Updated on 2025/07/06

写真b

 
ABE Takuro
 
*Items subject to periodic update by Rikkyo University (The rest are reprinted from information registered on researchmap.)
Affiliation*
College of Science Department of Mathematics
Graduate School of Science Doctoral Program in Mathematics
Graduate School of Science Master's Program in Mathematics
Title*
Professor
Degree
博士（理学） （ 京都大学 ）
Research Interests

  • Algebraic Geometry

  • Root systems

  • Vector bundles

  • Logarithmic vector fields

  • Arrangements of hyperplanes

    • Campus Career*
    • 4 2023 - Present 
      College of Science   Department of Mathematics   Professor
    • 4 2023 - Present 
      Graduate School of Science   Master's Program in Mathematics   Professor
    • 4 2023 - Present 
      Graduate School of Science   Doctoral Program in Mathematics   Professor
     

    Research Areas

    • Natural Science / Algebra  / Arrangements of hyperplanes

    • Natural Science / Algebra  / Algebraic Geometry

    Research History

    • 4 2023 - Present 
      Rikkyo University   Department of Mathematics, Faculty of Science   Professor

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      Country：Japan

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    • 7 2019 - 3 2023 
      Kyushu University   Institute of Mathematics for Industry   Professor

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    • 3 2016 - 6 2019 
      Kyushu University   Institute of Mathematics for Industry   Associate Professor

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    • 10 2010 - 2 2016 
      Kyoto University   Graduate School of Engineering   Lecturer

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    • 10 2008 - 9 2010 
      Kyoto University   Graduade School of Science   Program specific assistant professor (GCOE)

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    • 4 2008 - 9 2008 
      JSPS

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    • 4 2006 - 3 2008 
      Hokkaido University   Graduate School of Science

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    Education

    • 4 2003 - 3 2006 
      Kyoto University

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    • 4 2001 - 3 2003 
      Kyoto University   Graduate School of Science   Division of Mathematics

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    • 4 1997 - 3 2001 
      Kyoto University   Faculty of Science

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    Committee Memberships

    • 4 2018 - 3 2019 
      日本数学会   九州支部評議委員

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      Committee type：Academic society

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    Papers

    • Worpitzky-compatible sets and the freeness of arrangements between Shi and Catalan Peer-reviewed International coauthorship

      Takuro Abe, Tan Nhat Tran

      Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, accepted   4 2025

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      Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

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    • Projective dimension of weakly chordal graphic arrangements Peer-reviewed

      Takuro Abe, Lukas Kühne, Paul Mücksch, Leonie Mühlherr

      Algebraic Combinatorics8 ( 1 ) 157 - 174   3 3 2025

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      Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Cellule MathDoc/Centre Mersenne  

      DOI： 10.5802/alco.403

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    • Free reflection multiarrangements and quasi-invariants Peer-reviewed International coauthorship

      Takuro Abe, Naoya Enomoto, Misha Feigin, Masahiko Yoshinaga

      International Mathematics Research Notices2024 ( 23 ) 14157 - 14177   12 2024

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      Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

      DOI： 10.1093/imrn/rnae236

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    • Projective dimensions of hyperplane arrangements Peer-reviewed

      Takuro Abe

      Transactions of the American Mathematical Society377 ( 11 ) 7793 - 7827   11 2024

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      Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

      DOI： 10.1090/tran/9196

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    • A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups Peer-reviewed

      Takuro Abe, Gerhard Roehrle, Christian Stump, Masahiko Yoshinaga

      Journal of Combinatorial Algebra8 ( 3/4 ) 251 - 278   23 7 2024

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      Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

      DOI： 10.4171/JCA/94

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    • Vertex-weighted digraphs and freeness of arrangements between Shi and Ish Peer-reviewed

      Takuro Abe, Tan Nhat Tran, Shuhei Tsujie

      European Journal of Combinatorics118   5 2024

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      Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

      DOI： 10.1016/j.ejc.2024.103920

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    • Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one Peer-reviewed

      ABE, TAKURO

      Algebraic Combinatorics7 ( 2 ) 413 - 429   29 4 2024

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      Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

      DOI： 10.5802/alco.340

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    • On some freeness-type properties for line arrangements Peer-reviewed

      Takuro Abe, Denis Ibadula, Anca Măcinic

      ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE25 ( 1 ) 427 - 447   2 2024

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      Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Scuola Normale Superiore - Edizioni della Normale  

      DOI： 10.2422/2036-2145.202105_038

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    • Addition-deletion theorems for the Solomon-Terao polynomials and B-sequences of hyperplane arrangements Peer-reviewed International journal

      Abe, Takuro

      Mathematische Zeitschrift306 ( 205 )   11 1 2024

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

      DOI： 10.1007/s00209-023-03426-z

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    • Addition-deletion theorem for free hyperplane arrangements and combinatorics Peer-reviewed

      Takuro Abe

      Journal of Algebra610   1 - 17   19 7 2022

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      Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

      DOI： 10.1016/j.jalgebra.2022.06.028

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    • Double points of free projective line arrangements Peer-reviewed

      Takuro Abe

      International Mathematical Research Notices2022 ( 3 ) 1811 - 1824   2 2022

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      Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

      DOI： 10.1093/imrn/rnaa145

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    • Locally heavy hyperplanes in multiarrangements Peer-reviewed

      Takuro Abe, Lukas Kühne

      Journal of Pure and Applied Algebra226 ( 1 ) 106791 - 106791   1 2022

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      Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

      DOI： 10.1016/j.jpaa.2021.106791

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    • Roots of the characteristic polynomials of hyperplane arrangements and their restrictions and localizations Peer-reviewed

      Takuro Abe

      Topology and its Applications (special volume), to appear   12 2021

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      Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

      DOI： 10.1016/j.topol.2021.107990

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    • A Hyper-surface Arrangement Model of Ranking Distributions Peer-reviewed

      Shizuo Kaji, Akira Horiguchi, Takuro Abe, Yohsuke Watanabe

      Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining   796 - 804   14 8 2021

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      Language：English   Publishing type：Research paper (international conference proceedings)  

      DOI： 10.1145/3447548.3467253

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    • A Characterization of High Order Freeness for Product Arrangements and Answers to Holm’s Questions Peer-reviewed International journal

      Takuro Abe, Norihiro Nakashima

      Algebras and Representation Theory24 ( 3 ) 585 - 599   6 2021

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

      DOI： 10.1007/s10468-020-09961-1

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    • Plus-one generated and next to free arrangements of hyperplanes Peer-reviewed

      Takuro Abe

      International Mathematical Research Notices2021 ( 12 ) 9233 - 9261   6 2021

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

      DOI： 10.1093/imrn/rnz099

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    • Addition–deletion results for the minimal degree of logarithmic derivations of hyperplane arrangements and maximal Tjurina line arrangements

      Takuro Abe, Alexandru Dimca, Gabriel Sticlaru

      Journal of Algebraic Combinatorics   16 11 2020

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      Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

