Rennie, Adam C.

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
2019	Boundaries, spectral triples and K-homology Published In Journal of Noncommutative Geometry Volume 13 Pages 407 - 472 ISSN 1661-6952 Altmetric
2019	Constructing KMS states from infinite-dimensional spectral triples Published In Journal of Geometry and Physics Volume 143 Pages 107 - 149 ISSN 0393-0440 Altmetric
2019	Factorisation of equivariant spectral triples in unbounded KK-theory Published In Journal of the Australian Mathematical Society Volume 107 Pages 145 - 180 ISSN 1446-7887 Altmetric
2019	Poincare duality for Cuntz–Pimsner algebras Published In Advances in Mathematics Volume 347 Pages 1112 - 1172 ISSN 0001-8708 Altmetric
2019	Untwisting twisted spectral triples Published In International Journal of Mathematics Altmetric
2018	Chern Numbers, Localisation and the Bulk-edge Correspondence for Continuous Models of Topological Phases Published In Mathematical Physics, Analysis and Geometry Volume 21 Pages 16-1 - 16-62 ISSN 1385-0172 Altmetric
2017	Groupoid Fell bundles for product systems over quasi-lattice ordered groups Published In Cambridge Philosophical Society: Mathematical Proceedings Volume 163 Pages 561 - 580 ISSN 0305-0041 Altmetric
2017	Groupoid algebras as Cuntz-Pimsner algebras Published In Mathematica Scandinavica: ediderunt societates mathematicae Daniae Fenniae Islandiae Norvegiae Sveci Volume 120 Pages 115 - 123 ISSN 0025-5521 Altmetric
2017	Non-commutative vector bundles for non-unital algebras Published In Symmetry, Integrability and Geometry: Methods and Applications Volume 13 Pages 041-1 - 041-12 ISSN 1815-0659 Altmetric
2017	The K-theoretic bulk-edge correspondence for topological insulators Published In Annales Henri Poincare Volume Online First Pages 1 - 34 ISSN 0018-0238 Altmetric
2017	The extension class and KMS states for Cuntz–Pimsner algebras of some bi-Hilbertian bimodules Published In Journal of Topology and Analysis Volume 9 Pages 297 - 327 ISSN 1793-5253 Altmetric
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 Volume 28 Pages 1650004-1 - 1650004-51 ISSN 0129-055X Altmetric
2016	Generalised time functions and finiteness of the Lorentzian distance Published In Journal of Geometry and Physics Volume 106 Pages 108 - 121 ISSN 0393-0440 Altmetric
2016	Indefinite Kasparov modules and pseudo-Riemannian manifolds Published In Annales Henri Poincare Volume 17 Pages 3255 - 3286 ISSN 0018-0238 Altmetric
2016	Nonunital spectral triples and metric completeness in unbounded KK-theory Published In Journal of Functional Analysis Volume 271 Pages 2460 - 2538 ISSN 0022-1236 Altmetric
2016	Shift¿tail equivalence and an unbounded representative of the Cuntz¿Pimsner extension Published In Ergodic Theory and Dynamical Systems Pages 1 - 33 ISSN 0143-3857 Altmetric
2016	Universal measurability and the Hochschild class of the Chern character Published In Journal of Spectral Theory Volume 6 Pages 1 - 41 Altmetric
2015	Spectral flow for nonunital spectral triples Published In Canadian Journal of Mathematics Volume 67 Pages 759 - 794 ISSN 0008-414X Altmetric
2015	The bulk-edge correspondence for the quantum hall effect in Kasparov Theory Published In Letters in Mathematical Physics Volume 105 Pages 1253 - 1273 ISSN 0377-9017 Altmetric
