu),
Communications in Mathematical Physics,316 (2012) 279-286.[1108.5045]
Bundle gerbes and moduli spaces
(with P. Bouwknegt and S. Wu),
Journal of Geometry and Physics,62 (2012) 1-10,[1107.3687]
Analytic torsion for twisted de Rham complexes,
(with
S. Wu), Journal of Differential Geometry,88 (2011) 297-332,[0810.4204]
Operator algebra quantum homogeneous spaces of universal gauge groups,
(with S. Mahanta), Letters in Mathematical Physics,97 (2011) 263-277.[1012.5893]
Parametrised strict deformation quantization of
C*-bundles and Hilbert C*-modules,
(with K. Hannabuss), Journal of the Australian Mathematical Society,90 no. 01 (2011) 25-38,[1007.4696]
Noncommutative principal torus bundles via parametrised
strict deformation quantization,
(with K. Hannabuss),
AMS Proceedings of Symposia in Pure Mathematics,81 (2010) 133-148,[0911.1886]
The index of projective families of elliptic operators: the decomposable case,
(with R.B. Melrose and I.M. Singer),
Astérisque,328 (2009) 255-296.[0809.0028]
The geometry of determinant line bundles in noncommutative geometry
(with P. Chakraborty),
Journal of Noncommutative Geometry,3 no.4 (2009) 559-578. [0804.3232v2]
Noncommutative correspondences, duality and D-branes in bivariant K-theory
(with J. Brodzki, J. Rosenberg and R. Szabo),
Advances in Theoretical and Mathematical Physics,13 no. 2 (2009) 497-552. [0708.2648]
D-branes, KK-theory and
duality on noncommutative spaces
(with J. Brodzki, J. Rosenberg and R. Szabo),
Journal of Physics: Conference Series,103 (2008) 012004,
13 pages.
[0709.2128]
Equivariant and fractional index of projective elliptic operators, (with
R.B. Melrose and I.M. Singer),
Journal of Differential Geometry, 78 no.3 (2008) 465-473.[math.DG/0611819]
D-Branes, RR-Fields and Duality on Noncommutative Manifolds
(with J. Brodzki, J. Rosenberg and R. Szabo),
Communications in Mathematical Physics,277, no.3 (2008) 643-706. [hep-th/0607020]
Some earlier refereed publications (since 1997)
T-duality in type II string theory via noncommutative geometry and beyond,
in "Noncommutative Geometry and Quantum Spacetime in Physics",
Proceedings of the 21st Nishinomiya-Yukawa Memorial Symposium,
Edited by N. Sasakura and S. Watamura,
Progress of Theoretical Physics Supplement,171, (2007) 237-257.
Entire cyclic homology of stable continuous trace algebras, (with
Danny Stevenson), Bulletin of the London Mathematical Society, 39 no. 1 (2007) 71-75 , [math.KT/0412485]
On mysteriously missing T-duals, H-flux and the T-duality
group
(with J. Rosenberg),
pages 350-358, in "Differential Geometry and Physics",
editors Mo-Lin Ge and Weiping Zhang,
Nankai Tracts in Mathematics, Volume 10,
World Scientific 2006.
[hep-th/0409073]
Quantum Hall effect and noncommutative geometry,
(with A. Carey
and K. Hannabuss), Journal of Geometry and Symmetry in Physics, 6 (2006) 16-37,[math.OA/0008115]
Flux compactification on projective spaces and the S-duality puzzle,
(with P. Bouwknegt, J. Evslin, B. Jurco and H. Sati),
Advances in Theoretical and Mathematical Physics,10 no. 3 (2006) 345-394 [hep-th/0501110]
K-theory,
pages 246-254, Encyclopedia of Mathematical Physics,
Editors: J. P. Francoise, G. Naber and S. T. Tsou, Elsevier, 2006.
Heat kernels and the range of the trace on completions of twisted group algebras
(with appendix by I. Chatterji), Contemporary Mathematics, 398
(2006) 321-346.
[math.KT/0606790]
Kato's inequality and asymptotic spectral
properties for discrete magnetic Laplacians
(with J. Dodziuk), Contemporary Mathematics, 398
(2006) 69-81. [math.SP/0312450]
Towards the fractional
quantum Hall effect: a noncommutative geometry perspective,
(with M. Marcolli),
"Noncommutative Geometry and Number Theory".
Editors C.Consani, M. Marcolli, Aspects of Mathematics, Vieweg Verlag,
Wiesbaden, 2006,
pages 235-261.
[cond-mat/0502356]
Arithmetic properties of eigenvalues of
generalized Harper operators on graphs,
(with J. Dodziuk and S. Yates), 28 pages,
Communications in Mathematical Physics, 262 no. 2 (2006) 269-297.
[math.SP/0311315]
T-duality for torus
bundles with H-fluxes
via noncommutative topology, II: the high-dimensional case
and the T-duality group
(with J. Rosenberg),
Advances in Theoretical and Mathematical Physics,10 no. 1 (2006) 123-158. [hep-th/0508084]
T-duality for principal torus
bundles and dimensionally reduced Gysin sequences
(with P. Bouwknegt and K. Hannabuss),
Advances in Theoretical and Mathematical Physics,9 no. 5 (2005) 749-773.
