Details of the Researcher

PHOTO

Michio Yoshiwaki
Section
Mathematical Science Center for Co-creative Society
Job title
Associate Professor
Degree

  • 博士（理学）（大阪市立大学）

  • 修士（理学）（大阪市立大学）

Research History 20

  • 2024/10 - Present
    Tohoku University　Mathematical Science Center for Co-creative Society　Associate Professor

  • 2020/11 - Present
    Japan Science and Technology Agency　Center for Research and Development Strategy (CRDS)

  • 2016/04 - Present
    Osaka Central University Advanced Mathematical Institute　Reseacher(Additional Post Member)

  • 2018/04 - 2022/03
    RIKEN　Center for Advanced Intelligence Project/Generic Technology Research Group/Topological Data Analysis Team　Reseach Scientist

  • 2020/04 - 2020/10
    Kyoto University

  • 2018/04 - 2020/10
    Kyoto University　Institute for Advanced Study/Center for Advanced Study　Special Appointed Researcher

  • 2016/04 - 2018/03
    Shizuoka University　Faculty of Science　Reseach Fellow (CREST)

  • 2015/04 - 2016/03
    Osaka Kyoiku University

  • 2015/04 - 2016/03
    Osaka City University Advanced Mathematical Institute　Reseacher

  • 2012/04 - 2016/03
    Konan University

  • 2015/04 - 2015/09
    Kansai University

  • 2014/04 - 2015/03
    Osaka City University Advanced Mathematical Institute　Associate Professor(Special Appointment)

  • 2011 - 2015
    Osaka City University

  • 2013/04 - 2014/03
    Osaka City university Advanced Mathematical Institute　Assistant Professor(Special Appointments)

  • 2011/04 - 2013/03
    Osaka City university Advanced Mathematical Institute　Researcher

  • 2011/06 - 2012/03
    Osaka Prefecture University

  • 2010/04 - 2011/03
    大阪府立三国丘高等学校　SSH-TA(数学担当)

  • 2006/04 - 2007/03
    Osaka City University

  • 2005/04 - 2006/03
    Osaka City University

  • 2004/04 - 2004/09
    Osaka City University

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Education 4

  • Osaka City University　Graduate School of Science　Mathematics and Physics Course

    2004/04 - 2011/03

  • 病気療養による休学

    2007/04 - 2009/03

  • Osaka City University　Graduate School of Science　Mathematics and Physics Course