2014	Dense domains, symmetric operators and spectral triples Published In The New York Journal of Mathematics Volume 20 Pages 1001 - 1020 ISSN 1076-9803
2014	Index theory for locally compact noncommutative geometries Published In Memoirs of the American Mathematical Society Volume 231 Pages 1 - 131 ISSN 0065-9266 Altmetric
2014	The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podle´s sphere Published In Journal of Noncommutative Geometry Volume 8 Pages 1 - 43 ISSN 1661-6952 Altmetric
2013	Pseudo-Riemannian spectral triples and the harmonic oscillator Published In Journal of Geometry and Physics Volume 73 Pages 37 - 55 ISSN 0393-0440 Altmetric
2013	The K-theory of Heegaard quantum lens spaces Published In Journal of Noncommutative Geometry Volume 7 Pages 1185 - 1216 ISSN 1661-6952 Altmetric
2013	Twisted cyclic cohomology and modular fredholm modules Published In Symmetry, Integrability and Geometry: Methods and Applications Volume 9 Pages 1 - 15 ISSN 1815-0659 Altmetric
2012	A residue formula for the fundamental Hochschild 3-cocycle for SUq(2) Published In Journal of Lie Theory Volume 22 Pages 557 - 585 ISSN 0940-2268
2012	Integration on locally compact noncommutative spaces Published In Journal of Functional Analysis Volume 263 Pages 383 - 414 ISSN 0022-1236 Altmetric
2012	KK-theory and spectral flow in von Neumann algebras Published In Journal of K-theory Volume 10 Pages 241 - 277 ISSN 1865-2433 Altmetric
2012	Riemannian manifolds in noncommutative geometry Published In Journal of Geometry and Physics Volume 62 Pages 1611 - 1638 ISSN 0393-0440 Altmetric
2011	Families of type III KMS states on a class of C∗-algebras containing On and QN Published In Journal of Functional Analysis Volume 260 Pages 1637 - 1681 ISSN 0022-1236 Altmetric
2011	Twisted cyclic theory, equivariant KK-theory and KMS states Published In Journal fuer die Reine und Angewandte Mathematik: Crelle's journal Volume 2011 Pages 161 - 191 ISSN 0075-4102 Altmetric
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 Volume 2010 Pages 59 - 109 ISSN 0075-4102 Altmetric
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 Volume 6 Pages 339 - 380 ISSN 1865-2433 Altmetric
2009	Noncommutative manifolds from Graph and k-Graph C-algebras Published In* Communications in Mathematical Physics Volume 292 Pages 607 - 636 ISSN 0010-3616 Altmetric
2009	Spectral flow invariants and twisted cyclic theory for the Haar state on SUq(2) Published In Journal of Geometry and Physics Volume 59 Pages 1431 - 1452 ISSN 0393-0440 Altmetric
2008	Orbifolds are not commutative geometries Published In Journal of the Australian Mathematical Society Volume 84 Pages 109 - 116 ISSN 1446-7887 Altmetric
2008	The chern character of semifinite spectral triples Published In Journal of Noncommutative Geometry Volume 2 Pages 253 - 283 ISSN 1661-6952
2008	The noncommutative geometry of k-graph C-algebras Published In* Journal of K-theory Volume 1 Pages 259 - 304 ISSN 1865-2433 Altmetric
2007	KK-theory and spectral flow in von Neumann algebras Published In Journal of K-theory Volume 10 Pages 1 - 29 ISSN 1865-2433
2007	The Dixmier trace and asymptotics of zeta functions Published In Journal of Functional Analysis Volume 249 Pages 253 - 283 ISSN 0022-1236 Altmetric

