Rennie, Adam

Top Publications

Year	Title
2016	Nonunital spectral triples and metric completeness in unbounded KK-theory Published in Journal of Functional Analysis
2017	The K-theoretic bulk-edge correspondence for topological insulators Published in Annales Henri Poincare
2014	Index theory for locally compact noncommutative geometries Published in Memoirs of the American Mathematical Society
2012	Riemannian manifolds in noncommutative geometry Published in Journal of Geometry and Physics
2011	Twisted cyclic theory, equivariant KK-theory and KMS states Published in Journal fuer die Reine und Angewandte Mathematik: Crelle's journal

Research Areas

Research Overview

My main topics of research fall under the heading of noncommutative geometry. This is a new approach to geometric and physical questions inspired by quantum mechanics.

As well as broadening and deepening our appreciation of geometry, this topic unsurprisingly has applications in physics. Much of what I do is about refining the mathematical toolkit to be more useful for the physical applications.

Available as Research Supervisor

Member Of

Australia and New Zealand Association of Mathematical Physics Member
Australian Mathematical Society Member
International Association of Mathematical Physics Member

Selected Publications

Journal Article

Year	Title
2022	Curvature of differentiable Hilbert modules and Kasparov modules Published In Advances in Mathematics
2022	The Friedrichs angle and alternating projections in Hilbert C^⁎-modules Published In Journal of Mathematical Analysis and Applications
2021	A Cuntz-Pimsner model for the C^⁎-algebra of a graph of groups Published In Journal of Mathematical Analysis and Applications
2020	The Cayley transform in complex, real and graded K -theory Published In International Journal of Mathematics
2020	The KO-valued spectral flow for skew-adjoint Fredholm operators Published In Journal of Topology and Analysis
2020	The godbillon-vey invariant and equivariant K K-theory Published In Annals of K-Theory
2019	Boundaries, spectral triples and K-homology Published In Journal of Noncommutative Geometry
2019	Constructing KMS states from infinite-dimensional spectral triples Published In Journal of Geometry and Physics
2019	Factorisation of equivariant spectral triples in unbounded KK-theory Published In Journal of the Australian Mathematical Society
2019	Poincare duality for Cuntz–Pimsner algebras Published In Advances in Mathematics
2019	The Cuntz-pimsner extension and mapping cone exact sequences Published In Mathematica Scandinavica
2019	Untwisting twisted spectral triples Published In International Journal of Mathematics
2018	Chern Numbers, Localisation and the Bulk-edge Correspondence for Continuous Models of Topological Phases Published In Mathematical Physics, Analysis and Geometry
2018	Erratum to: Groupoid algebras as cuntz-pimsner algebras (Mathematica Scandinavica (2018) 120: 1 (115–123) DOI: 10.7146/math.scand.a-25507) Published In Mathematica Scandinavica
2017	Corrigendum to “Generalised time functions and finiteness of the Lorentzian distance” [J. Geom. Phys. 106 (2016) 108–121] (S0393044016300614) (10.1016/j.geomphys.2016.03.018) Published In Journal of Geometry and Physics
2017	Groupoid Fell bundles for product systems over quasi-lattice ordered groups Published In Cambridge Philosophical Society: Mathematical Proceedings
2017	Groupoid algebras as Cuntz-Pimsner algebras Published In Mathematica Scandinavica: ediderunt societates mathematicae Daniae Fenniae Islandiae Norvegiae Sveci
2017	Non-commutative vector bundles for non-unital algebras Published In Symmetry, Integrability and Geometry: Methods and Applications
2017	The K-theoretic bulk-edge correspondence for topological insulators Published In Annales Henri Poincare
2017	The extension class and KMS states for Cuntz–Pimsner algebras of some bi-Hilbertian bimodules Published In Journal of Topology and Analysis
2016	A non-commutative framework for topological insulators Published In Reviews in Mathematical Physics: a journal for survey and expository articles in the field of mathematical physics
2016	Generalised time functions and finiteness of the Lorentzian distance Published In Journal of Geometry and Physics
2016	Indefinite Kasparov modules and pseudo-Riemannian manifolds Published In Annales Henri Poincare
2016	Nonunital spectral triples and metric completeness in unbounded KK-theory Published In Journal of Functional Analysis
2016	Shift¿tail equivalence and an unbounded representative of the Cuntz¿Pimsner extension Published In Ergodic Theory and Dynamical Systems
2016	Universal measurability and the Hochschild class of the Chern character Published In Journal of Spectral Theory
2015	Spectral flow for nonunital spectral triples Published In Canadian Journal of Mathematics
2015	The bulk-edge correspondence for the quantum hall effect in Kasparov Theory Published In Letters in Mathematical Physics
2014	Dense domains, symmetric operators and spectral triples Published In The New York Journal of Mathematics
2014	Index theory for locally compact noncommutative geometries Published In Memoirs of the American Mathematical Society
2014	The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podle´s sphere Published In Journal of Noncommutative Geometry
2013	Pseudo-Riemannian spectral triples and the harmonic oscillator Published In Journal of Geometry and Physics
2013	The K-theory of Heegaard quantum lens spaces Published In Journal of Noncommutative Geometry
2013	Twisted cyclic cohomology and modular fredholm modules Published In Symmetry, Integrability and Geometry: Methods and Applications
2012	A residue formula for the fundamental Hochschild 3-cocycle for SUq(2) Published In Journal of Lie Theory
2012	Integration on locally compact noncommutative spaces Published In Journal of Functional Analysis
2012	KK-theory and spectral flow in von Neumann algebras Published In Journal of K-theory
2012	Riemannian manifolds in noncommutative geometry Published In Journal of Geometry and Physics
2011	Families of type III KMS states on a class of C∗-algebras containing On and QN Published In Journal of Functional Analysis
2011	Twisted cyclic theory, equivariant KK-theory and KMS states Published In Journal fuer die Reine und Angewandte Mathematik: Crelle's journal
2010	Noncommutative atiyah-patodi-singer boundary conditions and index pairings in KK-theory Published In Journal fuer die Reine und Angewandte Mathematik: Crelle's journal
2010	Twisted cyclic theory and an index theory for the gauge invariant KMS state on the Cuntz algebra On Published In Journal of K-theory
2009	Noncommutative manifolds from Graph and k-Graph C-algebras Published In* Communications in Mathematical Physics
2009	Spectral flow invariants and twisted cyclic theory for the Haar state on SUq(2) Published In Journal of Geometry and Physics
2008	Orbifolds are not commutative geometries Published In Journal of the Australian Mathematical Society
2008	The Chern character of semifinite spectral triples Published In Journal of Noncommutative Geometry
2008	The chern character of semifinite spectral triples Published In Journal of Noncommutative Geometry
2008	The noncommutative geometry of k-graph C-algebras Published In* Journal of K-theory
2007	KK-theory and spectral flow in von Neumann algebras Published In Journal of K-theory
2007	The Dixmier trace and asymptotics of zeta functions Published In Journal of Functional Analysis
2004	Nonunital spectral triples associated to degenerate metrics Published In Reviews in Mathematical Physics
2004	The Hochschild class of the Chern character for semifinite spectral triples Published In Journal of Functional Analysis
2001	Commutative geometries are spin manifolds Published In Reviews in Mathematical Physics