    2002/04 - 2004/03

  • Osaka City University　Faculty of Science　Department of Mathematics

    1998/04 - 2002/03

Professional Memberships 1

  • THE MATHEMATICAL SOCIETY OF JAPAN

Research Interests 4

  • Topological data analysis

  • dimension of triangulated categories

  • representation theory of algebras

  • representation theory

Research Areas 2

  • Natural sciences / Applied mathematics and statistics /

  • Natural sciences / Algebra / representation theory of algebras

Awards 1

  1. 大阪市立大学数学研究会論文賞

    2011/03　大阪市立大学数学研究会

Papers 13

  1. Approximation by interval-decomposables and interval resolutions of persistence modules *

    Hideto Asashiba, Emerson G. Escolar, Ken Nakashima, Michio Yoshiwaki

    JOURNAL OF PURE AND APPLIED ALGEBRA　227　(10)　2023/10

    DOI： 10.1016/j.jpaa.2023.107397 　

    ISSN： 0022-4049

    eISSN： 1873-1376

  2. On approximation of 2D persistence modules by interval-decomposables

    Hideto Asashiba, Emerson G. Escolar, Ken Nakashima, Michio Yoshiwaki

    Journal of Computational Algebra　6-7　100007-100007　2023/09

    Publisher: Elsevier BV

    DOI： 10.1016/j.jaca.2023.100007 　

    ISSN： 2772-8277

  3. Field Choice Problem in Persistent Homology

    Ippei Obayashi, Michio Yoshiwaki

    Discrete & Computational Geometry　70　(3)　645-670　2023/08/18

    Publisher: Springer Science and Business Media LLC

    DOI： 10.1007/s00454-023-00544-7 　

    ISSN： 0179-5376

    eISSN： 1432-0444

    More details Close

    Abstract This paper tackles the problem of coefficient field choice in persistent homology. When we compute a persistence diagram, we need to select a coefficient field before computation. We should understand the dependence of the diagram on the coefficient field to facilitate computation and interpretation of the diagram. We clarify that the dependence is strongly related to the torsion part of $$\mathbb {Z}$$ relative homology in the filtration. We show the sufficient and necessary conditions of the independence of coefficient field choice. An efficient algorithm is proposed to verify the independence. A slight modification of the standard persistence algorithm gives the verification algorithm. In a numerical experiment with the algorithm, a persistence diagram rarely changes even when the coefficient field changes if we consider a filtration in $$\mathbb {R}^3$$. The experiment suggests that, in practical terms, changes in the field coefficient will not change persistence diagrams when the data are in $$\mathbb {R}^3$$.

  4. Resolution of the curse of dimensionality in single-cell RNA sequencing data analysis

    Yusuke Imoto, Tomonori Nakamura, Emerson G Escolar, Michio Yoshiwaki, Yoji Kojima, Yukihiro Yabuta, Yoshitaka Katou, Takuya Yamamoto, Yasuaki Hiraoka, Mitinori Saitou

    Life Science Alliance　5　(12)　e202201591-e202201591　2022/12

    Publisher: Life Science Alliance, LLC

    DOI： 10.26508/lsa.202201591 　

    eISSN： 2575-1077

    More details Close

    Single-cell RNA sequencing (scRNA-seq) can determine gene expression in numerous individual cells simultaneously, promoting progress in the biomedical sciences. However, scRNA-seq data are high-dimensional with substantial technical noise, including dropouts. During analysis of scRNA-seq data, such noise engenders a statistical problem known as the curse of dimensionality (COD). Based on high-dimensional statistics, we herein formulate a noise reduction method, RECODE (resolution of the curse of dimensionality), for high-dimensional data with random sampling noise. We show that RECODE consistently resolves COD in relevant scRNA-seq data with unique molecular identifiers. RECODE does not involve dimension reduction and recovers expression values for all genes, including lowly expressed genes, realizing precise delineation of cell fate transitions and identification of rare cells with all gene information. Compared with representative imputation methods, RECODE employs different principles and exhibits superior overall performance in cell-clustering, expression value recovery, and single-cell–level analysis. The RECODE algorithm is parameter-free, data-driven, deterministic, and high-speed, and its applicability can be predicted based on the variance normalization performance. We propose RECODE as a powerful strategy for preprocessing noisy high-dimensional data.

  5. On interval decomposability of 2D persistence modules

    Hideto Asashiba, Mickaël Buchet, Emerson G. Escolar, Ken Nakashima, Michio Yoshiwaki

    Computational Geometry　105-106　101879-101879　2022/08

    Publisher: Elsevier BV

    DOI： 10.1016/j.comgeo.2022.101879 　

    ISSN： 0925-7721

  6. Algebraic stability theorem for derived categories of zigzag persistence modules

    Yasuaki Hiraoka, Yuichi Ike, Michio Yoshiwaki

    Journal of Topology and Analysis　1-45　2022/07/29

    Publisher: World Scientific Pub Co Pte Ltd

    DOI： 10.1142/s1793525322500091 　

    ISSN： 1793-5253

    eISSN： 1793-7167

    More details Close

    We study distances on zigzag persistence modules from the viewpoint of derived categories and Auslander–Reiten quivers. The derived category of ordinary persistence modules is derived equivalent to that of arbitrary zigzag persistence modules, depending on a classical tilting module. Through this derived equivalence, we define and compute distances on the derived category of arbitrary zigzag persistence modules and prove an algebraic stability theorem. We also compare our distance with the distance for purely zigzag persistence modules introduced by Botnan–Lesnick and the sheaf-theoretic convolution distance due to Kashiwara–Schapira.