Chapter

Year	Title
2013	Semi-finite noncommutative geometry and some applications Published In Noncommutative geometry and physics, 3 Publisher World Scientific Pages 37 - 58
2013	The local index formula in noncommutative geometry revisited Published In Noncommutative geometry and physics, 3 Publisher World Scientific Pages 3 - 36 Altmetric
2011	Modular index invariants of Mumford curves Published In Noncommutative Geometry Publisher John Hopkins University Press Pages 31 - 73
2011	Spectral triples: examples and index theory Published In Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory Publisher Zurich Pages 175 - 265
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: American Mathematical Society Pages 29 - 40 ISBN 9780821848494
2008	Semifinite spectral triples associated with graph C∗-algebras Published In Traces in Number Theory, Geometry and Quantum Fields (Aspects of Mathematics) Publisher Vieweg Pages 35 - 56

Investigator On

Year	Title
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	C*-Algebras associated to graphs of groups
Doctor of Philosophy	The American put options under modified Black-Scholes models	Qiu, Xinzi
Doctor of Philosophy	Conductivity of Incommensurate Gapped Graphene-Topological Insulator Heterostructures.	Zuber, Jack
Doctor of Philosophy	Applications of Geometry and Topology in Quantum Physics	Alexander, Angus

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
2019	Boundaries, spectral triples and K-homology Published In Journal of Noncommutative Geometry Volume 13 Pages 407 - 472 ISSN 1661-6952 Altmetric
2019	Constructing KMS states from infinite-dimensional spectral triples Published In Journal of Geometry and Physics Volume 143 Pages 107 - 149 ISSN 0393-0440 Altmetric
2019	Factorisation of equivariant spectral triples in unbounded KK-theory Published In Journal of the Australian Mathematical Society Volume 107 Pages 145 - 180 ISSN 1446-7887 Altmetric
2019	Poincare duality for Cuntz–Pimsner algebras Published In Advances in Mathematics Volume 347 Pages 1112 - 1172 ISSN 0001-8708 Altmetric
2019	Untwisting twisted spectral triples Published In International Journal of Mathematics Altmetric
2018	Chern Numbers, Localisation and the Bulk-edge Correspondence for Continuous Models of Topological Phases Published In Mathematical Physics, Analysis and Geometry Volume 21 Pages 16-1 - 16-62 ISSN 1385-0172 Altmetric
2017	Groupoid Fell bundles for product systems over quasi-lattice ordered groups Published In Cambridge Philosophical Society: Mathematical Proceedings Volume 163 Pages 561 - 580 ISSN 0305-0041 Altmetric
2017	Groupoid algebras as Cuntz-Pimsner algebras Published In Mathematica Scandinavica: ediderunt societates mathematicae Daniae Fenniae Islandiae Norvegiae Sveci Volume 120 Pages 115 - 123 ISSN 0025-5521 Altmetric
2017	Non-commutative vector bundles for non-unital algebras Published In Symmetry, Integrability and Geometry: Methods and Applications Volume 13 Pages 041-1 - 041-12 ISSN 1815-0659 Altmetric
2017	The K-theoretic bulk-edge correspondence for topological insulators Published In Annales Henri Poincare Volume Online First Pages 1 - 34 ISSN 0018-0238 Altmetric
2017	The extension class and KMS states for Cuntz–Pimsner algebras of some bi-Hilbertian bimodules Published In Journal of Topology and Analysis Volume 9 Pages 297 - 327 ISSN 1793-5253 Altmetric
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 Volume 28 Pages 1650004-1 - 1650004-51 ISSN 0129-055X Altmetric
2016	Generalised time functions and finiteness of the Lorentzian distance Published In Journal of Geometry and Physics Volume 106 Pages 108 - 121 ISSN 0393-0440 Altmetric
2016	Indefinite Kasparov modules and pseudo-Riemannian manifolds Published In Annales Henri Poincare Volume 17 Pages 3255 - 3286 ISSN 0018-0238 Altmetric
2016	Nonunital spectral triples and metric completeness in unbounded KK-theory Published In Journal of Functional Analysis Volume 271 Pages 2460 - 2538 ISSN 0022-1236 Altmetric
2016	Shift¿tail equivalence and an unbounded representative of the Cuntz¿Pimsner extension Published In Ergodic Theory and Dynamical Systems Pages 1 - 33 ISSN 0143-3857 Altmetric
2016	Universal measurability and the Hochschild class of the Chern character Published In Journal of Spectral Theory Volume 6 Pages 1 - 41 Altmetric
2015	Spectral flow for nonunital spectral triples Published In Canadian Journal of Mathematics Volume 67 Pages 759 - 794 ISSN 0008-414X Altmetric
2015	The bulk-edge correspondence for the quantum hall effect in Kasparov Theory Published In Letters in Mathematical Physics Volume 105 Pages 1253 - 1273 ISSN 0377-9017 Altmetric
