Updated on 2024/10/07

写真a

 
BOURNE Christopher jack
 
Organization
Institute of Liberal Arts and Sciences Education Planning & Development Center Associate professor
Graduate School
Graduate School of Mathematics
Title
Associate professor
Homepage
https://sites.google.com/site/khomologyzone/home
Other name(s)
Chris Bourne
External link

Degree 2

  1. Doctor of Mathematics （ 2015.12   Australian National University ） 

  2. Bachelor of Science (Honours) （ 2012.4   Flinders University ） 

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Research Interests 3

  1. Noncommutative geometry

  2. Operator algebras

  3. Topological phases

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Research Areas 2

  1. Natural Science / Basic analysis  / Operator algebras

  2. Natural Science / Geometry  / Noncommutative geometry

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Current Research Project and SDGs 1

  1. Index theory and noncommutative geometry in physics and quantum information theory

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Research History 6

  1. Nagoya University   Institute of Liberal Arts and Sciences   Associate professor

    2023.4

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    Country：Japan

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  2. RIKEN   Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS)   Visiting Scientist

    2018.5

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  3. Tohoku University   Advanced Institute for Materials Research (AIMR)   Assistant Professor

    2018.4 - 2023.3

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  4. Tohoku University   Graduate School of Science   Postdoctoral fellowship for overseas researchers

    2016.11 - 2018.3

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  5. Friedrich-Alexander Universität Erlangen-Nürnberg   Department Mathematik   Lehrstuhl für Mathematik (postdoc)

    2016.1 - 2016.11

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  6. Australian National University   Mathematical Sciences Institute   Postdoctoral fellow

    2015.8 - 2015.12

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Education 1

  1. Australian National University   Mathematical Sciences Institute   PhD

    2012.2 - 2015.8

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Awards 1

  1. Best Paper Prize 2020

    2020.8   Journal of Physics A: Mathematical and Theoretical  

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    Award type：International academic award (Japan or overseas) 

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Papers 16

  1. The K-Theoretic Classification of Topological Insulators and Superconductors

    Chris Bourne

    Encyclopedia of Mathematical Physics     page： 56 - 65   2025

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    Publishing type：Part of collection (book)   Publisher：Elsevier  

    File： KitaevZirnbauer_standalone.pdf

    DOI： 10.1016/b978-0-323-95703-8.00045-8

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  2. Index Theory of Chiral Unitaries and Split-Step Quantum Walks Reviewed

    Chris Bourne

    Symmetry, Integrability and Geometry: Methods and Applications   Vol. 19   2023

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    Publishing type：Research paper (scientific journal)   Publisher：SIGMA (Symmetry, Integrability and Geometry: Methods and Application)  

    Building from work by Cedzich et al. and Suzuki et al., we consider topological and index-theoretic properties of chiral unitaries, which are an abstraction of the time evolution of a chiral-symmetric self-adjoint operator. Split-step quantum walks provide a rich class of examples. We use the index of a pair of projections and the Cayley transform to define topological indices for chiral unitaries on both Hilbert spaces and Hilbert $C^*$-modules. In the case of the discrete time evolution of a Hamiltonian-like operator, we relate the index for chiral unitaries to the index of the Hamiltonian. We also prove a double-sided winding number formula for anisotropic split-step quantum walks on Hilbert $C^*$-modules, extending a result by Matsuzawa.

    DOI： 10.3842/SIGMA.2023.053

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  3. The KO-Valued Spectral Flow for Skew-Adjoint Fredholm Operators Reviewed

    Chris Bourne, Alan L. Carey, Matthias Lesch, Adam Rennie

    Journal of Topology and Analysis   Vol. 14 ( 02 ) page： 505 - 556   2022.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：World Scientific Pub Co Pte Ltd  

    In this paper, we give a comprehensive treatment of a “Clifford module flow” along paths in the skew-adjoint Fredholm operators on a real Hilbert space that takes values in [Formula: see text] via the Clifford index of Atiyah–Bott–Shapiro. We develop its properties for both bounded and unbounded skew-adjoint operators including an axiomatic characterization. Our constructions and approach are motivated by the principle that [Formula: see text] That is, we show how the [Formula: see text]-valued spectral flow relates to a [Formula: see text]-valued index by proving a Robbin–Salamon type result. The Kasparov product is also used to establish a [Formula: see text] result at the level of bivariant [Formula: see text]-theory. We explain how our results incorporate previous applications of [Formula: see text]-valued spectral flow in the study of topological phases of matter.