      DOI： 10.1007/s10801-020-00986-9

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      Other Link： http://link.springer.com/article/10.1007/s10801-020-00986-9/fulltext.html

    • On A_1^2 restrictions of Weyl arrangements Peer-reviewed

      Takuro Abe, Hiroaki Terao, Tan Nhat Tran

      Journal of Algebraic Combinatorics   18 9 2020

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

      DOI： 10.1007/s10801-020-00979-8

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      Other Link： http://link.springer.com/article/10.1007/s10801-020-00979-8/fulltext.html

    • Hessenberg varieties and hyperplane arrangements Peer-reviewed

      Takuro Abe, Tatsuya Horiguchi, Mikiya Masuda, Satoshi Murai, Takashi Sato

      Journal für die reine und angewandte Mathematik (Crelles Journal)2020 ( 764 ) 241 - 286   1 7 2020

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：Walter de Gruyter GmbH  

      <title>Abstract</title>Given a semisimple complex linear algebraic group <inline-formula id="j_crelle-2018-0039_ineq_9999_w2aab3b7e1517b1b6b1aab1c14b1b1Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_1056.png" /><tex-math>{ { G } }</tex-math></alternatives></inline-formula> and a lower ideal <italic>I</italic> in positive roots of <italic>G</italic>, three objects arise:
      the ideal arrangement <inline-formula id="j_crelle-2018-0039_ineq_9998_w2aab3b7e1517b1b6b1aab1c14b1b7Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_0652.png" /><tex-math>{\mathcal{A}_{I } }</tex-math></alternatives></inline-formula>, the regular nilpotent Hessenberg variety <inline-formula id="j_crelle-2018-0039_ineq_9997_w2aab3b7e1517b1b6b1aab1c14b1b9Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_0711.png" /><tex-math>{\operatorname{Hess}(N,I)}</tex-math></alternatives></inline-formula>, and the regular semisimple Hessenberg variety <inline-formula id="j_crelle-2018-0039_ineq_9996_w2aab3b7e1517b1b6b1aab1c14b1c11Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_0713.png" /><tex-math>{\operatorname{Hess}(S,I)}</tex-math></alternatives></inline-formula>.
      We show that
      a certain graded ring derived from the logarithmic derivation module of <inline-formula id="j_crelle-2018-0039_ineq_9995_w2aab3b7e1517b1b6b1aab1c14b1c13Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_0652.png" /><tex-math>{\mathcal{A}_{I } }</tex-math></alternatives></inline-formula> is isomorphic to
      <inline-formula id="j_crelle-2018-0039_ineq_9994_w2aab3b7e1517b1b6b1aab1c14b1c15Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_0431.png" /><tex-math>{H^{*}(\operatorname{Hess}(N,I))}</tex-math></alternatives></inline-formula> and <inline-formula id="j_crelle-2018-0039_ineq_9993_w2aab3b7e1517b1b6b1aab1c14b1c17Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_0432.png" /><tex-math>{H^{*}(\operatorname{Hess}(S,I))^{W } }</tex-math></alternatives></inline-formula>,
      the invariants in <inline-formula id="j_crelle-2018-0039_ineq_9992_w2aab3b7e1517b1b6b1aab1c14b1c19Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_0433.png" /><tex-math>{H^{*}(\operatorname{Hess}(S,I))}</tex-math></alternatives></inline-formula> under an action of the Weyl group <italic>W</italic> of <italic>G</italic>.
      This isomorphism is shown
      for general Lie type,
      and generalizes Borel’s celebrated theorem showing that the coinvariant algebra of <italic>W</italic> is isomorphic to the cohomology ring of the flag variety <inline-formula id="j_crelle-2018-0039_ineq_9991_w2aab3b7e1517b1b6b1aab1c14b1c27Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_0410.png" /><tex-math>{G/B}</tex-math></alternatives></inline-formula>.

      This surprising connection between Hessenberg varieties and hyperplane
      arrangements enables us to produce a number of interesting
      consequences. For instance, the surjectivity of the restriction map
      <inline-formula id="j_crelle-2018-0039_ineq_9990_w2aab3b7e1517b1b6b1aab1c14b2b1Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_0428.png" /><tex-math>{H^{*}(G/B)\to H^{*}(\operatorname{Hess}(N,I))}</tex-math></alternatives></inline-formula> announced by Dale
      Peterson
      and an affirmative answer to
      a conjecture of Sommers and Tymoczko are immediate consequences. We also
      give an explicit ring presentation of <inline-formula id="j_crelle-2018-0039_ineq_9989_w2aab3b7e1517b1b6b1aab1c14b2b3Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_0431.png" /><tex-math>{H^{*}(\operatorname{Hess}(N,I))}</tex-math></alternatives></inline-formula> in
      types <italic>B</italic>, <italic>C</italic>, and <italic>G</italic>. Such a presentation was already known in type
      <italic>A</italic> and when <inline-formula id="j_crelle-2018-0039_ineq_9988_w2aab3b7e1517b1b6b1aab1c14b2c13Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_0711.png" /><tex-math>{\operatorname{Hess}(N,I)}</tex-math></alternatives></inline-formula> is the Peterson variety. Moreover, we find
      the volume polynomial of <inline-formula id="j_crelle-2018-0039_ineq_9987_w2aab3b7e1517b1b6b1aab1c14b2c15Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_0711.png" /><tex-math>{\operatorname{Hess}(N,I)}</tex-math></alternatives></inline-formula> and see that the hard
      Lefschetz property and the Hodge–Riemann relations hold for
      <inline-formula id="j_crelle-2018-0039_ineq_9986_w2aab3b7e1517b1b6b1aab1c14b2c17Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2018-0039_eq_0711.png" /><tex-math>{\operatorname{Hess}(N,I)}</tex-math></alternatives></inline-formula>, despite the fact that it is a singular variety in general.

      DOI： 10.1515/crelle-2018-0039

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      Other Link： https://www.degruyter.com/downloadpdf/journals/crll/2020/764/article-p241.xml

    • On complex supersolvable line arrangements Peer-reviewed

      Takuro Abe, Alexandru Dimca

      Journal of Algebra552   38 - 51   6 2020

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

      DOI： 10.1016/j.jalgebra.2020.02.007

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    • Multiple addition, deletion and restriction theorems for hyperplane arrangements Peer-reviewed

      Takuro Abe, Hiroaki Terao

      Proceedings of the American Mathematical Society147 ( 11 ) 4835 - 4845   11 2019

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

      DOI： 10.1090/proc/14592

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    • Solomon-Terao algebra of hyperplane arrangements Peer-reviewed

      Abe, Takuro, Maeno, Toshiaki, Mural, Satoshi, Numata, Yasuhide

      JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN71 ( 4 ) 1027 - 1047   10 2019

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

      DOI： 10.2969/jmsj/79957995

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    • Deletion theorem and combinatorics of hyperplane arrangements Peer-reviewed

      Takuro Abe

      Mathematische Annalen373 ( 1--2 ) 581 - 595   2 2019

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

      DOI： 10.1007/s00208-018-1713-9

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    • Heavy hyperplanes in multiarrangements and their freeness Peer-reviewed