  7. Viewpoint Planning of Projector Placement for Spatial Augmented Reality using Star-Kernel Decomposition

    Takefumi Hiraki, Tomohiro Hayase, Yuichi Ike, Takashi Tsuboi, Michio Yoshiwaki

    2021 IEEE Conference on Virtual Reality and 3D User Interfaces Abstracts and Workshops (VRW)　583-584　2021/03

    Publisher: IEEE

    DOI： 10.1109/vrw52623.2021.00174 　

  8. On isomorphisms of generalized multifold extensions of algebras without nonzero oriented cycles Peer-reviewed

    H. Asashiba, M. Kimura, K. Nakashima, M. Yoshiwaki

    Communications in Algebra　1-23　2020/10/18

    Publisher: Informa UK Limited

    DOI： 10.1080/00927872.2020.1826958 　

    ISSN： 0092-7872

    eISSN： 1532-4125

  9. Relative derived dimensions for cotilting modules Peer-reviewed

    Michio Yoshiwaki

    Journal of algebra　490　437-440　2017/08

    More details Close

    For a Noetherian ring $R$ and a cotilting $R$-module $T$ of injective<br /> dimension at least $1$, we prove that the derived dimension of $R$ with respect<br /> to the category $\mathcal{X}_T$ is precisely the injective dimension of $T$ by<br /> applying Auslander-Buchweitz theory and Ghost Lemma. In particular, when $R$ is<br /> a commutative Noetherian local ring with a canonical module $\omega_R$ and<br /> $\dim R\ge1$, the derived dimension of R with respect to the category of<br /> maximal Cohen-Macaulay modules is precisely $\dim R$.

  10. Decomposition theory of modules: the case of Kronecker algebra Peer-reviewed

    Hideto Asashiba, Ken Nakashima, Michio Yoshiwaki

    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS　34　(2)　489-507　2017/08

    DOI： 10.1007/s13160-017-0247-y 　

    ISSN： 0916-7005

    eISSN： 1868-937X

  11. Dimensions of triangulated categories with respect to subcategories Peer-reviewed

    Takuma Aihara, Tokuji Araya, Osamu Iyama, Ryo Takahashi, Michio Yoshiwaki

    JOURNAL OF ALGEBRA　399　205-219　2014/02

    DOI： 10.1016/j.jalgebra.2013.09.035 　

    ISSN： 0021-8693

    eISSN： 1090-266X

  12. ON SELF-INJECTIVE ALGEBRAS OF STABLE DIMENSION ZERO Peer-reviewed

    Michio Yoshiwaki

    NAGOYA MATHEMATICAL JOURNAL　203　101-108　2011/09

    DOI： 10.1215/00277630-1331872 　

    ISSN： 0027-7630

  13. On selfinjective algebras having stable dimension zero Peer-reviewed

    Yoshiwaki Michio

    Osaka City University　2011/03

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Misc. 10

  1. Approximation by interval-decomposables and interval resolutions of 2D persistence modules

    H. Asashiba, E.G. Escolar, K. Nakashima, M. Yoshiwaki

    Proceedings of the 54th Symposium on Ring Theory and Representation Theory　11-18　2023

  2. Algebraic stability theorem for derived categories of zigzag persistence modules

    Y. Hiraoka, Y. Ike, M. Yoshiwaki

    Proceedings of the 53rd Symposium on Ring Theory and Representation Theory　87-104　2022

  3. Algebraic stability theorem for derived categories of zigzag persistence modules

    Yasuaki Hiraoka, Yuichi Ike, Michio Yoshiwaki

    2020/06/12

    More details Close

    We study distances on zigzag persistence modules from the viewpoint of derived categories. It is known that the derived categories of ordinary and arbitrary zigzag persistence modules are equivalent. Through this derived equivalence, we define distances on the derived category of arbitrary zigzag persistence modules and prove an algebraic stability theorem. We also compare our distance with the distance for purely zigzag persistence modules introduced by Botnan--Lesnick and the sheaf-theoretic convolution distance due to Kashiwara--Schapira.