    DOI： 10.1142/S1793525320500557

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  4. Locally equivalent quasifree states and index theory Reviewed

    Chris Bourne

    Journal of Physics A: Mathematical and Theoretical   Vol. 55 ( 10 ) page： 104004-1 - 104004-38   2022.3

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    Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing  

    <title>Abstract</title>
    We consider quasifree ground states of Araki’s self-dual canonical anti-commutation relation algebra from the viewpoint of index theory and symmetry protected topological (SPT) phases. We first review how Clifford module indices characterise a topological obstruction to connect pairs of symmetric gapped ground states. This construction is then generalised to give invariants in <inline-formula>
    <tex-math><?CDATA $K{O}_{\ast }({A}^{\mathfrak{r } })$?>
    </tex-math>
    <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll">
    <mml:mi>K</mml:mi>
    <mml:msub>
    <mml:mrow>
    <mml:mi>O</mml:mi>
    </mml:mrow>
    <mml:mrow>
    <mml:mo>*</mml:mo>
    </mml:mrow>
    </mml:msub>
    <mml:mrow>
    <mml:mo stretchy="false">(</mml:mo>
    <mml:mrow>
    <mml:msup>
    <mml:mrow>
    <mml:mi>A</mml:mi>
    </mml:mrow>
    <mml:mrow>
    <mml:mi mathvariant="fraktur">r</mml:mi>
    </mml:mrow>
    </mml:msup>
    </mml:mrow>
    <mml:mo stretchy="false">)</mml:mo>
    </mml:mrow>
    </mml:math>
    <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="aac508bieqn1.gif" xlink:type="simple" />
    </inline-formula> with <italic>A</italic> a <inline-formula>
    <tex-math><?CDATA ${C}^{\ast ,\mathfrak{r } }$?>
    </tex-math>
    <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll">
    <mml:msup>
    <mml:mrow>
    <mml:mi>C</mml:mi>
    </mml:mrow>
    <mml:mrow>
    <mml:mo>*</mml:mo>
    <mml:mo>,</mml:mo>
    <mml:mi mathvariant="fraktur">r</mml:mi>
    </mml:mrow>
    </mml:msup>
    </mml:math>
    <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="aac508bieqn2.gif" xlink:type="simple" />
    </inline-formula>-algebra of allowed deformations. When <italic>A</italic> = <italic>C</italic>*(<italic>X</italic>), the Roe algebra of a coarse space <italic>X</italic>, and we restrict to gapped ground states that are locally equivalent with respect <italic>X</italic>, a <italic>K</italic>-homology class is also constructed. The coarse assembly map relates these two classes and clarifies the relevance of <italic>K</italic>-homology to free-fermionic SPT phases.

    DOI： 10.1088/1751-8121/ac508b

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    Other Link： https://iopscience.iop.org/article/10.1088/1751-8121/ac508b/pdf

  5. Localised Module Frames and Wannier Bases from Groupoid Morita Equivalences Reviewed

    Chris Bourne, Bram Mesland

    Journal of Fourier Analysis and Applications   Vol. 27 ( 4 )   2021.8

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    Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    DOI： 10.1007/s00041-021-09873-8

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    Other Link： https://link.springer.com/article/10.1007/s00041-021-09873-8/fulltext.html

  6. The classification of symmetry protected topological phases of one-dimensional fermion systems Reviewed

    Chris Bourne, Yoshiko Ogata

    Forum of Mathematics, Sigma   Vol. 9 ( e25 ) page： 1 - 45   2021.3

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    Publishing type：Research paper (scientific journal)   Publisher：Cambridge University Press (CUP)  

    <title>Abstract</title>
    We introduce an index for symmetry-protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group <italic>G</italic>. This index takes values in
    <inline-formula>
    <alternatives>
    <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050509421000190_inline1.png" />
    <tex-math>$\mathbb {Z}_2 \times H^1(G,\mathbb {Z}_2) \times H^2(G, U(1)_{\mathfrak {p } })$</tex-math>
    </alternatives>
    </inline-formula> with a generalised Wall group law under stacking. We show that this index is an invariant of the classification of SPT phases. When the ground state is translation invariant and has reduced density matrices with uniformly bounded rank on finite intervals, we derive a fermionic matrix product representative of this state with on-site symmetry.