      Takuro Abe, Lukas Kuehne

      Journal of Algebraic Combinatorics48 ( 4 ) 581 - 606   12 2018

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

      DOI： 10.1007/s10801-017-0806-y

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    • Splitting types of bundles of logarithmic vector fields along plane curves Peer-reviewed

      Takuro Abe, Alexandru Dimca

      International Journal of Mathematics29 ( 8 )   2018

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

      DOI： 10.1142/S0129167X18500556

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    • A basis construction of the extended Catalan and Shi arrangements of the type &ITA&IT2 Peer-reviewed

      Takuro Abe, Daisuke Suyama

      JOURNAL OF ALGEBRA493   20 - 35   1 2018

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

      DOI： 10.1016/j.jalgebra.2017.09.024

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    • The freeness of Ish arrangements Peer-reviewed

      Takuro Abe, Daisuke Suyama, Shuhei Tsujie

      JOURNAL OF COMBINATORIAL THEORY SERIES A146   169 - 183   2 2017

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

      DOI： 10.1016/j.jcta.2016.09.008

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    • Restrictions of free arrangements and the division theorem Peer-reviewed

      Takuro Abe

      Springer INdAM Series19   389 - 401   2017

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      Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer International Publishing  

      DOI： 10.1007/978-3-319-58971-8_14

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    • Non-recursive freeness and non-rigidity Peer-reviewed

      T. Abe, M. Cuntz, H. Kawanoue, T. Nozawa

      DISCRETE MATHEMATICS339 ( 5 ) 1430 - 1449   5 2016

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

      DOI： 10.1016/j.disc.2015.12.017

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    • Divisionally free arrangements of hyperplanes Peer-reviewed

      Takuro Abe

      INVENTIONES MATHEMATICAE204 ( 1 ) 317 - 346   4 2016

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

      DOI： 10.1007/s00222-015-0615-7

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    • Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements Peer-reviewed

      Takuro Abe, Hiroaki Terao

      JOURNAL OF ALGEBRAIC COMBINATORICS43 ( 1 ) 33 - 44   2 2016

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

      DOI： 10.1007/s10801-015-0624-z

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    • The freeness of ideal subarrangements of Weyl arrangements Peer-reviewed

      T. Abe, M. Barakat, M. Cuntz, T. Hoge, H. Terao

      JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY18 ( 6 ) 1339 - 1348   2016

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

      DOI： 10.4171/JEMS/615

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    • LOGARITHMIC BUNDLES OF DEFORMED WEYL ARRANGEMENTS OF TYPE A(2) Peer-reviewed

      Takuro Abe, Daniele Faenzi, Jean Valles

      BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE144 ( 4 ) 745 - 761   2016

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

      DOI： 10.24033/bsmf.2726

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    • A mathematical problem for security analysis of hash functions and pseudorandom generators Peer-reviewed

      Koji Nuida, Takuro Abe, Shizuo Kaji, Toshiaki Maeno, Yasuhide Numata

      International Journal of Foundations of Computer Science26 ( 2 ) 169 - 194   8 2 2015

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

      DOI： 10.1142/S0129054115500100

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    • Simple-root bases for Shi arrangements Peer-reviewed

      Takuro Abe, Hiroaki Terao

      JOURNAL OF ALGEBRA422   89 - 104   1 2015

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

      DOI： 10.1016/j.jalgebra.2014.09.011

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    • Roots of characteristic polynomials and intersection points of line arrangements. Peer-reviewed

      Takuro Abe

      Journal of Singularities8   100 - 117   10 2014

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

      DOI： 10.5427/jsing.2014.8h

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    • Free arrangements and coefficients of characteristic polynomials Peer-reviewed

      Takuro Abe, Masahiko Yoshinaga

      Mathematische Zeitschrift275 ( 3-4 ) 911 - 919   12 2013

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

      DOI： 10.1007/s00209-013-1165-6

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    • Chambers of 2-affine arrangements and freeness of 3-arrangements Peer-reviewed

      Takuro Abe

      JOURNAL OF ALGEBRAIC COMBINATORICS38 ( 1 ) 65 - 78   8 2013

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

      DOI： 10.1007/s10801-012-0393-x

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    • Characteristic Polynomials, eta-Complexes, and Freeness of Tame Arrangements Peer-reviewed

      Takuro Abe

      MICHIGAN MATHEMATICAL JOURNAL62 ( 1 ) 117 - 130   2013

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    • Equivariant multiplicities of Coxeter arrangements and invariant bases Peer-reviewed

      Takuro Abe, Hiroaki Terao, Atsushi Wakamiko

      ADVANCES IN MATHEMATICS230 ( 4-6 ) 2364 - 2377   7 2012

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

      DOI： 10.1016/j.aim.2012.04.015

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    • Exponents of 2-multiarrangements and multiplicity lattices Peer-reviewed

      Takuro Abe, Yasuhide Numata

      JOURNAL OF ALGEBRAIC COMBINATORICS35 ( 1 ) 1 - 17   2 2012

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

      DOI： 10.1007/s10801-011-0291-7

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    • ON A CONJECTURE OF ATHANASIADIS RELATED TO FREENESS OF A FAMILY OF HYPERPLANE ARRANGEMENTS Peer-reviewed

      Takuro Abe

      MATHEMATICAL RESEARCH LETTERS19 ( 2 ) 469 - 474   2012

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    • The freeness of Shi-Catalan arrangements Peer-reviewed

      Takuro Abe, Hiroaki Terao

      EUROPEAN JOURNAL OF COMBINATORICS32 ( 8 ) 1191 - 1198   11 2011

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

      DOI： 10.1016/j.ejc.2011.06.005

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    • Primitive filtrations of the modules of invariant logarithmic forms of Coxeter arrangements Peer-reviewed

      Takuro Abe, Hiroaki Terao

      JOURNAL OF ALGEBRA330 ( 1 ) 251 - 262   3 2011

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

      DOI： 10.1016/j.jalgebra.2010.12.010

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    • A primitive derivation and logarithmic differential forms of Coxeter arrangements Peer-reviewed

      Takuro Abe, Hiroaki Terao

      MATHEMATISCHE ZEITSCHRIFT264 ( 4 ) 813 - 828   4 2010

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

      DOI： 10.1007/s00209-009-0489-8

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    • Coxeter multiarrangements with quasi-constant multiplicities Peer-reviewed

      Takuro Abe, Masahiko Yoshinaga

      JOURNAL OF ALGEBRA322 ( 8 ) 2839 - 2847   10 2009

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

      DOI： 10.1016/j.jalgebra.2009.07.025

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    • Signed-eliminable graphs and free multiplicities on the braid arrangement Peer-reviewed

      Takuro Abe, Koji Nuida, Yasuhide Numata

      JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES80   121 - 134   8 2009

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

      DOI： 10.1112/jlms/jdp019

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    • The Stability of the Family of B2-Type Arrangements Peer-reviewed

