Details of the Researcher

PHOTO

Shunsuke Tada
Section
Mathematical Science Center for Co-creative Society
Job title
Specially Appointed Research Fellow

Education 3

  • Kobe University　Graduate School of Human Development and Environment　Division of Human Environmental Science

    2022/04 - 2025/03

  • Tokyo Institute of Technology　math

    2020/04 - 2022/03

  • Tokyo Institue of Technology　math

    2016/04 - 2020/03

Professional Memberships 1

  • The Mathematical Society of Japan

    2023/10 - Present

Research Interests 3

  • Topological Data Analysis

  • Representation theory

  • persistent homology

Papers 3

  1. Summand-injectivity of interval covers and monotonicity of interval resolution global dimensions Peer-reviewed

    Toshitaka Aoki, Emerson G. Escolar, Shunsuke Tada

    Journal of Applied and Computational Topology　9　(2)　2025/05/21

    Publisher: Springer Science and Business Media LLC

    DOI： 10.1007/s41468-025-00210-2 　

    ISSN： 2367-1726

    eISSN： 2367-1734

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    Abstract Recently, there is growing interest in the use of relative homological algebra to develop invariants using interval covers and interval resolutions (i.e., right minimal approximations and resolutions relative to interval-decomposable modules) for multi-parameter persistence modules. In this paper, the set of all interval modules over a given poset plays a central role. Firstly, we show that the restriction of interval covers of modules to each indecomposable direct summand is injective. This result suggests a way to simplify the computation of interval covers. Secondly, we show the monotonicity of the interval resolution global dimension, i.e., if Q is a full subposet of P, then the interval resolution global dimension of Q is not larger than that of P. Finally, we provide a complete classification of posets whose interval resolution global dimension is zero.

  2. Bipath persistence Peer-reviewed

    Toshitaka Aoki, Emerson G. Escolar, Shunsuke Tada

    Japan Journal of Industrial and Applied Mathematics　42　(1)　453-486　2024/12/17

    Publisher: Springer Science and Business Media LLC

    DOI： 10.1007/s13160-024-00681-3 　

    ISSN： 0916-7005

    eISSN： 1868-937X

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    Abstract In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this setting, and propose the use of bipath persistent homology, which can be used to study the persistence of topological features across a pair of filtrations connected at their ends, to compare the two filtrations. In this setting, interval-decomposability is guaranteed, and we provide an algorithm for computing persistence diagrams for bipath persistent homology and discuss the interpretation of bipath persistence diagrams.

  3. PRIME TENSOR IDEALS IN ABELIAN CATEGORIES OF REPRESENTATIONS OF QUIVERS OF TYPE A Peer-reviewed

    Shunsuke TADA

    Kyushu Journal of Mathematics　77　(1)　159-177　2023

    Publisher: Faculty of Mathematics, Kyushu University

    DOI： 10.2206/kyushujm.77.159 　

    ISSN： 1340-6116

    eISSN： 1883-2032

Misc. 2

  1. On preservation of relative resolutions for poset representations

    Toshitaka Aoki, Shunsuke Tada

    2025/06/26

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    The concept of Galois connections (i.e., adjoint pairs between posets) is ubiquitous in mathematics. In representation theory, it is interesting because it naturally induces the adjoint quadruple between the categories of persistence modules (representations) of the posets via Kan extensions. One of central subjects in multiparameter persistent homology analysis is to understand structures of persistence modules. In this paper, we mainly study a class of Galois connections whose left adjoint is the canonical inclusion of a full subposet. We refer to such a subposet as an interior system, with its corresponding right adjoint given by the floor function. In the induced adjoint quadruple, we call the left Kan extension along its floor function the contraction functor. From its construction, it is left adjoint to the induction functor. Under this setting, we firstly prove that this adjoint pair gives an adjoint pair between finitely presentable persistence modules. Moreover, we introduce a special class of interior systems called aligned interior systems, and prove that both induction and contraction functors over them preserve interval-decomposability of modules. Then, we use them to analyze interval covers and resolutions. We also compute interval resolution global dimensions for certain classes of finite posets.

  2. Stability of Bipath Persistence Diagrams

    Shunsuke Tada

    2025/03/03

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    Recently, bipath persistent homology has been proposed as an extension of standard persistent homology, along with its visualization (bipath persistence diagram) and computational methods. In the setting of standard persistent homology, the stability theorem with respect to real-valued functions on a topological space is one of the fundamental results, which gives a mathematical justification for using persistent homology to noisy data. In proving the stability theorem, the algebraic stability theorem/the isometry theorem for persistence modules plays a central role. In this point of view, the stability property for bipath persistent homology is desired for analyzing data. In this paper, we prove the stability theorem of bipath persistent homology with respect to bipath functions on a topological space. This theorem suggests a stability of bipath persistence diagrams: small changes in a bipath function (except at their ends) result in only small changes in the bipath persistence diagram. Similar to the stability theorem of standard persistent homology, we deduce the stability theorem of bipath persistent homology by using the algebraic stability theorem/the isometry theorem of bipath persistence modules.

Presentations 13

  1. Proposal of Bipath Persistent Homology: Visualization, Algorithm, and Stability

    Shunsuke Tada

    2025/10/25

  2. Stability of Bipath Persistence Diagrams

    Shunsuke Tada

    2025/09/04

  3. Bipath Persistent homology and its stability

    Shunsuke Tada

    TSVP Symposium: Representation Theory and Topological Data Analysis　2025/07/22

  4. Ａ Computation of Bipath Persistent Homology and Bipath Persistence Diagrams Invited

    Shunsuke Tada

    Asia Pacific Seminar on Applied Topology and Geometry　2024/09/20

  5. Bipath persistence and interval approximation for persistence modules over finite posets Invited

    Shunsuke Tada

    Seminar, Applied CAT　2024/04/16

  6. パーシステントホモロジーにおける区間表現のホモロジー代数的性質 Invited

    多田駿介

    パーシステントホモロジーと表現論2024　2024/02/02

  7. Posets whose persistence modules are always interval decomposable and homological invariants Invited

    Toshitaka Aoki, Emerson G. Escolar, Shunsuke Tada

    2024 Joint Mathematics Meetings (JMM 2024), AIM-AMS Special Session on Applied Topology Beyond Persistence Diagrams　2024/01/05

  8. パーシステントホモロジー解析における 区間表現のホモロジー代数的性質

    青木 利隆, ESCOLAR, Emerson Gaw, 多田 駿介

    2023年度応用数学合同研究集会　2023/12/16

  9. On interval global dimension of posets: a characterization of case 0

    Toshitaka Aoki, Emerson G. Escolar, Shunsuke Tada

    The Mathematical Society of Japan, Autumn Meeting 2023　2023/09/22

  10. On interval global dimension of posets: a characterization of case 0

    Toshitaka Aoki, Emerson Gaw Escolar, Shunsuke Tada

    The 55th Symposium on Ring Theory and Representation Theory　2023/09/05

  11. Interval resolution global dimension and interval cover

    Toshitaka Aoki, Emerson G. Escolar, Shunsuke Tada

    TDA week 2023　2023/07/31

  12. パーシステント加群と区間表現

    多田駿介

    第6回数理新人セミナー　2023/02/21

  13. Prime ideals in categories of representations of quivers of type A

    Shunsuke Tada

    AATRN virtual poster session　2022/09/20

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Research Projects 1

  1. バイパス・パーシステントホモロジー理論の応用への展開 ー逆解析手法の構築と実装ー

    多田 駿介

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 研究活動スタート支援

    Institution: 東北大学

    2025/07/31 - 2027/03/31