Bourne Christopher Jack ボーンクリストファー・ジャック

Researcher Number	20830110
Other IDs	https://orcid.org/0000-0001-8234-0081
Affiliation (Current)	2025: 名古屋大学, 教養教育院, 准教授
Affiliation (based on the past Project Information) *help	2023 – 2024: 名古屋大学, 教養教育院, 准教授 2019 – 2022: 東北大学, 材料科学高等研究所, 助教
Review Section/Research Field	Principal Investigator Basic Section 12010:Basic analysis-related
Keywords	Principal Investigator Quantum walk / Floquet systems / Quantum information / K-theory / spectral flow / ground state / gapped ground state / operator algebras / SPT phase / Gapped ground state … More / Operator Algebras / Topological phases / Quantum walks / 指数理論 / トポロジカル相 / 作用素環論 / Index theory / Operator algebras / Topological phase Less

Operator algebras and index theory in quantum walks and quantum information theoryPrincipal Investigator
- Principal Investigator
  
  ボーンクリストファー・ジャック
- Project Period (FY)
  2024 – 2027
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 12010:Basic analysis-related
- Research Institution
  Nagoya University
Interacting topological phases and operator algebrasPrincipal Investigator
- Principal Investigator
  
  Bourne Christopher Jack
- Project Period (FY)
  2019 – 2023
- Research Category
  
  Grant-in-Aid for Early-Career Scientists
- Review Section
  
  Basic Section 12010:Basic analysis-related
- Research Institution
  Nagoya University
  Tohoku University

All 2024 2023 2022 2021 2020 2019

All Journal Article Presentation

[Journal Article] Index Theory of Chiral Unitaries and Split-Step Quantum Walks2023
- Author(s)
  Bourne Chris, Nagoya University, Japan
- Journal Title
  
  Symmetry, Integrability and Geometry: Methods and Applications
  
  Volume: 19 (053) Pages: 1-39
- DOI
  10.3842/sigma.2023.053
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-19K14548
[Journal Article] Locally equivalent quasifree states and index theory2022
- Author(s)
  Chris Bourne
- Journal Title
  
  Journal of Physics A: Mathematical and Theoretical
  
  Volume: 55 Issue: 10 Pages: 104004-104004
- DOI
  10.1088/1751-8121/ac508b
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Journal Article] Localised Module Frames and Wannier Bases from Groupoid Morita Equivalences2021
- Author(s)
  Bourne Chris、Mesland Bram
- Journal Title
  
  Journal of Fourier Analysis and Applications
  
  Volume: 27 Issue: 4 Pages: 1-39
- DOI
  10.1007/s00041-021-09873-8
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Journal Article] The classification of symmetry protected topological phases of one-dimensional fermion systems2021
- Author(s)
  Bourne Chris、Ogata Yoshiko
- Journal Title
  
  Forum of Mathematics, Sigma
  
  Volume: 9 Pages: 1-45
- DOI
  10.1017/fms.2021.19
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K03534, KAKENHI-PROJECT-19K14548
[Journal Article] On Z_2-indices for ground states of fermionic chains2020
- Author(s)
  Bourne Chris、Schulz-Baldes Hermann
- Journal Title
  
  Reviews in Mathematical Physics
  
  Volume: 32 Issue: 09 Pages: 2050028-2050028
- DOI
  10.1142/s0129055x20500282
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Journal Article] The Cayley transform in complex, real and graded K-theory2020
- Author(s)
  Bourne Chris、Kellendonk Johannes、Rennie Adam
- Journal Title
  
  International Journal of Mathematics
  
  Volume: 31 Issue: 09 Pages: 1-50
- DOI
  10.1142/s0129167x20500743
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Journal Article] The KO-valued spectral flow for skew-adjoint Fredholm operators2020
- Author(s)
  Bourne Chris、Carey Alan L.、Lesch Matthias、Rennie Adam
- Journal Title
  