    DOI： 10.1017/fms.2021.19

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  7. On ℤ2-indices for ground states of fermionic chains Reviewed

    Chris Bourne, Hermann Schulz-Baldes

    Reviews in Mathematical Physics   Vol. 32 ( 9 ) page： 2050028   2020.10

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1142/S0129055X20500282

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  8. The Cayley transform in complex, real and graded K-theory Reviewed

    Chris Bourne, Johannes Kellendonk, Adam Rennie

    International Journal of Mathematics   Vol. 31 ( 9 ) page： 2050074   2020.8

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    Publishing type：Research paper (scientific journal)   Publisher：World Scientific Pub Co Pte Lt  

    DOI： 10.1142/S0129167X20500743

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  9. Index Theory and Topological Phases of Aperiodic Lattices Reviewed

    C. Bourne, B. Mesland

    Annales Henri Poincaré   Vol. 20 ( 6 ) page： 1969 - 2038   2019.6

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    Publishing type：Research paper (scientific journal)   Publisher：Springer Nature  

    © 2019, Springer Nature Switzerland AG. We examine the non-commutative index theory associated with the dynamics of a Delone set and the corresponding transversal groupoid. Our main motivation comes from the application to topological phases of aperiodic lattices and materials and applies to invariants from tilings as well. Our discussion concerns semifinite index pairings, factorisation properties of Kasparov modules and the construction of unbounded Fredholm modules for lattices with finite local complexity.

    DOI： 10.1007/s00023-019-00764-9

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  10. Chern Numbers, Localisation and the Bulk-edge Correspondence for Continuous Models of Topological Phases Reviewed

    C. Bourne, A. Rennie

    Mathematical Physics Analysis and Geometry   Vol. 21 ( 3 )   2018.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Netherlands  

    In order to study continuous models of disordered topological phases, we construct an unbounded Kasparov module and a semifinite spectral triple for the crossed product of a separable C∗-algebra by a twisted ℝd-action. The spectral triple allows us to employ the non-unital local index formula to obtain the higher Chern numbers in the continuous setting with complex observable algebra. In the case of the crossed product of a compact disorder space, the pairing can be extended to a larger algebra closely related to dynamical localisation, as in the tight-binding approximation. The Kasparov module allows us to exploit the Wiener–Hopf extension and the Kasparov product to obtain a bulk-boundary correspondence for continuous models of disordered topological phases.

    DOI： 10.1007/s11040-018-9274-4

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  11. Non-commutative Chern numbers for generic aperiodic discrete systems Reviewed

    Chris Bourne, Emil Prodan

    Journal of Physics A: Mathematical and Theoretical   Vol. 51 ( 23 ) page： 235202   2018.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Physics Publishing  

    The search for strong topological phases in generic aperiodic materials and meta-materials is now vigorously pursued by the condensed matter physics community. In this work, we first introduce the concept of patterned resonators as a unifying theoretical framework for topological electronic, photonic, phononic etc (aperiodic) systems. We then discuss, in physical terms, the philosophy behind an operator theoretic analysis used to systematize such systems. A model calculation of the Hall conductance of a 2-dimensional amorphous lattice is given, where we present numerical evidence of its quantization in the mobility gap regime. Motivated by such facts, we then present the main result of our work, which is the extension of the Chern number formulas to Hamiltonians associated to lattices without a canonical labeling of the sites, together with index theorems that assure the quantization and stability of these Chern numbers in the mobility gap regime. Our results cover a broad range of applications, in particular, those involving quasi-crystalline, amorphous as well as synthetic (i.e. algorithmically generated) lattices.