      Takuro Abe

      COMMUNICATIONS IN ALGEBRA37 ( 4 ) 1193 - 1215   2009

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

      DOI： 10.1080/00927870802465969

      J-GLOBAL

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    • TOTALLY FREE ARRANGEMENTS OF HYPERPLANES Peer-reviewed

      Takuro Abe, Hiroaki Terao, Masahiko Yoshinaga

      PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY137 ( 4 ) 1405 - 1410   2009

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

      DOI： 10.1090/S0002-9939-08-09755-4

      J-GLOBAL

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    • The Euler multiplicity and addition-deletion theorems for multiarrangements Peer-reviewed

      Takuro Abe, Hiroaki Terao, Max Wakefield

      JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES77   335 - 348   4 2008

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

      DOI： 10.1112/jlms/jdm110

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    • Splitting criterion for reflexive sheaves Peer-reviewed

      Takuro Abe, Masahiko Yoshinaga

      PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY136 ( 6 ) 1887 - 1891   2008

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

      DOI： 10.1090/S0002-9939-08-09367-2

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    • The characteristic polynomial of a multiarrangement Peer-reviewed

      Takuro Abe, Hiroaki Terao, Max Wakefield

      ADVANCES IN MATHEMATICS215 ( 2 ) 825 - 838   11 2007

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

      DOI： 10.1016/j.aim.2007.04.019

      J-GLOBAL

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    • Free and non-free multiplicity on the deleted A(3) arrangement Peer-reviewed

      Takuro Abe

      PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES83 ( 7 ) 99 - 103   10 2007

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

      DOI： 10.3792/pjaa.83.99

      CiNii Article

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    • The elementary transformation of vector bundles on regular schemes Peer-reviewed

      Takuro Abe

      TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY359 ( 9 ) 4285 - 4295   2007

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

      DOI： 10.1090/S0002-9947-07-04161-X

      J-GLOBAL

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    • The stability of the family of A<sub>2</sub>-type arrangements Peer-reviewed

      T. Abe

      Journal of Mathematics of Kyoto University46 ( 3 ) 617 - 636   2006

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    Misc.

    • A Mathematical Problem for Security Analysis of Hash Functions and Pseudorandom Generators. Peer-reviewed

      Koji Nuida, Takuro Abe, Shizuo Kaji, Toshiaki Maeno, Yasuhide Numata

      Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)7038 LNCS   144 - 160   2011

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    Presentations

    • Free path and restrictions of hyperplane arrangements International conference

      Takuro Abe

      Oberseminar Groups and Geometry  1 7 2025  Bielefeld University

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      Event date： 1 7 2025 - 1 7 2025

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

      Venue：Bielefeld University  

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    • Solomon-寺尾理論入門

      Takuro Abe

      Arrangement Days in NITech 2025  12 6 2025  NITech

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      Event date： 11 6 2025 - 12 6 2025

      Language：Japanese   Presentation type：Oral presentation (general)  

      Venue：NITech  

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    • Tame arrangements Invited

      Abe, Takuro

      Moduli and Friends II  26 5 2025 

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      Event date： 26 5 2025 - 26 5 2025

      Language：English   Presentation type：Oral presentation (general)  

      Venue：online  

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    • Tame arrangements Invited International conference

      Takuro Abe

      New perspectives on hyperplane arrangements  14 5 2025  Ruhr University Bochum

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      Event date： 12 5 2025 - 16 5 2025

      Language：English   Presentation type：Oral presentation (general)  

      Venue：Ruhr University Bochum  

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    • Tame arrangements Invited

      ABE, Takuro

      Arrangement Days in Osaka  26 3 2025  Masahiko Yoshinaga;Ryo Uchiumi

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      Event date： 24 3 2025 - 26 3 2025

      Language：Japanese   Presentation type：Oral presentation (general)  

      Venue：Osaka University  

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    • Graphic arrangements and logarithmic modules

      Takuro Abe

      Combinatorics Seminar  3 2025  Department of Mathematics, Binghamton University

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      Event date： 3 2025 - 6 3 2025

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

      Venue：Binghamton University  

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    • Solomon-Terao polynomials and Castelnouvo-Mumford regularity of hyperplane arrangements Invited International conference

      Abe, Takuro

      Special session ``Algebraic combinatorics and matroids'', Joint Meeting of the NZMS, AustMS and AMS  11 12 2024  NZMS, AustMS and AMS

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      Event date： 9 12 2024 - 13 12 2024

      Language：English   Presentation type：Oral presentation (general)  

      Venue：University of Auckland  

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    • Castelnouvo-Mumford regularity and Solomon-Terao polynomials of hyperplane arrangements Invited

      Abe, Takuro

      Commutative Algebra and Projective Algebraic Geometry in Kumamoto, -- on the occasion of Prof. Miyazaki's 65  6 12 2024 

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      Event date： 4 12 2024 - 7 12 2024

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

      Venue：Kumamoto University  

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    • Hessenberg variety and Solomon-Terao algebra of hyperplane arrangements Invited

      Takuro Abe

      16 11 2024 

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      Event date： 16 11 2024 - 18 11 2024

      Language：Japanese   Presentation type：Oral presentation (general)  

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    • Cokernel of the Euler restriction map of projective line arrangements Invited International conference

      Takuro Abe

      One-day workshop "Bundles and lattices"  25 8 2024 

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      Event date： 25 8 2024 - 25 8 2024

      Language：English   Presentation type：Oral presentation (general)  

      Venue：Osaka University  

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    • Double points of line arrangements in the complex projective plane Invited International conference

      Takuro Abe

      Suzhou Workshop on Matroid Theory  10 7 2024  Soochow University, University of Science and Technology of China

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      Event date： 8 7 2024 - 12 7 2024

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

      Venue：Soochow University  

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    • Double Points of Line Arrangements in the Complex Projective Plane International conference

      Takuro Abe

      BICMR Lecture - Algebraic Geometry  14 5 2024  BICMR

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      Event date： 14 5 2024 - 14 5 2024

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

      Venue：University of Beijing  

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    • Multi-Euler derivation

      Abe Takuro

      Multiarrangements of type B_2 and related topics  27 3 2024 

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      Event date： 26 3 2024 - 27 3 2024

      Language：Japanese   Presentation type：Oral presentation (general)  

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    • Regularity of logarithmic modules and Solomon-Terao polynomials of hyperplane arrangements

      Abe, Takuro

      Semianr of Algebra  27 2 2024  University of Sevilla

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      Event date： 27 2 2024 - 27 2 2024

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

      Venue：University of Sevilla  

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    • Multi-Euler derivations Invited

      Takuro Abe

      OBERSEMINAR "ARRANGEMENTS AND SYMMETRIES"  15 1 2024  Ruhr University Bochum

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      Event date： 15 1 2024 - 15 1 2024

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

      Venue：Ruhr University Bochum  

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    • Projective dimensions of weakly chordal graphic arrangements Invited