Chapter

Year	Title
2013	Semi-finite noncommutative geometry and some applications Published In Noncommutative geometry and physics, 3
2013	The local index formula in noncommutative geometry revisited Published In Noncommutative geometry and physics, 3
2011	Modular index invariants of Mumford curves Published In Noncommutative Geometry
2011	Spectral triples: examples and index theory Published In Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory
2011	Type III KMS States on a Class of C-Algebras Containing O-n and Q(N) and Their Modular Index Published In* Perspectives on Noncommutative Geometry Publisher United States
2008	Semifinite spectral triples associated with graph C∗-algebras Published In Traces in Number Theory, Geometry and Quantum Fields (Aspects of Mathematics)

Investigator On

Year	Title
2022 - 2024	Topological stability from spectral analysis Awarded by: Australian Research Council (ARC) Funding Scheme: Discovery Projects
2012 - 2015	Invariants for dynamics via operator algebras Awarded by: Australian Research Council (ARC) Funding Scheme: Discovery Projects
2008	Modular index theory Awarded by: Australian Research Council (ARC) Funding Scheme: Discovery Projects

Impact Story

By definition, my research has no impact
Summary
``Impact'' is defined, in research management lingo, as a measurable effect on something outside academia. Measurable usually means concrete evidence of change to some economic or social variable. My work is in mathematics with applications in theoretical physics. So my ``end-users'' are not relevant for this exercise.