    DOI： 10.1088/1751-8121/aac093

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  12. Application of Semifinite Index Theory to Weak Topological Phases Reviewed

    Chris Bourne, Hermann Schulz-Baldes

    2016 MATRIX Annals     page： 203   2018

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    Publisher：Springer International Publishing  

    DOI： 10.1007/978-3-319-72299-3_10

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  13. The K-Theoretic Bulk-Edge Correspondence for Topological Insulators Reviewed

    Chris Bourne, Johannes Kellendonk, Adam Rennie

    ANNALES HENRI POINCARE   Vol. 18 ( 5 ) page： 1833 - 1866   2017.5

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER BASEL AG  

    We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact sequence. We construct unbounded Kasparov modules encoding the dynamics of the crossed product. We then link bulk and edge Kasparov modules using the Kasparov product. Because of the anti-linear symmetries that occur in topological insulator models, real -algebras and KKO-theory must be used.

    DOI： 10.1007/s00023-016-0541-2

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  14. TOPOLOGICAL STATES OF MATTER AND NONCOMMUTATIVE GEOMETRY Reviewed

    Chris Bourne

    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY   Vol. 94 ( 2 ) page： 349 - 349   2016.10

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    Language：English   Publisher：CAMBRIDGE UNIV PRESS  

    DOI： 10.1017/S000497271600037X

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  15. A non-commutative framework for topological insulators Reviewed

    C. Bourne, A. L. Carey, A. Rennie

    REVIEWS IN MATHEMATICAL PHYSICS   Vol. 28 ( 2 ) page： 1650004   2016.3

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    Language：English   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

    We study topological insulators, regarded as physical systems giving rise to topological invariants determined by symmetries both linear and anti-linear. Our perspective is that of non-commutative index theory of operator algebras. In particular, we formulate the index problems using Kasparov theory, both complex and real. We show that the periodic table of topological insulators and superconductors can be realized as a real or complex index pairing of a Kasparov module capturing internal symmetries of the Hamiltonian with a spectral triple encoding the geometry of the sample's (possibly non-commutative) Brillouin zone.

    DOI： 10.1142/S0129055X16500045

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  16. The Bulk-Edge Correspondence for the Quantum Hall Effect in Kasparov Theory Reviewed

    Chris Bourne, Alan L. Carey, Adam Rennie

    LETTERS IN MATHEMATICAL PHYSICS   Vol. 105 ( 9 ) page： 1253 - 1273   2015.9

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

    We prove the bulk-edge correspondence in K-theory for the quantum Hall effect by constructing an unbounded Kasparov module from a short exact sequence that links the bulk and boundary algebras. This approach allows us to represent bulk topological invariants explicitly as a Kasparov product of boundary invariants with the extension class linking the algebras. This paper focuses on the example of the discrete integer quantum Hall effect, though our general method potentially has much wider applications.

    DOI： 10.1007/s11005-015-0781-y

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Presentations 37

  1. Unique gapped fermionic ground states and index theory Invited

    Chris Bourne

    Princeton University Mathematical Physics Seminar  2024.9.17 

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    Event date： 2024.9

    Country：United States  

  2. Spectral properties of discrete operators with prescribed spatial asymptotics Invited

    Chris Bourne

    Yeshiva University Mathematical Physics Seminar  2024.9.11 

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    Event date： 2024.9

    Country：United States  

  3. Spectral and topological properties of quantum walks Invited

    Chris Bourne

    Himeji Conference on Partial Differential Equations  2024.3.4 

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    Event date： 2024.3

    Language：English   Presentation type：Oral presentation (invited, special)  

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  4. Operator algebras and index theory in quantum walks Invited International conference

    Chris Bourne

    Noncommutative Geometry, Analysis on Groups, and Mathematical Physics  2024.2.26 

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    Event date： 2024.2

    Language：English   Presentation type：Oral presentation (invited, special)  

    Country：Belgium  

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  5. An operator algebraic approach to quantum walks Invited

    Chris Bourne

    Workshop on operator theory and operator algebras  2023.11.24 

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    Event date： 2023.11

    Language：Japanese   Presentation type：Oral presentation (invited, special)  

    Venue：Kyushu University  

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  6. An operator algebraic approach to quantum walks Invited

    Chris Bourne

    Studies on long time behavior for quantum walks  2023.11.21 

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    Event date： 2023.11

    Language：Japanese   Presentation type：Oral presentation (invited, special)  

