ORCID Profile
0000-0002-1100-3595
Current Organisation
University of Adelaide
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Research Topics
In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Top 5 Research Topics
ANZSRC Field of Research (FoR)
Pure Mathematics | Geometry | Operator Algebras and Functional Analysis | Algebraic and Differential Geometry | Category Theory, K Theory, Homological Algebra | Topology And Manifolds | Topology | Theoretical Physics | Category Theory, K Theory, Homological Algebra | Functional Analysis | Statistical Mechanics, Physical Combinatorics and Mathematical Aspects of Condensed Matter | Mathematical Aspects of Quantum and Conformal Field Theory, Quantum Gravity and String Theory | Partial Differential Equations
ANZSRC Socio-Economic Objective (SEO)
Expanding Knowledge in the Mathematical Sciences | Mathematical sciences | Expanding Knowledge in the Physical Sciences | Physical sciences |
Related Links
Publications
Quantum Hall effect on the hyperbolic plane in the presence of disorder
Publisher: Springer Science and Business Media LLC
Date: 1999
Quantising proper actions on $\mathrm{Spin}^c$-manifolds
Publisher: International Press of Boston
Date: 2017
Type-I D-branes in an H-flux and twisted KO-theory
Publisher: Springer Science and Business Media LLC
Date: 24-11-2003
Arithmetic properties of eigenvalues of generalized Harper operators on graphs
Publisher: Springer Science and Business Media LLC
Date: 20-12-2006
Inequalities for the Novikov-Shubin invariants
Publisher: American Mathematical Society (AMS)
Date: 1996
DOI: 10.1090/S0002-9939-96-03406-5
Abstract: In this paper, we prove that the Novikov-Shubin invariants satisfy a sequence of inequalities and deduce some useful consequences of this result.
Bundle gerbes and moduli spaces
Publisher: Elsevier BV
Date: 2012
Harmonic Cheeger–Simons characters with applications
Publisher: Elsevier BV
Date: 05-2009
L2 TORSION WITHOUT THE DETERMINANT CLASS CONDITION AND EXTENDED L2 COHOMOLOGY
Publisher: World Scientific Pub Co Pte Lt
Date: 08-2005
DOI: 10.1142/S0219199705001866
Abstract: We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L 2 torsions which, unlike the work of the previous authors, requires no additional assumptions in particular we do not impose the determinant class condition. The resulting torsions are elements of the determinant line of the extended L 2 cohomology. Under the determinant class assumption the L 2 torsions of this paper specialize to the invariants studied in our previous work [6]. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler [3] we obtain a Cheeger–Müller type theorem stating the equality between the combinatorial and the analytic L 2 torsions.
HEAT KERNELS AND THOM FORMS
Publisher: Elsevier BV
Date: 02-1992
T-Duality Simplifies Bulk-Boundary Correspondence
Publisher: Springer Science and Business Media LLC
Date: 22-03-2016
PARAMETRIZED STRICT DEFORMATION QUANTIZATION OF C*-BUNDLES AND HILBERT C*-MODULES
Publisher: Cambridge University Press (CUP)
Date: 02-2011
DOI: 10.1017/S1446788711001170
Abstract: In this paper, we review the parametrized strict deformation quantization of C * -bundles obtained in a previous paper, and give more ex les and applications of this theory. In particular, it is used here to classify H 3 -twisted noncommutative torus bundles over a locally compact space. This is extended to the case of general torus bundles and their parametrized strict deformation quantization. Rieffel’s basic construction of an algebra deformation can be mimicked to deform a monoidal category, which deforms not only algebras but also modules. As a special case, we consider the parametrized strict deformation quantization of Hilbert C * -modules over C * -bundles with fibrewise torus action.
Approximating spectral invariants of Harper operators on graphs II
Publisher: American Mathematical Society (AMS)
Date: 20-09-2002
DOI: 10.1090/S0002-9939-02-06739-4
Abstract: We study Harper operators and the closely related discrete magnetic Laplacians (DML) on a graph with a free action of a discrete group, as defined by Sunada. The spectral density function of the DML is defined using the von Neumann trace associated with the free action of a discrete group on a graph. The main result in this paper states that when the group is amenable, the spectral density function is equal to the integrated density of states of the DML that is defined using either Dirichlet or Neumann boundary conditions. This establishes the main conjecture in a paper by Mathai and Yates. The result is generalized to other self adjoint operators with finite propagation speed.