Detail View

Detail View Summary View
Field of Research
Countries / Regions
Beneficiaries

Beneficiary Quantification Description
External Partners
Evidence of Impact

Evidence Description
UOW Centres / Programs
UOW Researchers / Collaborators

Available as Research Supervisor

Potential Supervision Topics

Numerous topics in and around index theory, non-commutative geometry, operator algebras and their applications to physics.

Advisees

Graduate Advising Relationship

Degree	Research Title	Advisee
Doctor of Philosophy	Equilibrium States of C*-Algebras Associated to Graphs of Groups	Pedersen, Thomas
Doctor of Philosophy	Applications of Geometry and Topology in Quantum Physics	Alexander, Angus
Doctor of Philosophy	Gauge Theory in Noncommutative Geometry	Masters, Ada

Reviewer Of

many (Academic Article)

Contact Or Provider For Service

Head of Postgraduate Studies for Mathematics and Statistics Access Service

Organizer Of Event

Gongfest 2012 - 2018

Education And Training

Ph.D. in Pure mathematics, Adelaide University, Statistics, Pure and Applied Mathematics, Title: Noncommutative Spin Geometry

Keywords

Mathematical physics

Non-commutative geometry

Index theory

Full Name

Adam Rennie

Mailing Address

Northfields Ave

Wollongong

2522

Australia

Geographic Location

University of Wollongong

Orcid Id

http://orcid.org/0000-0001-7484-217X (confirmed)

Top Publications

Year	Title
2016	Nonunital spectral triples and metric completeness in unbounded KK-theory Published in Journal of Functional Analysis
2017	The K-theoretic bulk-edge correspondence for topological insulators Published in Annales Henri Poincare
2014	Index theory for locally compact noncommutative geometries Published in Memoirs of the American Mathematical Society
2012	Riemannian manifolds in noncommutative geometry Published in Journal of Geometry and Physics
2011	Twisted cyclic theory, equivariant KK-theory and KMS states Published in Journal fuer die Reine und Angewandte Mathematik: Crelle's journal

Research Areas

Research Overview

My main topics of research fall under the heading of noncommutative geometry. This is a new approach to geometric and physical questions inspired by quantum mechanics.

As well as broadening and deepening our appreciation of geometry, this topic unsurprisingly has applications in physics. Much of what I do is about refining the mathematical toolkit to be more useful for the physical applications.

Member Of

Australia and New Zealand Association of Mathematical Physics Member
Australian Mathematical Society Member
International Association of Mathematical Physics Member