  4. Interleavings and Matchings as Representations

    Emerson G. Escolar, Killian Meehan, Michio Yoshiwaki

    2020/04/08

    More details Close

    In order to better understand and to compare interleavings between persistence modules, we elaborate on the algebraic structure of interleavings in general settings. In particular, we provide a representation-theoretic framework for interleavings, showing that the category of interleavings under a fixed translation is isomorphic to the representation category of what we call a shoelace. Using our framework, we show that any two interleavings of the same pair of persistence modules are themselves interleaved. Furthermore, in the special case of persistence modules over $\mathbb{Z}$, we show that matchings between barcodes correspond to the interval-decomposable interleavings.

  5. On Approximation of $2$D Persistence Modules by Interval-decomposables

    Hideto Asashiba, Emerson G. Escolar, Ken Nakashima, Michio Yoshiwaki

    2019/11/05

    More details Close

    In this work, we propose a new invariant for $2$D persistence modules called<br /> the compressed multiplicity and show that it generalizes the notions of the<br /> dimension vector and the rank invariant. In addition, we propose an<br /> &quot;interval-decomposable approximation&quot; $\delta^{\ast}(M)$ of a $2$D persistence<br /> module $M$. In the case that $M$ is interval-decomposable, we show that<br /> $\delta^{\ast}(M) = M$. Furthermore, even for representations $M$ not<br /> necessarily interval-decomposable, $\delta^{\ast}(M)$ preserves the dimension<br /> vector and the rank invariant of $M$.

  6. On Interval Decomposability of 2D Persistence Modules

    Hideto Asashiba, Mickaël Buchet, Emerson G. Escolar, Ken Nakashima, Michio Yoshiwaki

    2018/12/13

    More details Close

    In persistent homology of filtrations, the indecomposable decompositions<br /> provide the persistence diagrams. In multidimensional persistence it is known<br /> to be impossible to classify all indecomposable modules. One direction is to<br /> consider the subclass of interval-decomposable persistence modules, which are<br /> direct sums of interval representations. We introduce the definition of<br /> pre-interval representations, a more algebraic definition, and study the<br /> relationships between pre-interval, interval, and indecomposable thin<br /> representations. We show that over the `equioriented&#039; commutative $2$D grid,<br /> these concepts are equivalent. Moreover, we provide an algorithm for<br /> determining whether or not an $n$D persistence module is<br /> interval/pre-interval/thin-decomposable, under certain finiteness conditions<br /> and without explicitly computing decompositions.

  7. On isomorphisms of generalized multifold extensions of algebras without nonzero oriented cycles

    Yoshiwaki Michio

    2018/03

  8. Decomposition theory of modules: the case of Kronecker algebra(proceeding)

    Hideto Asashiba, Ken Nakashima, Michio Yoshiwaki

    Proceedings of the 49th Symposium on Ring Theory and Representation Theory　161-168　2017/02

  9. On selnjective algebras of stable dimension zero

    Yoshiwaki Michio

    Proceedings of the 43rd Symposium on Ring Theory and Representation Theory　85-93　2011/01