[hep-th/0412268]
L^{2}-torsion without the determinant
class
condition
and extended L^{2} cohomology,
(with M. Braverman, A. Carey and M. Farber), Communications in
Contemporary Mathematics,7 no. 4 (2005) 421-462.[math.DG/0406222]
Equivalence of spectral projections in
semiclassical limit and a vanishing theorem for higher traces in
K-theory,
(with
Y. Kordyukov and M.A. Shubin), J. Reine
Angew. Math. (Crelle Journal), 581 (2005) 193 - 236. [math.DG/0305189]
The index of projective families of elliptic
operators, (with
R.B. Melrose and I.M. Singer), Geometry and Topology, 9 (2005) 341-373. [math.DG/0206002]
Approximating L^{2}-invariants and the
Atiyah conjecture
(with J. Dodziuk, P. Linnell, T. Schick and S. Yates),
Communications on Pure and Applied Mathematics,56, no. 7, (2003), 839-873.
Chern character in twisted K-theory: equivariant
and
holomorphic cases, (with D. Stevenson), Communications in
Mathematical
Physics,236,
no. 1 (2003), 161-186.
The Novikov conjecture for low degree cohomology
classes, Geometriae Dedicata, (to appear).
Approximating Spectral invariants of Harper
operators on graphs II,
(with T. Schick and S. Yates), Proc. Amer. Math. Soc.,
131, no. 6 (2003), 1917-1923.
Twisted K-theory and K-theory of bundle
gerbes,(with P.
Bouwknegt, A. Carey, M. Murray and D. Stevenson), Communications in
Mathematical
Physics, 228, no. 1, (2002) 17-49.
Semiclassical asymptotics and gaps in the
spectra of
magnetic Schrödinger operators (with M. Shubin), Geometriae
Dedicata, 91, no. 1, (2002) 155-173.
Approximating spectral invariants of Harper
operators on graphs
(with S. Yates), J. Functional Analysis,
188 (2002), no. 1, 111--136.
Twisted index theory on good orbifolds,II:
fractional quantum
numbers, (with M. Marcolli) Communications in Mathematical
Physics, 217, no.1 (2001) 55-87.
On positivity of the Kadison constant and
noncommutative Bloch
theory, Tohoku Mathematical Publications,20 (2001)
107-124.
D-Branes, B-Fields and twisted K-theory (with
P. Bouwknegt),J. High Energy Phys., 03
(2000) 007 (11 pages).
Correspondences, von Neumann algebras and
holomorphic
L^{2} torsion (with A. Carey and M. Farber), Canadian
Journal of Mathematics , 52, (2000) no. 4,
695-736.
Quantum Hall effect on the hyperbolic plane in
the presence of
disorder (with A. Carey,
K. Hannabuss),Lett. Math. Phys., 47
(1999) 215-236.
K-theory of twisted group C^{*}-algebras
and positive
scalar curvature, Rothenberg Festschrift, Contemporary
Mathematics, 231(1999) 203-225.
Discrete Morse Theory and extended L^{2}
homology(with
S. Yates), J. Functional Analysis, 168
(1999) 84-110.
Twisted index theory on good orbifolds, I:
noncommutative Bloch
theory (with M. Marcolli),Communications in Contemporary
Mathematics, 1 (1999) 553-587.
On analytic torsion over C^{*} algebras
(with
A. Carey and A. Mishchenko), Banach Center
Publications, 49 (1999) 43-67.
L^{2} invariants on covering spaces, Geometric
analysis and Lie theory in mathematics and physics,
eds. A. Carey, M. Murray, Australian
Math. Soc. Lecture Series
No. 11,pp. 209-242, Cambridge University Press
(1998).
Quantum Hall Effect on the hyperbolic plane(with
A. Carey, K.
Hannabus and P. McCann), Communications in Mathematical
Physics, 190 No. 3 (1998) 629-673.
On the homotopy invariance of L^{2}
torsion for
covering spaces (with M. Rothenberg), Proc. Amer. Math. Soc.,126
(1998)
887-897.
Von Neumann spectra near the spectral gap(with
A. Carey,
T. Coulhon and J. Phillips),Bulletin des Sciences
Mathematiques, 122 (1998) 203-242.
Approximating L^{2} invariants for
amenable covering
spaces: a combinatorial approach (with J. Dodziuk), J. Functional Analysis,154
(1998) 1-21.
Von Neumann algebra invariants of Dirac
operators,J. Functional Analysis, 152 (1998)
1-21.
Equivariant holomorphic Morse inequalities: a
heat kernel
proof (with S. Wu), J. Differential Geometry, 46
(1997) 78-98.
Determinant Lines, Von Neumann algebras and L^{2}
torsion(with A. Carey and M. Farber),J. Reine
Angew. Math. (Crelle Journal), 484 (1997)
153-181.
Approximating L^{2} invariants for
amenable covering
spaces:a heat kernel approach (with J. Dodziuk),Contemporary
Mathematics, 211 (1997) 151-167.
Homotopy invariance of Novikov-Shubin invariants
and
L^{2} Betti numbers (with J. Block and
S. Weinberger),Proc. Amer. Math. Soc., 125
(1997) 3757-3762.