      Takuro Abe

      JSPS-VAST Bilateral Joint Research Project Workshop "Topology of Singularities and Related Topics"  14 9 2023 

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      Event date： 11 9 2023 - 15 9 2023

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

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    • Algebraic understanding of integer roots of characteristic polynomials of hyperplane arrangements

      Order Seminar  3 7 2023 

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      Event date： 3 7 2023 - 3 7 2023

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

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    • B-sequences of logarithmic modules of hyperplane arrangements Invited International conference

      Takuro Abe

      Characteristic Polynomials of Hyperplane Arrangements and Ehrhart Polynomials of Convex Polytopes  16 2 2023  RIMS

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      Event date： 14 2 2023 - 17 2 2023

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

      Venue：RIMS  

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    • B-sequences of the logarithmic modules International conference

      Takuro Abe

      Combinatorics, geometry and commutative algebra of hyperplane arrangements  16 1 2023 

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      Event date： 16 1 2023 - 20 1 2023

      Language：English   Presentation type：Oral presentation (general)  

      Venue：Kyushu University  

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    • Addition-restriction theorems and projective dimensions of logarithmic vector fields of hyperplane arrangements Invited

      Takuro Abe

      Project seminar — Moduli and Friends (online)  24 10 2022 

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      Event date： 24 10 2022 - 24 10 2022

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

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    • Sylvester-Gallai theorem and the splitting type of logarithmic vector fields Invited

      Takuro Abe

      20 10 2022 

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      Event date： 18 10 2022 - 21 10 2022

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

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    • Addition theorem for free arrangements, revisited

      Takuro Abe

      超平面配置の数学とその進展2022  16 2 2022 

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      Event date： 16 2 2022 - 16 2 2022

      Language：Japanese   Presentation type：Oral presentation (general)  

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    • Logarithmic modules of hyperplane arrangements and their freeness Invited

      Takuro Abe

      JSPS-VAST Bilateral Joint Research Project Workshop "Singularities, arrangements, and low-dim. topology"  10 12 2021 

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      Event date： 6 12 2021 - 10 12 2021

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

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    • Double points and free deletions of plane arrangements

      Takuro Abe

      Discrete Geometric Structure Seminar  17 11 2021 

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      Event date： 17 11 2021 - 17 11 2021

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

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    • Projective dimension of logarithmic modules of hyperplane arrangements Invited

      Takuro Abe

      RIMS x OIST Jointly-funded Workshop: "Interactions of New Trends in Algebraic Geometry and Singularities"  11 10 2021 

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      Event date： 11 10 2021 - 15 10 2021

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

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    • Logarithmic vector fields and differential forms revisited Invited International coauthorship International conference

      Takuro Abe

      Oberseminar Arrangements and Symmetries  12 7 2021  Ruhr University Bochum

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      Event date： 12 7 2021 - 12 7 2021

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

      Venue：online  

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    • Projective dimensions and addition-deletion theorems for hyperplane arrangements Invited International conference

      Takuro Abe

      Arrangements at Home, III: Algebraic Aspects  14 8 2020 

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      Event date： 13 8 2020 - 14 8 2020

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

      Venue：online  

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    • Double points and freeness of line arrangements in the projective plane Invited International conference

      Takuro Abe

      Afternoon Seminars on Hyperplanes on line  26 6 2020  Shinshu University

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      Event date： 26 6 2020 - 26 6 2020

      Language：English   Presentation type：Oral presentation (general)  

      Venue：online  

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    • Sylvester's problem and logarithmic vector fields of projective line arrangements

      Takuro Abe

      Seminaires de Mathematiques et de leurs Applications  18 2 2020  University of Pau and Pays de l'Adour, Pau, France

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      Language：English   Presentation type：Oral presentation (general)  

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    • 複素数体上の超可解配置の Dirac-Motzkin 予想と対数的ベクト ル場の分裂型 Invited

      阿部 拓郎

      第7回 代数幾何学研究集会-宇部-  11 1 2020  宇部工業高等専門学校

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      Event date： 11 1 2020 - 12 1 2020

      Language：Japanese   Presentation type：Oral presentation (general)  

      Venue：山口県宇部市  

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    • Free arrangements, combinatorics and geometry Invited International conference

      Takuro Abe

      Hyperplane Arrangements and Singularities  6 12 2019  University of Tokyo

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      Event date： 2 12 2019 - 6 12 2019

      Language：English   Presentation type：Oral presentation (general)  

      Venue：University of Tokyo  

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    • Recent developments on free arrangements and combinatorics

      Takuro Abe

      Seminar of Algebra  16 10 2019  Universidad de Sevilla

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

      Venue：Sevilla  

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    • Free arrangements, restrictions and related topics Invited International conference

      Takuro Abe

      Hyperplane Arrangements and Reflection Groups  27 9 2019  Leibniz Universität Hannover

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

      Venue：Leibniz Universität Hannover, Germany  

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    • Solomon-Terao algebra of hyperplane arrangements and singularities Invited International conference

      Takuro Abe

      Special Session on Geometry and Topology of Singularities  15 9 2019  University of Wisconsin-Madison

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

      Venue：University of Wisconsin-Madison, Madison  

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    • Around free arrangements and Solomon-Terao algebras Invited

      Takuro Abe

      Hyperplane Arrangements in Wakkanai  23 8 2019 

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      Language：English   Presentation type：Oral presentation (general)  

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    • Recent topics on free arrangements Invited International conference

      Takuro Abe

      Arrangements at Western  23 5 2019  Western University

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：London, Canada  

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    • Combinatorics of the addition-deletion theorems for free arrangements International conference

      Takuro Abe

      CIMPA - IMH Research School HYPERPLANE ARRANGEMENTS: RECENT ADVANCES AND OPEN PROBLEMS  21 3 2019  VAST and CIMPA

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：Hanoi  

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    • Combinatorics of the addition-deletion theorems for arrangements Invited International conference

      Takuro Abe

      On hyperplane arrangements, configuration spaces and related topics  21 2 2019  Hokkaido University

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：北海道大学  

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    • Logarithmic vector fields and freeness of hyperplane arrangements (three times talks) Invited International conference

      Takuro Abe

      Free divisors and Hyperplane arrangements  18 12 2018  University Paris Diderot, Paris, France

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：University Paris Diderot  

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    • Hessenberg varieties and hyperplane arrangements Invited International conference

      Takuro Abe

      Hessenberg varieties 2018 in Osaka  13 12 2018  Osaka City University

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：Osaka City University  

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    • Combinatorial dependency of the addition-deletion theorems for hyperplane arrangements Invited

      Takuro Abe

      29 11 2018 

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

      Venue：Shinshu University  

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    • Hessenbergs and hyperplane arrangements part II Invited International conference

      Takuro Abe

      Hessenberg Varieties in Combinatorics, Geometry and Representation Theory  25 10 2018  BIRS, Banff, Canada

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

      Venue：BIRS, Banff, Canada  

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    • Logarithmic vector fields and freeness of hyperplane arrangements Invited

      Takuro Abe

      日本数学会秋季総合分科会  27 9 2018  MSJ

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

      Venue：Okayama University  

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    • The b_2-equality and free arrangements Invited International conference

      Takuro Abe

      New perspectives in hyperplane arrangements  14 9 2018  Ruhr University Bochum, Bochum, Germany.