2014	Dense domains, symmetric operators and spectral triples Published In The New York Journal of Mathematics Volume 20 Pages 1001 - 1020 ISSN 1076-9803
2014	Index theory for locally compact noncommutative geometries Published In Memoirs of the American Mathematical Society Volume 231 Pages 1 - 131 ISSN 0065-9266 Altmetric
2014	The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podle´s sphere Published In Journal of Noncommutative Geometry Volume 8 Pages 1 - 43 ISSN 1661-6952 Altmetric
2013	Pseudo-Riemannian spectral triples and the harmonic oscillator Published In Journal of Geometry and Physics Volume 73 Pages 37 - 55 ISSN 0393-0440 Altmetric
2013	The K-theory of Heegaard quantum lens spaces Published In Journal of Noncommutative Geometry Volume 7 Pages 1185 - 1216 ISSN 1661-6952 Altmetric
2013	Twisted cyclic cohomology and modular fredholm modules Published In Symmetry, Integrability and Geometry: Methods and Applications Volume 9 Pages 1 - 15 ISSN 1815-0659 Altmetric
2012	A residue formula for the fundamental Hochschild 3-cocycle for SUq(2) Published In Journal of Lie Theory Volume 22 Pages 557 - 585 ISSN 0940-2268
2012	Integration on locally compact noncommutative spaces Published In Journal of Functional Analysis Volume 263 Pages 383 - 414 ISSN 0022-1236 Altmetric
2012	KK-theory and spectral flow in von Neumann algebras Published In Journal of K-theory Volume 10 Pages 241 - 277 ISSN 1865-2433 Altmetric
2012	Riemannian manifolds in noncommutative geometry Published In Journal of Geometry and Physics Volume 62 Pages 1611 - 1638 ISSN 0393-0440 Altmetric
2011	Families of type III KMS states on a class of C∗-algebras containing On and QN Published In Journal of Functional Analysis Volume 260 Pages 1637 - 1681 ISSN 0022-1236 Altmetric
2011	Twisted cyclic theory, equivariant KK-theory and KMS states Published In Journal fuer die Reine und Angewandte Mathematik: Crelle's journal Volume 2011 Pages 161 - 191 ISSN 0075-4102 Altmetric
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 Volume 2010 Pages 59 - 109 ISSN 0075-4102 Altmetric
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 Volume 6 Pages 339 - 380 ISSN 1865-2433 Altmetric
2009	Noncommutative manifolds from Graph and k-Graph C-algebras Published In* Communications in Mathematical Physics Volume 292 Pages 607 - 636 ISSN 0010-3616 Altmetric
2009	Spectral flow invariants and twisted cyclic theory for the Haar state on SUq(2) Published In Journal of Geometry and Physics Volume 59 Pages 1431 - 1452 ISSN 0393-0440 Altmetric
2008	Orbifolds are not commutative geometries Published In Journal of the Australian Mathematical Society Volume 84 Pages 109 - 116 ISSN 1446-7887 Altmetric
2008	The chern character of semifinite spectral triples Published In Journal of Noncommutative Geometry Volume 2 Pages 253 - 283 ISSN 1661-6952
2008	The noncommutative geometry of k-graph C-algebras Published In* Journal of K-theory Volume 1 Pages 259 - 304 ISSN 1865-2433 Altmetric
2007	KK-theory and spectral flow in von Neumann algebras Published In Journal of K-theory Volume 10 Pages 1 - 29 ISSN 1865-2433
2007	The Dixmier trace and asymptotics of zeta functions Published In Journal of Functional Analysis Volume 249 Pages 253 - 283 ISSN 0022-1236 Altmetric

Chapter

Year	Title
2013	Semi-finite noncommutative geometry and some applications Published In Noncommutative geometry and physics, 3 Publisher World Scientific Pages 37 - 58
2013	The local index formula in noncommutative geometry revisited Published In Noncommutative geometry and physics, 3 Publisher World Scientific Pages 3 - 36 Altmetric
2011	Modular index invariants of Mumford curves Published In Noncommutative Geometry Publisher John Hopkins University Press Pages 31 - 73
2011	Spectral triples: examples and index theory Published In Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory Publisher Zurich Pages 175 - 265
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: American Mathematical Society Pages 29 - 40 ISBN 9780821848494
2008	Semifinite spectral triples associated with graph C∗-algebras Published In Traces in Number Theory, Geometry and Quantum Fields (Aspects of Mathematics) Publisher Vieweg Pages 35 - 56

Investigator On

Year	Title
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	C*-Algebras associated to graphs of groups
Doctor of Philosophy	The American put options under modified Black-Scholes models	Qiu, Xinzi
Doctor of Philosophy	Conductivity of Incommensurate Gapped Graphene-Topological Insulator Heterostructures.	Zuber, Jack
Doctor of Philosophy	Applications of Geometry and Topology in Quantum Physics	Alexander, Angus

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