  10. Tilting objects in Grothendieck categories

    Yoshiwaki Michio

    Proceedings of the 2nd COE Kinosaki Young Researchers' Seminar　225-234　2005

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Presentations 62

  1. ジグザグパーシステントホモロジーの導来圏に対する代数的安定性定理

    吉脇 理雄

    第2回 MfIP連携探索ワークショップ　2024/09/17

  2. Algebraic stability theorem for derived categories of zigzag persistence modules

    Y. Hiraoka, Y. Ike, M. Yoshiwaki

    TDA week 2023　2023/07/31

  3. パーシステントホモロジーのノイズ安定性と導来圏

    吉脇 理雄

    研究集会「パーシステントホモロジーと表現論」　2023/02/15

  4. Approximation by interval-decomposables and interval resolutions of 2D persistence modules

    2022/09/13

  5. 可換梯子型パーシステンス 加群の表現論的区間分解の計算法

    中島 健, 浅芝 秀人, Emerson G. Escolar, 吉脇 理雄

    日本応用数理学会 2022年度年会　2022/09/08

  6. Approximation by interval-decomposables and interval resolutions of persistence modules

    the 54rd Symposium on Ring Theory and Representation Theory　2022/09/06

  7. Interleavings and Matchings as Representations

    2022/03/09

  8. Algebraic stability theorem for derived categories of zigzag persistence modules

    the 53rd Symposium on Ring Theory and Representation Theory　2021/09/09

  9. パーシステンス加群の導来圏と代数的安定性定理

    吉脇 理雄

    九州大学マス・フォ ア・インダストリ研究所 共同利用研究「位相的データ解析の理論と応用」　2021/08/05

  10. 区間表現による2Dパーシステント表現の近似

    浅芝 秀人, Emerson G. Escolar, 中島 健, 吉脇 理雄

    日本応用数理学会第１７回研究部会連合発表会　2021/03/04

  11. 高次元統計解析に基づく遺伝子発現データのノイズ削減法

    井元 佑介, 平岡 裕章, 吉脇 理雄, Emerson G. Escolar, 中村 友紀, 山本 拓也, 斎藤 通紀

    2020年度科研費シンポジウム「多様な分野のデータに対する統計科学・機械学習的アプローチ」　2020/09/28

  12. ジグザグパーシステント加群に対する代数的安定性定理

    平岡 裕章, 吉脇 理雄

    日本数学会2020年度秋季総合分科会　2020/09/24

  13. Field choice problem on persistent homology

    大林 一平, 吉脇 理雄

    日本数学会2020年度年会, 日本大学理工学部　2020/03/18

  14. Every pair of $\Lambda$-interleavings is $\widetilde{\Lambda}$-interleaved

    E.G. Escolar, K.F. Meehan, 吉脇理雄

    日本数学会2020年度年会, 日本大学理工学部　2020/03/18

  15. On approximation of 2D persistence modules by interval-decomposables,

    浅芝 秀人, E.G. Escolar, 中島 健, 吉脇 理雄

    日本数学会2020年度年会, 日本大学理工学部　2020/03/18

  16. Persistent homology and Representation theory

    吉脇 理雄

    情報系 WINTER FESTA Episode 5，一橋講堂　2019/12/25

  17. パーシステントホモロジーの体の問題

    大林 一平, 吉脇 理雄

    2019年度応用数学合同研究集会，龍谷大学瀬田キャンパス　2019/12/13

  18. Topological data analysis and representation theory International-presentation

    Yoshiwaki Michio

    UK-Japan Robotics and AI research collaboration workshop　2019/09/17

  19. An algebraic stability theorem for the derived category of persistence modules International-presentation Invited

    Yoshiwaki Michio

    Workshop "Computational Applications of Quiver Representations: TDA and QPA", Bielefeld University, Bielefeld, Germany　2019/05/02