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

      Venue：Ruhr University Bochum, Bochum, Germany.  

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    • 超平面配置の代数・自由性と組み合わせ論 Invited

      Takuro Abe

      組合せ論サマースクール2018  9 8 2018 

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

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    • Free arrangements of hyperplanes and applications (three times talks) Invited International conference

      Takuro Abe

      Workshop on Algebraic Geometry  26 6 2018  Academy of Mathematics and Systems Science, Beijing, China

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

      Venue：Beijing, China  

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    • Generators for logarithmic derivation modules of hyperplane arrangements Invited International conference

      Takuro Abe

      Topology and Geometry: A conference in memory of Stefan Papadima (1953-2018)  29 5 2018  Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：Bucharest, Romania  

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    • Generators of logarithmic derivation modules of hyperplane arrangements Invited International conference

      Takuro Abe

      Arrangements of Hypersurfaces  21 4 2018  AMS and Northeastern University, Boston, USA

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

      Venue：Northeastern University, Boston, USA  

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    • Poincare polynomials and free arrangements Invited International conference

      Takuro Abe

      A walk between hyperplane arrangements, computer algebra and algorithms  2 2 2018  Hokkaido University

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：Sapporo, Japan  

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    • Solomon-Terao algebra of hyperplane arrangements Invited International conference

      Takuro Abe

      Hyperplane arrangement and representation stability  19 1 2018  MFO, Oberwolfach, Germany

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

      Venue：Oberwolfach, Germany  

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    • Solomon-Terao algebra of hyperplane arrangements Invited International conference

      Takuro Abe

      Toric Topology 2017 in Osaka  11 12 2017  Osaka City University

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      Language：English   Presentation type：Oral presentation (general)  

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    • 自由配置に関する近年の進展とその応用 Invited

      Takuro Abe

      10 11 2017  Hokkaido University

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      Language：Japanese   Presentation type：Oral presentation (general)  

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    • Hyperplane arrangements and Hessenberg varieties Invited International conference

      Takuro Abe

      The 5th Franco-Japan-Vietnamese Symposium on Singularities  2 11 2017  University of Kagoshima

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      Language：English   Presentation type：Oral presentation (general)  

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    • Freeness and combinatorics of hyperplane arrangements

      Takuro Abe

      Seminaires de Mathematiques et de leurs Applications  21 9 2017  University of Pau and Pays de l'Adour, Pau, France

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：University of Pau and Pays de l'Adour, Pau, France  

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    • Free arrangements and vector bundles International conference

      Takuro Abe

      VIIIe rencontre Pau-Zaragoza d'Algebra et Geometrie  14 9 2017  University of Pau and Pays de l'Adour, Pau, France

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：University of Pau and Pays de l'Adour, Pau, France  

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    • The $b_2$-inequality and freeness of the restrictions of hyperplane arrangements Invited International conference

      Takuro Abe

      Advances in Hyperplane Arrangements  16 8 2017  University of Bremen, Bremen, Germany

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：University of Bremen, Bremen, Germany  

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    • Hyperplane arrangements and Hessenberg varieties Invited International conference

      Takuro Abe

      Advances in Arrangement Theory  26 7 2017  CMS, SMC

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：Centre Mont-Royal, Montreal, Canada  

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    • Hyperplane arrangements and Hessenberg varieties Invited International conference

      Takuro Abe

      Arrangements and beyond  7 6 2017  Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy  

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    • Hyperplane arrangments, Solomon-Terao algebras and applications to Hessenberg varieties Invited

      Takuro Abe

      26 5 2017  RIMS

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：Kyoto  

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    • Algebra and geometry of Solomon-Terao's formula Invited International conference

      Takuro Abe

      Hyperplane Arrangements and related topics  14 2 2017  Hokkaido University

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      Language：English   Presentation type：Oral presentation (general)  

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    • Algebra and combinatorics of hyperplane arrangements Invited International conference

      Takuro Abe

      The 15th Japan-Korea Workshop on Algebra and Combinatorics  10 2 2017  Kumamoto University

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      Language：English   Presentation type：Oral presentation (general)  

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    • Divisionally free arrangements of hyperplanes Invited

      Takuro Abe

      第61回代数学シンポジウム  9 9 2016 

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

      Venue：Saga University  

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    • Recent topics on free arrangements of hyperplanes Invited International conference

      Takuro Abe

      Summer Conference on Hyperplane Arrangements(SCHA) in Sapporo  11 8 2016  Hokkaido University

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：Sapporo, Japan  

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    • Freeness and flags of hyperplane arrangements Invited International conference

      Takuro Abe

      Special Session on Topology and Combinatorics of Arrangements (in honor of Mike Falk)  3 2016  AMS Sectional Meeting, at Stony Brook University, USA.

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

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    • Divisionally free arrangements of hyperplanes Invited

      Takuro Abe

      26 11 2015  Fukuoka University

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      Language：Japanese   Presentation type：Oral presentation (general)  

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    • Divisional freeness and the second Betti number of hyperplane arrangements Invited International conference

      Takuro Abe

      Hyperplane arrangements and reflection groups  11 8 2015  Leibniz Universität Hannover

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：Hannover, Germany  

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    • Divisionally free arrangements of hyperplanes(講演） Invited International conference

      Takuro Abe

      Differential and combinatorial aspects of singularities  6 8 2015  Technische Universitat Kaiserslautern

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

      Venue：Kaiserslautern, Germany  

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    • Division free theorem for line arrangements and divisionally free arrangements of hyperplanes Invited International conference

      Takuro Abe

      Arrangements of plane curves and related problems  17 3 2015  Tokyo Metropolitan University

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：Tokyo Metropolitan University  

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    • Division and localization of characteristic polynomials of hyperplane arrangements" Invited International conference

      Takuro Abe

      Combinatorics and Algebraic Topology of Configurations  19 2 2015  Centro De Giorgi

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：Pisa, Italy  

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    • 直線配置の数え上げ幾何とベッチ数 Invited

      阿部 拓郎

      信州大学数理科学談話会  6 2 2015 

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      Language：Japanese   Presentation type：Oral presentation (general)  

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    • Intersection points, chambers and the freeness of line arrangements

      Takuro Abe

      Algebraic and Complex geometry seminar at Osaka University  19 12 2014 

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      Language：Japanese   Presentation type：Oral presentation (general)  

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    • Freeness and Geometry of line arrangements Invited International conference

      Takuro Abe

      Hokkaido University - University of Bremen Joint Symposium Special session:Arrangements of Hyperplanes  3 12 2014  University of Bremen and Hokkaido University

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

      Venue：Bremen, Germany  

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    • The freeness of ideal subarrangements of Weyl arrangements