  Journal of Topology and Analysis
  
  Volume: online first Issue: 02 Pages: 1-52
- DOI
  10.1142/s1793525320500557
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Spectral and topological properties of quantum walks2024
- Author(s)
  Chris Bourne
- Organizer
  Himeji Conference on Partial Differential Equations
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Operator algebras and index theory in quantum walks2024
- Author(s)
  Chris Bourne
- Organizer
  Noncommutative Geometry, Analysis on Groups, and Mathematical Physics
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Spectral properties of quantum walk unitaries2024
- Author(s)
  Chris Bourne
- Organizer
  ANU Partial Differential Equations and Analysis Seminar
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] An operator algebraic approach to quantum walks2023
- Author(s)
  Chris Bourne
- Organizer
  Studies on long time behavior for quantum walks
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Topological indices/phases of gapped fermionic ground states2023
- Author(s)
  Chris Bourne
- Organizer
  Workshop on Operator Algebras, Deformation Quantization and Related Field Theories
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Index theory and topological phases for symmetric quantum walks2023
- Author(s)
  Chris Bourne
- Organizer
  CREST Research Seminar on "Theoretical studies of topological phases of matter"
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Topological stability of quantum walks and related2023
- Author(s)
  Chris Bourne
- Organizer
  10th International Congress on Industrial and Applied Mathematics (ICIAM)
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] 量子ウォークへの作用素環的なアプローチ2023
- Author(s)
  Chris Bourne
- Organizer
  作用素論・作用素環論研究集会
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Split-step quantum walks, chiral unitaries and K-theory2022
- Author(s)
  Chris Bourne
- Organizer
  University of Wollongong Operator Algebras and Noncommutative Geometry Seminar
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] SPT phases of quaisfree ground states and coarse geometry2022
- Author(s)
  Chris Bourne
- Organizer
  Oxford University QFT Seminar Series
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Fermionic gapped ground states, topological phases and index theory2022
- Author(s)
  Chris Bourne
- Organizer
  Winter School and Conference on Noncommutative Geometry and Geometric Analysis
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Locally equivalent quasifree states and the coarse index2021
- Author(s)
  Chris Bourne
- Organizer
  65th Annual Meeting of the Australian Mathematics Society
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Aperiodic and amorphous topological phases2021
- Author(s)
  Chris Bourne
- Organizer
  RIKEN iTHEMS Quantum Matter Study Group Seminar
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Fermionic gapped ground states and topological phases in the infinite volume limit2021
- Author(s)
  Chris Bourne
- Organizer
  CREST Research Seminar on "Theoretical studies of topological phases of matter"
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Localized/de-localized Wannier bases of aperiodic Schroedinger operators2021
- Author(s)
  Chris Bourne
- Organizer
  ICMP Satellite Workshop: Topological Phases of Matter
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Symmetry protected topological (SPT) phases of infinite fermion chains2021
- Author(s)
  Chris Bourne
- Organizer
  Wollongong Operator Algebra and Noncommutative Geometry Seminar
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Symmetry protected topological (SPT) phases of infinite fermion chains2021
- Author(s)
  Chris Bourne
- Organizer
  65th Annual Meeting of the Australian Mathematics Society
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] KK-theory and free fermionic topological phases2021
- Author(s)
  Chris Bourne
- Organizer
  Simon's Center online workshop: C*-algebras, K-theories and Noncommutative Geometries of Correlated Condensed Matter Systems
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Introduction to the mathematics of (aperiodic) topological materials2020
- Author(s)
  Chris Bourne
- Organizer
  Joint Applied Math Online Seminar
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Symmetry protected topological (SPT) phases of infinite fermion chains2020
- Author(s)
  Chris Bourne
- Organizer
  The Second Joint RIKEN-Tohoku Workshop
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] The Cayley transform in complex, real and graded K-theory2020
- Author(s)
  Chris Bourne
- Organizer
  Bonn University Seminar in Global Analysis and Operator Algebras
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Spectral flow and topological phases2020
- Author(s)
  Chris Bourne
- Organizer
  Topological phenomena in non-Hermitian and non-equilibrium systems
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Spectral flow and topological phases2020
- Author(s)
  Chris Bourne
- Organizer
  Noncommutative Geometry, Analysis, and Topological Insulators
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Wannier bases and topology of aperiodic Schroedinger operators2020
- Author(s)
  Chris Bourne
- Organizer
  Rigorous Statistical Mechanics and Related Topics II
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Symmetry protected topological (SPT) phases of infinite fermion chains2020
- Author(s)
  Chris Bourne
- Organizer
  Wales Mathematical Physics - Physical Mathematics Seminar
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] The Cayley transform and K-theory2020
- Author(s)
  Chris Bourne
- Organizer
  University of Erlangen-Nuremberg Mathematical Physics Seminar
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Spectral flow, index theory and free-fermionic topological phases2020
- Author(s)
  Chris Bourne
- Organizer
  Cologne University Theoretical Physics Seminar
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Groupoid cocycles and Delone dynamical systems2019
- Author(s)
  Chris Bourne
- Organizer
  Groupoids, Graphs and Algebras
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] The Cayley transform and K-theory2019
- Author(s)
  Chris Bourne
- Organizer
  Operator Algebras and Noncommutative Geometry seminar, University of Wollongong
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548
[Presentation] Z_2-indices of ground states of fermionic chains2019
- Author(s)
  Chris Bourne
- Organizer
  Topological Phases of Interacting Systems
- Invited
- Data Source
  KAKENHI-PROJECT-19K14548

1. OGATA Yoshiko

# of Collaborated Projects: 0 results

# of Collaborated Products: 1 results

Bourne Christopher Jack ボーン クリストファー・ジャック

Research Projects

Research Products

Co-Researchers

Operator algebras and index theory in quantum walks and quantum information theoryPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Interacting topological phases and operator algebrasPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

[Journal Article] Index Theory of Chiral Unitaries and Split-Step Quantum Walks2023

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Locally equivalent quasifree states and index theory2022

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Localised Module Frames and Wannier Bases from Groupoid Morita Equivalences2021

Author(s)

Journal Title

DOI

Data Source

[Journal Article] The classification of symmetry protected topological phases of one-dimensional fermion systems2021

Author(s)

Journal Title

DOI

Data Source

[Journal Article] On Z_2-indices for ground states of fermionic chains2020

Author(s)

Journal Title

DOI

Data Source

[Journal Article] The Cayley transform in complex, real and graded K-theory2020

Author(s)

Journal Title

DOI

Data Source

[Journal Article] The KO-valued spectral flow for skew-adjoint Fredholm operators2020

Author(s)

Journal Title

DOI

Data Source

[Presentation] Spectral and topological properties of quantum walks2024

Author(s)

Organizer

Data Source

[Presentation] Operator algebras and index theory in quantum walks2024

Author(s)

Organizer

Data Source

[Presentation] Spectral properties of quantum walk unitaries2024

Author(s)

Organizer

Data Source

[Presentation] An operator algebraic approach to quantum walks2023

Author(s)

Organizer

Data Source

[Presentation] Topological indices/phases of gapped fermionic ground states2023

Author(s)

Organizer

Data Source

[Presentation] Index theory and topological phases for symmetric quantum walks2023

Author(s)

Organizer

Data Source

[Presentation] Topological stability of quantum walks and related2023

Author(s)

Organizer

Data Source

[Presentation] 量子ウォークへの作用素環的なアプローチ2023

Bourne Christopher Jack ボーンクリストファー・ジャック