  20. トポロジカルデータ解析チーム, AIPシンポジウム2018年度成果報告会

    E. G. Escolar, 大林 一平, 平岡 裕章, 吉脇 理雄

    ＪＰタワーホール＆カンファレンス, 東京　2019/03/19

  21. パーシステント加群の導来圏における代数的安定性定理

    平岡 裕章, 吉脇 理雄

    日本数学会2019年度年会, 東京工業大学大岡山キャンパス　2019/03/17

  22. On interval decomposability of 2D persistence modules

    2019/03/17

  23. 多次元パーシステンス加群について

    吉脇 理雄

    第2回理研AIP数学系合同セミナー, ホテルリステル浜名湖, 静岡　2019/03/13

  24. On interval decomposability of 2D persistence modules

    Yoshiwaki Michio

    2019/03/05

  25. On interval decomposability of 2D persistence modules Invited

    Yoshiwaki Michio

    2019/02/19

  26. On Interval Decomposability of 2D Persistence Modules International-presentation

    H. Asashiba, M. Buchet, E. G. Escolar, K. Nakashima, M. Yoshiwaki

    2019/01/07

  27. On bocses (survey)

    Yoshiwaki Michio

    2018/06/15

  28. On Iwanaga-Gorenstein algebras of finite Cohen-Macaulay type International-presentation Invited

    Michio Yoshiwaki

    RIMS workshop: Noncommutative Algebraic Geometry and Related Topics　2017/09/26

  29. On isomorphisms of generalized multifold extensions of algebras without nonzero oriented cycles

    Hideto Asashiba, Mayu Kimura, Ken Nakashima, Michio Yoshiwaki

    2017/09/13

  30. Relative derived dimensions for cotilting modules 2

    Yoshiwaki Michio

    2017/03/27

  31. Decomposition theory of modules: the case of Kronecker algebra

    Hideto Asashiba, Ken Nakashima, Michio Yoshiwaki

    2016/09/15

  32. Decomposition theory of modules: the case of Kronecker algebra International-presentation

    Hideto Asashiba, Ken Nakashima, Michio Yoshiwaki

    2016/09/01

  33. Decomposition theory of modules: the case of Kronecker algebra Invited

    Michio Yoshiwaki

    2016/07/22

  34. Decomposition theory of modules: the case of Kronecker algebra Invited

    Hideto Asashiba, Ken Nakashima, Michio Yoshiwaki

    2016/06/24

  35. Relative derived dimensions for cotilting modules Invited

    Yoshiwaki Michio

    2015/12/19

  36. A construction of Iwanaga-Gorenstein algebras of finite Cohen-Macaulay type International-presentation

    Yoshiwaki Michio

    Derived categories of finite dimensional algebras -Conference honoring Hideto Asashiba on the occasion of his 60th birthday-Shizuoka University　2015/09/11

  37. Relative derived dimensions for cotilting modules

    Yoshiwaki Michio

    2015/03/22

  38. Relative derived dimensions for cotilting modules

    Yoshiwaki Michio

    2015/03/19

  39. 高校生に向けた群の導入 ―雲雀丘学園高等学校「One Day College ‐ 出張講義」における実践報告― Invited

    吉脇 理雄

    高等学校・大阪市立大学連携数学協議会 第10回シンポジウム　2014/11/15

  40. フェルマーの小定理と群論的な視点

    吉脇 理雄

    雲雀丘学園高等学校「One Day College ‐ 出張講義」　2014/07/05

  41. Dimensions of triangulated categories with respect to subcategories International-presentation Invited

    Yoshiwaki Michio

    Perspectives of Representation Theory of Algebras -Conference honoring Kunio Yamagata on the occasion of his 65th birthday- (The 13th International Conference by Graduate School of Mathematics, Nagoya University)　2013/11/14