      Takuro Abe

      Seminarie Geometrie et Systemes Dynamiques  28 11 2014  Université de Bourgogne

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      Language：English   Presentation type：Oral presentation (general)  

      Venue：Dijon, France  

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    • Algebra and Combinatorics of line arrangements 1 and 2

      Takuro Abe

      組合せ論と可換代数サマーセミナー2014  24 9 2014 

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      Language：Japanese   Presentation type：Oral presentation (general)  

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    • Stability of line arrangements in the projective plane International conference

      Takuro Abe

      The 1st Workshop of JSPS-MAE Sakura Program ``Geometry and Combinatorics of Hyperplane Arrangements and Related Problems''  2 9 2014  Masahiko Yoshinaga (Hokkaido University)

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

      Venue：Hokkaido University  

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    • Recent developments on algebra of line arrangements Invited International conference

      Takuro Abe

      The 2nd Franco-Japanese-Vietnamese Symposium on Singularities  27 8 2014  CNRS-JSPS-VAST

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

      Venue：University of Hokkaido  

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    • Intersection points and Betti numbers of line arrangements Invited International conference

      Takuro Abe

      Special Session ``D-modules and Singularities'' at the First Joint International Meeting RSME-SCM-SEMA-SIMAI-UMI  1 7 2014  RSME-SCM-SEMA-SIMAI-UMI

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

      Venue：The University of the Basque Country  

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    • Intersection points and Betti numbers of line arrangements

      Japan Conference on Graph Theory and Combinatorics  20 5 2014  KAWARABAYASHI Large Graph project and Nihon University

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      Language：English   Presentation type：Other  

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    • Intersection points and Betti numbers of the complements of line arrangements Invited International conference

      Takuro Abe

      Branched Coverings, Degenerations, and Related Topics 2014  10 3 2014  広島大学

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      Language：English   Presentation type：Oral presentation (general)  

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    • The freeness of ideal subarrangements of Weyl arrangements Invited International conference

      Takuro Abe

      New perspectives in hyperplane and reflection arrangements  10 2 2014  Ruhr University Bochum

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      Language：English   Presentation type：Oral presentation (general)  

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    • 平面直線の交点と補空間のベッチ数

      第5回 代数曲面ワークショップ at 秋葉原  26 10 2013  首都大学東京

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

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    • 平面中の直線配置の交点数と補空間のベッチ数

      情報セキュリティと関連する離散数学  9 8 2013  信州大学

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      Language：Japanese   Presentation type：Other  

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    • Roots of characteristic polynomials and intersection points of line arrangements International conference

      Takuro Abe

      Geometry and Topology of Arrangements of Hypersurfaces  29 6 2013  American Mathematical Society, Romanian Mathematical Society

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

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    • 超平面配置の代数と組み合わせ論

      大阪組み合わせ論セミナー  15 6 2013  大阪市立大学

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      Language：Japanese   Presentation type：Other  

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    • Height bases for Weyl arrangements Invited International conference

      Takuro Abe

      Hyperplane Arrangements: Combinatorial and Geometric Aspects  21 2 2013  Ruhr University Bochum, Germany

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

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    • Height basis for Weyl arrangements

      Workshop on Free Divisors and Differential Equations  8 11 2012  Tokyo University of Agriculture and Technology

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

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    • 関数密度問題とハッシュ関数の安全性評価

      情報セキュリティ基盤の数理構造と安全性解析  5 9 2012  九州大学マス・フォア・インダストリ研究所

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

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    • Digraphs and free deformations between Coxeter and Catalan arrangements of the type A

      代数幾何の関連する諸分野  8 8 2012  北海道大学

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

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    • 超平面配置の代数と幾何

      関数方程式サマーセミナー  2 8 2011 

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

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    • Chambers and freeness of line arrangements

      Workshop on free divisors  31 5 2011  University of Warwick

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

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    • Free Coxeter arrangements and applications

      The 2nd Kyushu University-POSTECH Joint Workshop --Algebraic Geometry and Related Topics--  18 3 2011  九州大学

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

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    • Exponents and freeness of 3-arrangements

      特異点と多様体の幾何学  16 9 2010  山形大学

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

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    • 原始微分とコクセター型多重配置

      RIMS研究集会``表現論と組合わせ論''  27 8 2009  北海道大学

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

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    • A logarithmic module of a generalized multiarrangement

      The 6th HU and SNU Symposium on Mathematics --Geometry and Topology-- as a part of The 11th HU-SNU Joint Symposium  8 11 2008  北海道大学

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

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    • Coxeter multiarrangements with quasi-constant multiplicities

      Geometry and Analysis on Complex Varieties  21 11 2007  東京農業工業大学

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

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    • The addition-deletion theorems for multiarrangements and graphic deformation of the braid arrangement

      CIMPA summer school on arrangements and local systems  18 6 2007  CIMPA, Galatasaray University

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

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    • Construction of rank two reflexive sheaves from finite fields

      Geometry and Analysis on Complex Algebraic Geometry  11 12 2006  RIMS

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

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    • The stability of A_2 and B_2-type arrangements Invited International conference

      Takuro Abe

      Recent Developments in Arrangements and Configulation Spaces  10 8 2006  MSRI, Berkeley

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

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    Teaching Experience

    • 10 2024 - 3 2025 
      群論入門 （ 立教大学 ）

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    • 4 2024 - 9 2024 
      代数学I（環論） （ 立教大学 ）

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    • 10 2023 - 3 2024 
      Advanced Linear ALgebra （ Rikkyo University ）

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    • 10 2023 - 3 2024 
      Algebra II （ Rikkyo University ）

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    • 4 2023 - 9 2023 
      Linear Algebra 2 （ Rikkyo University ）

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    • 10 2018 - 3 2019 
      Ordinary Differential equations （ Kyushu University ）

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    •  
      代数幾何学大意 （ 九州大学 ）

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    •  
      数理モデル概論 （ 九州大学 ）

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    •  
      複素関数論 （ 九州大学 ）

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    •  
      工業数学F1（複素関数論） （ 京都大学 ）

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    •  
      微分積分学続論B（常微分方程式） （ 京都大学 ）

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    •  
      微分積分学続論A（ベクトル解析） （ 京都大学 ）

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    •  
      微分積分学 （ 京都大学 ）

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    •  
      線形代数学続論 （ 京都大学 ）

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    •  
      線形代数学 （ 京都大学 ）

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    Professional Memberships

    •  
      THE MATHEMATICAL SOCIETY OF JAPAN

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    Research Projects

    • Developments of theory of hyperplane arrangements and application to black box of AI

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

      Abe, Takuro

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      4 2025 - 3 2030

      Grant number：25H00399

      Authorship：Principal investigator 

      Grant amount：\201630000 （ Direct Cost: \155100000 、 Indirect Cost：\46530000 ）

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    • Fusion of enumerative and algebraic geometry, and exploration of quasi-geomtric invariants