Flux compactifications on projective spaces and the $S$-duality puzzle
Publisher: International Press of Boston
Date: 2006
Some Relations between Twisted K-theory and E8 Gauge Theory
Publisher: Springer Science and Business Media LLC
Date: 05-03-2004
On the homotopy invariance of L-2 torsion for covering spaces
Publisher: American Mathematical Society (AMS)
Date: 1998
DOI: 10.1090/S0002-9939-98-04595-X
Abstract: We prove the homotopy invariance of L 2 L^2 torsion for covering spaces, whenever the covering transformation group is either residually finite or amenable. In the case when the covering transformation group is residually finite and when the L 2 L^2 cohomology of the covering space vanishes, the homotopy invariance was established by Lück. We also give some applications of our results.
T-duality for circle bundles via noncommutative geometry
Publisher: International Press of Boston
Date: 2014
T-duality for principal torus bundles
Publisher: Springer Science and Business Media LLC
Date: 05-03-2004
Exotic twisted equivariant K-theory
Publisher: Elsevier BV
Date: 12-2020
Von Neumann spectra near the spectral gap
Publisher: Elsevier BV
Date: 04-1998
T-Duality for Torus Bundles with H-Fluxes via Noncommutative Topology
Publisher: Springer Science and Business Media LLC
Date: 27-08-2004
Twisted K-Theory and K-Theory of Bundle Gerbes
Publisher: Springer Science and Business Media LLC
Date: 06-2002
Twisted analytic torsion
Publisher: Springer Science and Business Media LLC
Date: 03-2010
Superconnections, Thom classes and equivariant differential forms
Publisher: Elsevier BV
Date: 1986
T-duality for principal torus bundles and dimensionally reduced Gysin sequences
Publisher: International Press of Boston
Date: 2005
The Novikov conjecture for low degree cohomology classes
Publisher: Springer Science and Business Media LLC
Date: 2003
Twisted higher index theory on good orbifolds, II: fractional quantum numbers
Publisher: Springer Science and Business Media LLC
Date: 02-2001
$T$-duality simplifies bulk-boundary correspondence: the parametrised case
Publisher: International Press of Boston
Date: 2016
Chern Character in Twisted K -Theory: Equivariant and Holomorphic Cases
Publisher: Springer Science and Business Media LLC
Date: 05-2003
T-Duality: Topology Change from H-Flux
Publisher: Springer Science and Business Media LLC
Date: 11-06-2004
Von Neumann algebra invariants of Dirac operators
Publisher: Elsevier BV
Date: 1998
Positive scalar curvature metrics via end-periodic manifolds
Publisher: Mathematical Sciences Publishers
Date: 28-07-2020
Conformal invariants of twisted Dirac operators and positive scalar curvature
Publisher: Elsevier BV
Date: 08-2013
Fractional quantum numbers, complex orbifolds and noncommutative geometry
Publisher: IOP Publishing
Date: 07-2021
Twisted index theory on good orbifolds, I: Noncommutative Bloch theory
Publisher: World Scientific Pub Co Pte Lt
Date: 11-1999
DOI: 10.1142/S0219199799000213
Abstract: We study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group. We apply these results to obtain qualitative results on real and complex hyperbolic spaces in two and four dimensions, related to generalizations of the Bethe–Sommerfeld conjecture and the Ten Martini Problem, on the spectrum of self adjoint elliptic operators which are invariant under a projective action of a discrete cocompact group.