  42. 三角圏の次元と多元環の表現論 Invited

    吉脇 理雄

    OCAMI談話会, 大阪市立大学　2013/10/30

  43. Dimensions of triangulated categories with respect to subcategories 2

    相原 琢磨, 荒谷 督司, 伊山 修, 高橋 亮, 吉脇 理雄

    日本数学会2013年度年会, 京都大学　2013/03/21

  44. Dimensions of triangulated categories with respect to subcategories

    Yoshiwaki Michio

    2012/11/22

  45. Dimensions of triangulated categories with respect to subcategories

    相原 琢磨, 荒谷 督司, 伊山 修, 高橋 亮, 吉脇 理雄

    日本数学会2012年度秋季総合分科会, 九州大学　2012/09/20

  46. Functor categories and derived dimensions

    相原 琢磨, 荒谷 督司, 伊山 修, 高橋 亮, 吉脇 理雄

    第17回代数学若手研究会, 静岡大学　2012/03/04

  47. On the derived dimension of Iwanaga-Gorenstein algebras

    Yoshiwaki Michio

    2011/12/15

  48. On the derived dimension of Iwanaga Gorenstein algebras Invited

    Yoshiwaki Michio

    2011/11/26

  49. Dimensions and covering techniques Invited

    Yoshiwaki Michio

    2011/10/22

  50. Auslander-Reiten quiver 入門

    水野 有哉, 吉脇 理雄

    第8回可換環論サマースクール，名古屋大学　2011/08/23

  51. On selfinjective algebras of stable dimension zero

    吉脇 理雄

    2010年度大阪市立大学数学研究会論文賞受賞講演, 大阪市立大学　2011/03/16

  52. On stable dimension of selfinjective algebras Invited

    Yoshiwaki Michio

    2011/03/10

  53. On selfinjective algebras of stable dimension zero

    吉脇 理雄

    日本数学会2010年度秋季総合分科会, 名古屋大学　2010/09/22

  54. On selfinjective algebras of stable dimension zero International-presentation

    吉脇 理雄

    第43回環論および表現論シンポジウム, 鳴門教育大学　2010/09/11

  55. On selfinjective algebras of stable dimension zero International-presentation

    Yoshiwaki Michio

    International Conference on Representations of Algebras XIV (ICRA XIV), National Olympics Memorial Youth Center, Shibuya, Tokyo　2010/08/11

  56. Quiverの表現とAR理論 Invited

    吉脇 理雄

    2010年度院生談話会, 大阪市立大学大学院理学研究科　2010/05/24

  57. On selfinjective algebras of stable dimension zero

    吉脇 理雄

    第１５回代数学若手研究会, 名古屋大学　2010/03/05

  58. On selfinjective algebras of stable dimension zero Invited

    Michio Yoshiwaki

    Nagoya Seminar, Graduate School of Mathematics, Nagoya University, 19 February, 2010.　2010/02/19

  59. Grothendieck圏における傾対象について Invited

    吉脇 理雄

    2006年度院生談話会, 大阪市立大学大学院理学研究科　2006/05/20

  60. Complexes and Derived Functors (「Paul C. Roberts, Multiplicities and Chern Classes in Local Algebra, Cambridge Tracts in Mathematics 133.」Part I-3)

    吉脇 理雄

    第2回可換環論サマースクール, 立教大学，2005年8月30日.　2005/08/30

  61. Tilting objects in Grothendieck categories Invited

    吉脇 理雄

    第2回城崎新人セミナー(京都大学COE院生交流事業), 城崎　2005/02/22

  62. Derived equivalences and tilting theory

    吉脇 理雄

    第9回代数学若手研究会, 岡山大学　2004/03/06

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Research Projects 3

  1. Bridgeland安定性条件の位相的データ解析への応用

    吉脇 理雄

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 基盤研究(C)

    Institution: 大阪公立大学

    2024/04/01 - 2027/03/31

  2. 位相的時空間解析に向けたノイズ安定性の解明：導来同値の活用

    吉脇 理雄

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 基盤研究(C)

    Institution: 国立研究開発法人理化学研究所

    2020/04/01 - 2024/03/31

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    本研究の目的は位相的時空間解析を確立するのに必須である2パラメータパーシステントホモロジーについての、データのノイズに対する安定性を明らかにする ことである。より具体的には、導来同値を用いてより取り扱いやすいものへと帰着させる考えに基づいて、安定性の代数部分である代数的安定性定理を以下のよ うに明らかにすることであった。(い) 2パラメータパーシステントホモロジーと導来同値な対象で代数的安定性定理を示すこと。(ろ)代数的安定性定理は、導来同値のもとで伝播すること。(は)代数的安定性定理は、導来圏から制限可能であること。(に) 2パラメータパーシステントホモロジーと導来同値な対象について、その導来圏へ(い)の結果を拡張すること。 昨年度は（い）、（ろ）、（は）を達成し、本研究の手法が代数的安定性定理を導く上で、有効な手段であることを明確にできた。そのため今年度は引き続いて（に）について取り組んだ。具体的には2パラメータパーシステントホモロジーと導来同値な対象について、(い)の結果をその導来圏へ一部拡張でき、結果として、全体ではないが、一部の2パラメータパーシステントホモロジーの新たな距離を提案し、代数的安定性定理を示した。すなわち、今年度の計画していた（に）と（に）の結果として(ほ)2パラメータ パーシステントホモロジーの新たな距離を提案し，代数的安定性定理を示すことについて一部目標が達成された。 なお、国内の研究集会や国際会議で発表済み。