      Takuro Abe

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      6 2023 - 3 2029

      Grant number：23K17298

      Authorship：Principal investigator 

      Grant amount：\26000000 （ Direct Cost: \20000000 、 Indirect Cost：\6000000 ）

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    • Discrete structures related to hyperplane arrangements, generalization, deepening, and applications

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

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      4 2023 - 3 2028

      Grant number：23H00081

      Grant amount：\46540000 （ Direct Cost: \35800000 、 Indirect Cost：\10740000 ）

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    • Research of logarithmic vector fields of hyperplane arrangements

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

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      4 2021 - 3 2025

      Grant number：21H00975

      Grant amount：\17030000 （ Direct Cost: \13100000 、 Indirect Cost：\3930000 ）

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    • Fusion of algebra, geometry and combinatorics based on the roots of Poincare polynomials of hyperplane arrangements

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Challenging Research (Exploratory) 

      Takuro Abe

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      7 2020 - 3 2023

      Grant number：20K20880

      Authorship：Principal investigator 

      Grant amount：\6500000 （ Direct Cost: \5000000 、 Indirect Cost：\1500000 ）

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    • Explicit study of hyperplane arrangements and related stratified spaces via discrete structures

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

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      4 2018 - 3 2023

      Grant number：18H01115

      Grant amount：\16770000 （ Direct Cost: \12900000 、 Indirect Cost：\3870000 ）

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    • D加群を用いた超平面配置とSolomon-寺尾複体の革新的研究

      日本学術振興会  国際共同研究加速基金(国際共同研究強化(A)) 

      阿部 拓郎

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      4 2019 - 3 2022

      Authorship：Principal investigator  Grant type：Competitive

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    • 超平面配置の余不変式環論の創成とその表現論・幾何学の新展開

      日本学術振興会  科研費（基盤研究B） 

      阿部 拓郎

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      4 2016 - 3 2021

      Authorship：Principal investigator  Grant type：Competitive

      Grant amount：\17680000 （ Direct Cost: \13600000 、 Indirect Cost：\4080000 ）

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    • 超平面配置の自由性・トポロジーとランダムウォークの新潮流

      日本学術振興会  科研費（挑戦的萌芽研究） 

      阿部 拓郎

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      4 2016 - 3 2018

      Authorship：Principal investigator  Grant type：Competitive

      Grant amount：\3510000 （ Direct Cost: \2700000 、 Indirect Cost：\810000 ）

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    • Panoptic Study of Hyperplane arrangements

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

      Terao Hiroaki, ABE Takuro, KAMIYA Hidehiko, KOHNO Toshitake, TAKEMURA Akimichi, TERAOSOMA Tomohide, MATSUMOTO Kohji, Cuntz Michael, Hoge Torsten, NAKASHIMA Norihiro, Roehrle Gerhard, Schenck Hal

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      4 2012 - 3 2017

      Grant number：24244001

      Grant amount：\35620000 （ Direct Cost: \27400000 、 Indirect Cost：\8220000 ）

      The following three essential themes were selected to grasp the vastness of the research of hyperplane arrangements. The obtained results are as follows:
      (A) An explicit formula for a basis of the derivation module of the Shi arrangements coming from the Weyl arrangement of type A was obtained. In the formula, the Bernoulli polynomials naturally appear. We proved that any ideal subarrangement is free and that the height distribution and the exponents are dual to each other. (B) Hypergeometric integrals are regarded as a period map on the moduli space of arrangements of hyperplanes and can be described in terms of local system cohomology. In this context, a new method was obtained to compute the cohomology groups of the Aomoto complex. (C) The multiple addition theorem was proved. Consequently we learned that the class of hyperplane arrangements in which the so-called Terao conjecture holds true is quite large.

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    • 超平面配置の自由性の多角的解析と関連する幾何学の研究

      日本学術振興会  科研費（若手研究（B)) 

      阿部 拓郎

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      4 2012 - 3 2016

      Authorship：Principal investigator  Grant type：Competitive

      Grant amount：\4420000 （ Direct Cost: \3400000 、 Indirect Cost：\1020000 ）

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    • 多重配置の自由性の解析と関連する幾何学の創出

      日本学術振興会  科研費（若手研究（B)) 

      阿部 拓郎

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      4 2009 - 3 2012

      Authorship：Principal investigator  Grant type：Competitive

      Grant amount：\3640000 （ Direct Cost: \2800000 、 Indirect Cost：\840000 ）

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    • 多重配置の自由性の解析と関連する幾何学の創出

      日本学術振興会  科研費（特別研究員奨励費） 

      阿部 拓郎

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      4 2008 - 3 2009

      Authorship：Principal investigator  Grant type：Competitive

      Grant amount：\800000 （ Direct Cost: \800000 ）

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    • 超平面配置上の自由重複度の研究

      日本学術振興会  科学研究費助成事業 

      阿部 拓郎

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      2008 - 2008

      Grant number：20740001

      Grant amount：\1170000 （ Direct Cost: \900000 、 Indirect Cost：\270000 ）

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    Academic Activities

    • 日本数学会関東支部連絡責任評議員

      日本数学会  2 4 2025 - Present

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      Type：Academic society, research group, etc. 

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    • An editor of ``Commentarii Mathematici Universitatis Sancti Pauli''

      Rikkyo University  2023 - Present

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      Type：Other 

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    • Editor of `` Innovations in Incidence Geometry — Algebraic, Topological and Combinatorial''

      2021 - Present

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      Type：Other 

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    • FPSAC 2024 Program Committee

      Planning, management, etc.

      Ruhr-Universität Bochum  （ Ruhr-Universität Bochum ） 22 7 2024 - 26 7 2024

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      Type：Academic society, research group, etc. 

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    • ICIAM2023 Local Scientific Program Organizer

      Planning, management, etc.

      ICIAM  20 8 2023 - 25 8 2023

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      Type：Academic society, research group, etc. 

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    Social Contribution

    • おもしろサイエンスワールド2024

      Advisor,　Organizing member

      立教大学理学部  おもしろサイエンスワールド2024  8 8 2024 - 8 8 2024

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      Type：Science cafe

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    • 「わける」と「数える」がつなぐ数学

      Lecturer

      情報・システム研究機構統計数理研究所、明治大学先端数理科学インスティテュート、九州大学マス・フォア・インダストリ研究所、京都大学数理解析研究所、大阪公立大学数学研究所（主管）  数学・数理科学5研究拠点合同市民講演会「はじける数学！ブレークスルーって何だろう？  大阪公立大学  6 11 2022 - 6 11 2022

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      Audience： Junior students,　High school students,　General

      Type：Lecture

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    • 超平面配置の数学

      Appearance

      九州大学  2018年度九州大学公開講座「現代数学入門」  12 8 2018 - 12 8 2018

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      Type：Lecture

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    • 平面直線を用いた二次元植木算

      Lecturer

      九州大学  平成29年度九州大学オープンキャンパス数学科紹介プログラム, 企画講演  6 8 2017 - 6 8 2017

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      Type：University open house

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