T-duality as a duality of loop group bundles
Publisher: IOP Publishing
Date: 31-03-2009
Twisted chiral de Rham complex, generalized geometry, and T-duality
Publisher: Springer Science and Business Media LLC
Date: 06-06-2015
D-Branes, RR-Fields and Duality on Noncommutative Manifolds
Publisher: Springer Science and Business Media LLC
Date: 05-12-2007
D-branes, B fields and twisted K theory
Publisher: Springer Science and Business Media LLC
Date: 06-03-2000
Fractional quantum numbers via complex orbifolds
Publisher: Springer Science and Business Media LLC
Date: 27-06-2019
On Mysteriously Missing T-duals, H-flux and the T-duality Group
Publisher: WORLD SCIENTIFIC
Date: 12-2006
Geometry of pseudodifferential algebra bundles and Fourier integral operators
Publisher: Duke University Press
Date: 15-07-2017
The index of projective families of elliptic operators
Publisher: Mathematical Sciences Publishers
Date: 03-2005
A noncommutative sigma-model
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 2011
DOI: 10.4171/JNCG/75
Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality
Publisher: Elsevier BV
Date: 06-2015
Topology andH
Publisher:
American Physical Society (APS)
Date:
06-05-2004
Publisher: American Physical Society (APS)
Date: 06-05-2004
Differential Topology of Semimetals
Publisher: Springer Science and Business Media LLC
Date: 25-07-2017
Equivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in K-theory
Publisher: Walter de Gruyter GmbH
Date: 04-2005
Topology and Flux of T-Dual Manifolds with Circle Actions
Publisher: Springer Science and Business Media LLC
Date: 08-2012
Approximating L-2 invariants of amenable covering spaces: A combinatorial approach
Publisher: Elsevier BV
Date: 04-1998
T-duality of topological insulators
Publisher: IOP Publishing
Date: 23-09-2015
Chemistry of Sodium Lactate Formation under Simulated Alumina Refinery Conditions
Publisher: American Chemical Society (ACS)
Date: 30-05-2003
DOI: 10.1021/IE020817W
Geometric quantization and families of inner products
Publisher: Elsevier BV
Date: 09-2015
Group dualities, T-dualities, and twisted K-theory
Publisher: Wiley
Date: 15-11-2017
DOI: 10.1112/JLMS.12085
Nonassociative Strict Deformation Quantization of C*-Algebras and Nonassociative Torus Bundles
Publisher: Springer Science and Business Media LLC
Date: 17-06-2012
Spherical T-duality and the spherical Fourier–Mukai transform
Publisher: Elsevier BV
Date: 11-2018
Index type invariants for twisted signature complexes and homotopy invariance
Publisher: Cambridge University Press (CUP)
Date: 24-02-2014
DOI: 10.1017/S030500411400005X
Abstract: For a closed, oriented, odd dimensional manifold X , we define the rho invariant ρ( X , ${\\cal E}$ , H ) for the twisted odd signature operator valued in a flat hermitian vector bundle ${\\cal E}$ , where H = ∑ i j +1 H 2 j +1 is an odd-degree closed differential form on X and H 2 j +1 is a real-valued differential form of degree 2 j +1. We show that ρ( X , ${\\cal E}$ , H ) is independent of the choice of metrics on X and ${\\cal E}$ and of the representative H in the cohomology class [ H ]. We establish some basic functorial properties of the twisted rho invariant. We express the twisted eta invariant in terms of spectral flow and the usual eta invariant. In particular, we get a simple expression for it on closed oriented 3-dimensional manifolds with a degree three flux form. A core technique used is our analogue of the Atiyah–Patodi–Singer theorem, which we establish for the twisted signature operator on a compact, oriented manifold with boundary. The homotopy invariance of the rho invariant ρ( X , ${\\cal E}$ , H ) is more delicate to establish, and is settled under further hypotheses on the fundamental group of X .
Exotic Twisted Equivariant Cohomology of Loop Spaces, Twisted Bismut–Chern Character and T-Duality
Publisher: Springer Science and Business Media LLC
Date: 23-01-2015
On a generalised Connes–Hochschild–Kostant–Rosenberg theorem
Publisher: Elsevier BV
Date: 03-2006
Discrete Morse theory and extended L(2) homology
Publisher: Elsevier BV
Date: 10-1999
HOLOMORPHIC QUILLEN DETERMINANT LINE BUNDLES ON INTEGRAL COMPACT KAHLER MANIFOLDS
Publisher: Oxford University Press (OUP)
Date: 04-01-2013
DOI: 10.1093/QMATH/HAS040
Spectral flow, eta invariants, and von Neumann algebras
Publisher: Elsevier BV
Date: 11-1992
T-Duality in Type II String Theory via Noncommutative Geometry and Beyond
Publisher: Oxford University Press (OUP)
Date: 2007
DOI: 10.1143/PTPS.171.237
Global topology of Weyl semimetals and Fermi arcs
Publisher: IOP Publishing
Date: 10-02-2017