  3. Diversified research of ring theory and representation theory with derived categories as its center

    Asashiba Hideto, Iyama Osamu, Kawata Shigeto, Sato Masahisa, Yamaura Kota, Hoshino Mitsuo, Miyachi Jun-ichi, Mori Izuru, Aihara Takuma, Minamoto Hiroyuki, Koshitani Shigeo, Kunugi Naoko, Sanada Katsunori, Ueda Akira, Nishinaka Tsunekazu, Hida Akihiko, Kikumasa Isao, Mizuno Yuya, Adachi Takahide, Itaba Ayako, Yoshiwaki Michio, Nakashima Ken, Kimura Yuta, Kozakai Yuta

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Shizuoka University

    2013/04/01 - 2019/03/31

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    The central purpose of representation theory of algebras is in the study of the module category of an algebra. To this end the study of its derived category became important. In our research we investigated (1) structures of the derived categories; (2) constructions of tilting objects; (3) derived equivalence classifications of self-injective algebras; (4) related topics. The following are examples of our results: (1) for representation-infinite hereditary algebra A the bounded derived category of A is stably equivalent to the repetitive category of stable module category of A. (2) All the tilting complexes over preprojective algebras of Dynkin type were given. (3) The Broue's conjecture for the 1st Conway group was solved. (4) For any group G the smash product of a G-graded category and G is presented by quiver with relations. Also we supported the symposium on ring theory and representation theory (heavily related to our research) and published its proceedings.

Teaching Experience 11

  1. Linear algebra A　Kyoto University

  2. 代数学I・代数学I演習（前期）／代数学概論・代数学概論演習（後期）　大阪教育大学

  3. 線形代数及び演習I, II　甲南大学

  4. 社会安全のための数学１　関西大学

  5. 基礎数学Ａ（前期／2011，2013，2014），Ｂ（後期／2011，2012，2015）　大阪市立大学

  6. 数理科学Ａ（前期のみ）　大阪市立大学

  7. 線形数学Ｉ，ＩＩ　大阪府立大学

  8. 解析II TA　大阪市立大学

  9. 線形代数I TA　大阪市立大学

  10. 代数学I 及びI 演習TA　大阪市立大学

  11. 数学基礎演習II TA　大阪市立大学

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Other 7

  1. Persistent homology and representation theory

  2. 第３回JST 数学領域 未解決問題ワークショップ

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    セミナーハウス クロスウェーブ府中(2019/9/6-8) メインオーガナイザー https://sites.google.com/site/openproblem2019/

  3. Workshop on Applied Topology 2019

  4. Derived categories of finite dimensional algebras -Conference honoring Hideto Asashiba on the occasion of his 60th birthday-

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    Shizuoka University(2015/9/11-12)organizer

  5. 導来同値ワークショップ

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    大阪市立大学（2015/3/28-31）世話人 http://www.sci.osaka-cu.ac.jp/math/OCAMI/MODS/Mods.html

  6. 南大阪代数セミナー

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    大阪市立大学大阪府立大学合同 2014年度～2018年度世話人 https://sites.google.com/site/modseminar/

  7. 第 11 回代数学若手研究会

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    名古屋大学 (2006/3/3-5) 世話人 http://siva.cc.hirosaki-u.ac.jp/usr/ueyama/wakate/2006/wakate.html （旧http://kissme.shinshu-u.ac.jp/wakate/2006/wakate.html）

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