Rennie, Adam C. none

Associate Professor

  • Faculty of Engineering and Information Sciences
  • School of Mathematics and Applied Statistics
  • Institute for Mathematics and its Applications

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 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

Selected Publications


Impact Story


  • ``Impact'' is defined, in research management lingo, as a measurable effect on something outside academia.<br /><br />Measurable usually means concrete evidence of change to some economic or social variable.<br /><br />My work is in mathematics with applications in theoretical physics.<br /><br />So my ``end-users'' are not relevant for this exercise.

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 The American put options under modified Black-Scholes models Qiu, Xinzi
    Doctor of Philosophy Curvature Flow and Wound Healing. He, Shuhui
    Doctor of Philosophy Noncommutative geometry of foliations MacDonald, Lachlan
    Doctor of Philosophy A Noncommutative Approach to Fractal Geometry Mundey, Alexander
    Doctor of Philosophy Conductivity of Incommensurate Gapped Graphene-Topological Insulator Heterostructures. Zuber, Jack

Reviewer Of


  • many  (Academic Article)

Organizer Of Event


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

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 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.

Selected Publications


Impact Story


  • ``Impact'' is defined, in research management lingo, as a measurable effect on something outside academia.<br /><br />Measurable usually means concrete evidence of change to some economic or social variable.<br /><br />My work is in mathematics with applications in theoretical physics.<br /><br />So my ``end-users'' are not relevant for this exercise.

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 The American put options under modified Black-Scholes models Qiu, Xinzi
    Doctor of Philosophy Curvature Flow and Wound Healing. He, Shuhui
    Doctor of Philosophy Noncommutative geometry of foliations MacDonald, Lachlan
    Doctor of Philosophy A Noncommutative Approach to Fractal Geometry Mundey, Alexander
    Doctor of Philosophy Conductivity of Incommensurate Gapped Graphene-Topological Insulator Heterostructures. Zuber, Jack

Reviewer Of


  • many  (Academic Article)

Organizer Of Event


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