Selected Publications

Journal Article

Year	Title
2022	Curvature of differentiable Hilbert modules and Kasparov modules Published In Advances in Mathematics
2022	The Friedrichs angle and alternating projections in Hilbert C^⁎-modules Published In Journal of Mathematical Analysis and Applications
2021	A Cuntz-Pimsner model for the C^⁎-algebra of a graph of groups Published In Journal of Mathematical Analysis and Applications
2020	The Cayley transform in complex, real and graded K -theory Published In International Journal of Mathematics
2020	The KO-valued spectral flow for skew-adjoint Fredholm operators Published In Journal of Topology and Analysis
2020	The godbillon-vey invariant and equivariant K K-theory Published In Annals of K-Theory
2019	Boundaries, spectral triples and K-homology Published In Journal of Noncommutative Geometry
2019	Constructing KMS states from infinite-dimensional spectral triples Published In Journal of Geometry and Physics
2019	Factorisation of equivariant spectral triples in unbounded KK-theory Published In Journal of the Australian Mathematical Society
2019	Poincare duality for Cuntz–Pimsner algebras Published In Advances in Mathematics
2019	The Cuntz-pimsner extension and mapping cone exact sequences Published In Mathematica Scandinavica
2019	Untwisting twisted spectral triples Published In International Journal of Mathematics
2018	Chern Numbers, Localisation and the Bulk-edge Correspondence for Continuous Models of Topological Phases Published In Mathematical Physics, Analysis and Geometry
2018	Erratum to: Groupoid algebras as cuntz-pimsner algebras (Mathematica Scandinavica (2018) 120: 1 (115–123) DOI: 10.7146/math.scand.a-25507) Published In Mathematica Scandinavica
2017	Corrigendum to “Generalised time functions and finiteness of the Lorentzian distance” [J. Geom. Phys. 106 (2016) 108–121] (S0393044016300614) (10.1016/j.geomphys.2016.03.018) Published In Journal of Geometry and Physics
2017	Groupoid Fell bundles for product systems over quasi-lattice ordered groups Published In Cambridge Philosophical Society: Mathematical Proceedings
2017	Groupoid algebras as Cuntz-Pimsner algebras Published In Mathematica Scandinavica: ediderunt societates mathematicae Daniae Fenniae Islandiae Norvegiae Sveci
2017	Non-commutative vector bundles for non-unital algebras Published In Symmetry, Integrability and Geometry: Methods and Applications
2017	The K-theoretic bulk-edge correspondence for topological insulators Published In Annales Henri Poincare
2017	The extension class and KMS states for Cuntz–Pimsner algebras of some bi-Hilbertian bimodules Published In Journal of Topology and Analysis
2016	A non-commutative framework for topological insulators Published In Reviews in Mathematical Physics: a journal for survey and expository articles in the field of mathematical physics
2016	Generalised time functions and finiteness of the Lorentzian distance Published In Journal of Geometry and Physics
2016	Indefinite Kasparov modules and pseudo-Riemannian manifolds Published In Annales Henri Poincare
2016	Nonunital spectral triples and metric completeness in unbounded KK-theory Published In Journal of Functional Analysis
2016	Shift¿tail equivalence and an unbounded representative of the Cuntz¿Pimsner extension Published In Ergodic Theory and Dynamical Systems
2016	Universal measurability and the Hochschild class of the Chern character Published In Journal of Spectral Theory
2015	Spectral flow for nonunital spectral triples Published In Canadian Journal of Mathematics
2015	The bulk-edge correspondence for the quantum hall effect in Kasparov Theory Published In Letters in Mathematical Physics
2014	Dense domains, symmetric operators and spectral triples Published In The New York Journal of Mathematics
2014	Index theory for locally compact noncommutative geometries Published In Memoirs of the American Mathematical Society
2014	The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podle´s sphere Published In Journal of Noncommutative Geometry
2013	Pseudo-Riemannian spectral triples and the harmonic oscillator Published In Journal of Geometry and Physics
2013	The K-theory of Heegaard quantum lens spaces Published In Journal of Noncommutative Geometry
2013	Twisted cyclic cohomology and modular fredholm modules Published In Symmetry, Integrability and Geometry: Methods and Applications
2012	A residue formula for the fundamental Hochschild 3-cocycle for SUq(2) Published In Journal of Lie Theory
2012	Integration on locally compact noncommutative spaces Published In Journal of Functional Analysis
2012	KK-theory and spectral flow in von Neumann algebras Published In Journal of K-theory
2012	Riemannian manifolds in noncommutative geometry Published In Journal of Geometry and Physics
2011	Families of type III KMS states on a class of C∗-algebras containing On and QN Published In Journal of Functional Analysis
2011	Twisted cyclic theory, equivariant KK-theory and KMS states Published In Journal fuer die Reine und Angewandte Mathematik: Crelle's journal
2010	Noncommutative atiyah-patodi-singer boundary conditions and index pairings in KK-theory Published In Journal fuer die Reine und Angewandte Mathematik: Crelle's journal
2010	Twisted cyclic theory and an index theory for the gauge invariant KMS state on the Cuntz algebra On Published In Journal of K-theory
2009	Noncommutative manifolds from Graph and k-Graph C-algebras Published In* Communications in Mathematical Physics
2009	Spectral flow invariants and twisted cyclic theory for the Haar state on SUq(2) Published In Journal of Geometry and Physics
2008	Orbifolds are not commutative geometries Published In Journal of the Australian Mathematical Society
2008	The Chern character of semifinite spectral triples Published In Journal of Noncommutative Geometry
2008	The chern character of semifinite spectral triples Published In Journal of Noncommutative Geometry
2008	The noncommutative geometry of k-graph C-algebras Published In* Journal of K-theory
2007	KK-theory and spectral flow in von Neumann algebras Published In Journal of K-theory
2007	The Dixmier trace and asymptotics of zeta functions Published In Journal of Functional Analysis
2004	Nonunital spectral triples associated to degenerate metrics Published In Reviews in Mathematical Physics
2004	The Hochschild class of the Chern character for semifinite spectral triples Published In Journal of Functional Analysis
2001	Commutative geometries are spin manifolds Published In Reviews in Mathematical Physics