    Venue：RIMS, Kyoto Univeristy  

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  7. Topological stability of quantum walks and related Invited

    Chris Bourne

    10th International Congress on Industrial and Applied Mathematics  2023.8.22 

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    Event date： 2023.8

    Language：English   Presentation type：Oral presentation (invited, special)  

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  8. Topological indices/phases of gapped fermionic ground states Invited International conference

    Chris Bourne

    Workshop on Operator Algebras, Deformation Quantization and Related Field Theories 

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    Event date： 2023.7

    Language：English   Presentation type：Oral presentation (invited, special)  

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  9. Fermionic gapped ground states, topological phases and index theory Invited

    Chris Bourne

    Winter School and Conference in Noncommutative Geometry and Geometric Analysis 

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    Event date： 2022.12

    Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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  10. Aperiodic and amorphous topological phases Invited

    Chris Bourne

    RIKEN ITHEMS Quantum Matter Study Group Seminar  2021.5.12 

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    Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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  11. Introduction to the mathematics of (aperiodic) topological materials Invited

    Chris Bourne

    Online joint applied mathematics seminar  2020.7.7 

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    Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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  12. Wannier bases and topology of aperiodic Schrödinger operators Invited

    Chris Bourne

    Rigorous statistical mechanics and related topics II  2020.11.24 

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  13. Topological phases, localisation and delocalisation of random Schrödinger operators Invited International conference

    Chris Bourne

    Mathematical Aspects of Topological Phases of Matter and Quantum Computing  2017.7.25 

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    Language：English  

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  14. Topological phases, index theory and localisation of random magnetic Schrödinger operators Invited International conference

    Chris Bourne

    Spectral analysis in quantum theory  2018.7.23 

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    Language：English  

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  15. Topological phases and the bulk-edge correspondence of aperiodic and amorphous lattices International conference

    Chris Bourne

    Variety and universality of the bulk-edge correspondence in topological phases  2018.1.8 

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  16. Topological phases and Kasparov theory Invited International conference

    Chris Bourne

    Mathematical Approach to Topological Phases in Spintronics  2015.10.7 

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    Language：English  

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  17. The cocycle K-cycle and related constructions Invited International conference

    Chris Bourne

    Gongfest  2018.7.19 

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    Language：English  

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  18. Symmetry protected topological (SPT) phases of infinite fermion chains Invited

    Chris Bourne

    The Second Tohoku University - RIKEN Joint Workshop: "Math Meets Quantum Materials"  2020.9.30 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  19. Spectral flow and topological phases Invited

    Chris Bourne

    Noncommutative geometry, analysis and topoloigcal insulators  2020.2.4 

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    Language：English  

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  20. Spectral flow and topological phases Invited

    Chris Bourne

    Topological phenomena in non-Hermitian and non-equilibrium systems  2020.2.26 

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    Language：English   Presentation type：Oral presentation (general)  

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  21. Semifinite index theory and localisation of continuous models of topological insulators Invited International conference

    Chris Bourne

    Topological insulators and K-homology  2016.11.4 

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  22. On Z_2-indices for ground states of fermionic chains Invited International conference

    Chris Bourne

    Topological Phases of Interacting Quantum Systems  2019.6.4 

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    Language：English  

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  23. Notes on crystallographic pairings Invited

    Chris Bourne

    Topological Phase and K-theory  2018.3.2 

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    Language：English  

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  24. Noncommutative index theory and applications Invited International conference

    Chris Bourne

    Mini-workshop on Topological States and Non-commutative Geometry  2015.3.26 

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    Language：English  

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  25. Localized/de-localized Wannier bases of aperiodic Schrödinger operators Invited

    Chris Bourne

    Topological Phases of Matter  2021.7.26 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  26. KK-theory and free-fermionic topological phases from the viewpoint of symmetry protected topological phases Invited

    Chris Bourne

    Simons Center Workshop: C*-algebras, K-theories and Noncommutative Geometries of Correlated Condensed Matter Systems  2021.5.18 

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    Language：English   Presentation type：Oral presentation (invited, special)  

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  27. Index theory of aperiodic lattices and topological phases Invited International conference