$T$-duality for torus bundles with $H$-fluxes via noncommutative topology. {II}. The high-dimensional case and the $T$-duality group
Publisher: International Press of Boston
Date: 2006
Non-commutative correspondences, duality and D-branes in bivariant K-theory
Publisher: International Press of Boston
Date: 2009
Spherical T-Duality
Publisher: Springer Science and Business Media LLC
Date: 07-04-2015
Spherical T-duality II: An infinity of spherical T-duals for non-principal
Publisher:
Elsevier BV
Date:
06-2015
Publisher: Elsevier BV
Date: 06-2015
D-branes, KK-theory and duality on noncommutative spaces
Publisher: IOP Publishing
Date: 02-2008
Higher localised A-genera for proper actions and applications
Publisher: Elsevier BV
Date: 12-2022
Geometric quantization for proper actions
Publisher: Elsevier BV
Date: 10-2010
Approximating L2‐invariants and the Atiyah conjecture
Publisher: Wiley
Date: 23-04-2003
DOI: 10.1002/CPA.10076
On the Chern Character in Higher Twisted K-Theory and Spherical T-Duality
Publisher: Springer Science and Business Media LLC
Date: 05-05-2021
Analytic torsion of ℤ₂-graded elliptic complexes
Publisher: American Mathematical Society
Date: 2011
Topological phases on the hyperbolic plane: fractional bulk-boundary correspondence
Publisher: International Press of Boston
Date: 2019
Approximating spectral invariants of Harper operators on graphs
Publisher: Elsevier BV
Date: 2002
Spectral sections, twisted rho invariants and positive scalar curvature
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 2015
DOI: 10.4171/JNCG/209
L2-torsion invariants
Publisher: Elsevier BV
Date: 12-1992
Quantum Hall effect on the hyperbolic plane
Publisher: Springer Science and Business Media LLC
Date: 1998
L2-analytic torsion
Publisher: Elsevier BV
Date: 08-1992
Fractional analytic index
Publisher: International Press of Boston
Date: 10-2006
T-duality of singular spacetime compactifications in an H-flux
Publisher: Elsevier BV
Date: 07-2018
Homotopy invariance of Novikov-Shubin invariants and L-2 Betti numbers
Publisher: American Mathematical Society (AMS)
Date: 1997
T-Duality Simplifies Bulk–Boundary Correspondence: Some Higher Dimensional Cases
Publisher: Springer Science and Business Media LLC
Date: 10-06-2016
The Ring Structure of Twisted Equivariant KK-Theory for Noncompact Lie Groups
Publisher: Springer Science and Business Media LLC
Date: 14-06-2021
Operator Algebra Quantum Homogeneous Spaces of Universal Gauge Groups
Publisher: Springer Science and Business Media LLC
Date: 04-2011
T-Duality in an H-Flux: Exchange of Momentum and Winding
Publisher: Springer Science and Business Media LLC
Date: 28-02-2018
Yang–Mills theory for bundle gerbes
Publisher: IOP Publishing
Date: 03-05-2006
Witten Genus and Elliptic Genera for Proper Actions
Publisher: Springer Science and Business Media LLC
Date: 12-2022
T-duality simplifies bulk–boundary correspondence: the noncommutative case
Publisher: Springer Science and Business Media LLC
Date: 22-11-2017
Correspondences, von Neumann algebras and holomorphic L-2 torsion
Publisher: Canadian Mathematical Society
Date: 08-2000
Abstract: Given a holomorphic Hilbertian bundle on a compact complex manifold, we introduce the notion of holomorphic L 2 torsion, which lies in the determinant line of the twisted L 2 Dolbeault cohomology and represents a volume element there. Here we utilise the theory of determinant lines of Hilbertian modules over finite von Neumann algebras as developed in [CFM]. This specialises to the Ray-Singer-Quillen holomorphic torsion in the finite dimensional case. We compute ametric variation formula for the holomorphic L 2 torsion, which shows that it is not in general independent of the choice of Hermitian metrics on the complex manifold and on the holomorphic Hilbertian bundle, which are needed to define it. We therefore initiate the theory of correspondences of determinant lines, that enables us to define a relative holomorphic L 2 torsion for a pair of flat Hilbertian bundles, which we prove is independent of the choice of Hermitian metrics on the complex manifold and on the flat Hilbertian bundles.
Noncommutative principal torus bundles via parametrised strict deformation quantization
Publisher: American Mathematical Society
Date: 2010
Nonassociative Tori and Applications to T-Duality
Publisher: Springer Science and Business Media LLC
Date: 09-03-2006
Related Organisations
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View Funded ActivityAustralian Laureate Fellowships - Grant ID: FL170100020
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