Chapter

Year	Title
2013	Semi-finite noncommutative geometry and some applications Published In Noncommutative geometry and physics, 3
2013	The local index formula in noncommutative geometry revisited Published In Noncommutative geometry and physics, 3
2011	Modular index invariants of Mumford curves Published In Noncommutative Geometry
2011	Spectral triples: examples and index theory Published In Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory
2011	Type III KMS States on a Class of C-Algebras Containing O-n and Q(N) and Their Modular Index Published In* Perspectives on Noncommutative Geometry Publisher United States
2008	Semifinite spectral triples associated with graph C∗-algebras Published In Traces in Number Theory, Geometry and Quantum Fields (Aspects of Mathematics)

Investigator On

Year	Title
2022 - 2024	Topological stability from spectral analysis Awarded by: Australian Research Council (ARC) Funding Scheme: Discovery Projects
2012 - 2015	Invariants for dynamics via operator algebras Awarded by: Australian Research Council (ARC) Funding Scheme: Discovery Projects
2008	Modular index theory Awarded by: Australian Research Council (ARC) Funding Scheme: Discovery Projects

Impact Story

By definition, my research has no impact
Summary
``Impact'' is defined, in research management lingo, as a measurable effect on something outside academia. Measurable usually means concrete evidence of change to some economic or social variable. My work is in mathematics with applications in theoretical physics. So my ``end-users'' are not relevant for this exercise.

Detail View

Detail View Summary View
Field of Research
Countries / Regions
Beneficiaries

Beneficiary Quantification Description
External Partners
Evidence of Impact

Evidence Description
UOW Centres / Programs
UOW Researchers / Collaborators

Potential Supervision Topics

Numerous topics in and around index theory, non-commutative geometry, operator algebras and their applications to physics.

Advisees

Graduate Advising Relationship

Degree	Research Title	Advisee
Doctor of Philosophy	Equilibrium States of C*-Algebras Associated to Graphs of Groups	Pedersen, Thomas
Doctor of Philosophy	Applications of Geometry and Topology in Quantum Physics	Alexander, Angus
Doctor of Philosophy	Gauge Theory in Noncommutative Geometry	Masters, Ada

Reviewer Of

many (Academic Article)

Contact Or Provider For Service

Head of Postgraduate Studies for Mathematics and Statistics Access Service

Organizer Of Event

Gongfest 2012 - 2018

Education And Training

Ph.D. in Pure mathematics, Adelaide University, Statistics, Pure and Applied Mathematics, Title: Noncommutative Spin Geometry

Keywords

Mathematical physics

Non-commutative geometry

Index theory

Full Name

Adam Rennie

Mailing Address

Northfields Ave

Wollongong

2522

Australia

Geographic Location

University of Wollongong

Orcid Id

http://orcid.org/0000-0001-7484-217X (confirmed)

Overview

Top Publications

Research Areas

Research Overview

Available as Research Supervisor

Affiliation

Member Of

Publications

Selected Publications

Journal Article

Chapter

Funding

Investigator On

Impact

Impact Story

By definition, my research has no impact

Supervision

Available as Research Supervisor

Potential Supervision Topics

Advisees

Graduate Advising Relationship

Service

Reviewer Of

Contact Or Provider For Service

Organizer Of Event

Background

Education And Training

Keywords

Contact

Full Name

Mailing Address

Geographic Location

Identity

Orcid Id

Overview

Top Publications

Research Areas

Research Overview

Affiliation

Member Of

Publications

Selected Publications

Journal Article

Chapter

Funding

Investigator On

Impact

Impact Story

By definition, my research has no impact

Supervision

Potential Supervision Topics

Advisees

Graduate Advising Relationship

Service

Reviewer Of

Contact Or Provider For Service

Organizer Of Event

Background

Education And Training

Keywords

Contact

Full Name

Mailing Address

Geographic Location

Identity

Orcid Id

Visualisations

Research Areas