    Chris Bourne

    KK-theory, Gauge Theory and Topological Phases  2017.3.9 

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    Language：English  

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  28. Index theory and topological phases of aperiodic lattices Invited International conference

    Chris Bourne

    Australia-China conference in noncommutative geometry and related areas  2017.12.19 

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    Language：English  

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  29. Index theory and topological phases for symmetric quantum walks Invited

    Chris Bourne

    CREST Research Seminar on "Theoretical studies of topological phases of matter"  2023.1.20 

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    Language：English  

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  30. Groupoids of aperiodic lattices, index theory and topological phases Invited

    Chris Bourne

    14th Korean Operator Algebras Seminar  2018.6.20 

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    Language：English  

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  31. Groupoid cocycles and Delone dynamical systems Invited

    Chris Bourne

    Groupoids, Graphs and Algebras  2019.7.4 

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    Language：English  

    Venue：Univeristy of Sydney  

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  32. Fermionic gapped ground states and topological phases in the infinite volume limit Invited

    Chris Bourne

    CREST Research Seminar on "Theoretical studies of topological phases of matter"  2021.12.17 

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    Language：English   Presentation type：Oral presentation (general)  

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  33. Disordered topological states and Kasparov theory Invited International conference

    Chris Bourne

    KK-theory and Dynamics  2016.7.26 

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    Language：English  

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  34. Crystalline topological phases and equivariant K-theory Invited

    Chris Bourne

    65th Geometry Symposium  2018.8.28 

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    Language：English  

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  35. Operator algebras and index theory in physics and elsewhere Invited

    Chris Bourne

    Colloquium, Graduate School of Mathematics, Nagoya Univeristy  2024.4.10 

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  36. Spectral properties of discrete operators with prescribed spatial asymptotics Invited

    Chris Bourne

    Yeshiva University Mathematical Physics Seminar  2024.9.11 

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  37. Pure gapped fermionic ground states and index theory Invited

    Chris Bourne

    Princeton University Mathematical Physics Seminar  2024.9.17 

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Research Project for Joint Research, Competitive Funding, etc. 1

  1. Bilateral Program: Joint Research Seminar (with with Netherlands Organization for Scientific research) International coauthorship

    Grant number：JPJSBP 220214401  2021.4 - 2023.3

    Japan Society for the Promotion of Science (JSPS) 

    Chris Bourne

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    Authorship：Principal investigator 

    Grant amount：\3100000

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KAKENHI (Grants-in-Aid for Scientific Research) 5

  1. Operator algebras and index theory in quantum walks and quantum information theory

    Grant number：24K06756  2024.4 - 2028.3

    Japan Society for the Promotion of Science (JSPS)  Grant-in-Aid for Scientific Research (C)

    Chris Bourne

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  2. Grant-in-Aid for Early-Career Scientists

    2019.4 - 2024.3

    Japan Society for the Promotion of Science 

    Christopher Jack Bourne

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    Grant type：Competitive

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  3. Grant-in-Aid for JSPS Fellows

    2016.11 - 2018.3

    Japan Society for the Promotion of Science 

    Christopher Jack Bourne, Motoko Kotani

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    Grant type：Competitive

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  4. Postdoctoral Fellowship for Overseas Researchers

    2016.11 - 2018.3

    Japan Society for the Promotion of Science 

    Christopher Jack Bourne

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    Grant type：Competitive

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  5. Lift-Off Fellowship

    2016.7 - 2016.8

    Australian Mathematical Society 

    Christopher Jack Bourne

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    Grant type：Competitive

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Teaching Experience (On-campus) 8

  1. [G30]Calculus II

    2024

  2. [G30] Mathematics Tutorial IIa

    2024

  3. Mathematics Tutorial 2a

    2023

  4. Calculus II (G30)

    2023

  5. [G30]Introduction to Contemporary Mathematics

    2023

  6. [G30]Complex Analysis

    2023

  7. Topics in Mathematical Science Ⅷ

    2023

  8. Special Course on Mathematical Physics II

    2019

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    Intensive course
    Theme: An introduction to noncommutative geometry, index theory and its applications in physics.

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Teaching Experience (Off-campus) 1

  1. Fourier Analysis and Integral Operators

    2014.2 - 2014.6 （University of Wollongong）

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