Updated on 2025/04/11

写真a

 
BACHMANN Henrik lennart
 
Organization
Graduate School of Mathematics Division of Mathematics Fundamental Mathematics Associate professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Associate professor

Degree 1

  1. Ph.D. （ 2015.12 ） 

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Research Interests 3

  1. Number Theory

  2. Multiple zeta values

  3. Modular forms

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Research Areas 1

  1. Natural Science / Algebra

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Research History 5

  1. Nagoya University   Graduate School of Mathematics

    2022.10

  2. Nagoya University   Graduate School of Mathematics   Designated Associate Professor (Global 30 International Program)

    2019.10 - 2022.12

  3. Nagoya University   Institute for Advanced Research & Graduate School of Mathematics   Assistant professor (YLC)

    2017.4 - 2019.9

  4. Max-Planck Institute for Mathematics (Bonn/Germany)   Guest ​Scientist

    2017.4 - 2018.3

  5. Nagoya University   Graduate School of Mathematics   JSPS Postdoctoral fellow

    2016.4 - 2017.3

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Papers 12

  1. Sum formulas for Schur multiple zeta values Open Access

    Henrik Bachmann, Shin-ya Kadota, Yuta Suzuki, Shuji Yamamoto, Yoshinori Yamasaki

    Journal of Combinatorial Theory, Series A   Vol. 200   page： 105781 - 105781   2023.11

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

    DOI： 10.1016/j.jcta.2023.105781

  2. Generalized Jacobi–Trudi determinants and evaluations of Schur multiple zeta values Open Access

    Henrik Bachmann, Steven Charlton

    European Journal of Combinatorics   Vol. 87   page： 103133 - 103133   2020.6

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

    DOI： 10.1016/j.ejc.2020.103133

  3. The algebra of bi-brackets and regularized multiple Eisenstein series Reviewed Open Access

    H. Bachmann

    Journal of Number Theory   Vol. 200   page： 260 - 294   2019.7

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

    DOI： 10.1016/j.jnt.2018.12.006

    Open Access

  4. The algebra of bi-brackets and regularized multiple Eisenstein series Open Access

    Bachmann Henrik

    JOURNAL OF NUMBER THEORY   Vol. 200   page： 260 - 294   2019.7

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

    DOI： 10.1016/j.jnt.2018.12.006

    Web of Science

  5. Checkerboard style Schur multiple zeta values and odd single zeta values Reviewed Open Access

    Henrik Bachmann, Yoshinori Yamasaki

    Mathematische Zeitschrift   Vol. 290 ( 3-4 ) page： 1173 - 1197   2018.12

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

    DOI： 10.1007/s00209-018-2058-5

    Other Link： http://link.springer.com/content/pdf/10.1007/s00209-018-2058-5.pdf

  6. Cyclotomic analogues of finite multiple zeta values Open Access

    Bachmann Henrik, Takeyama Yoshihiro, Tasaka Koji

    COMPOSITIO MATHEMATICA   Vol. 154 ( 12 ) page： 2701 - 2721   2018.12

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

    DOI： 10.1112/S0010437X18007583

    Web of Science

  7. Cyclotomic analogues of finite multiple zeta values Reviewed

    H. Bachmann, Y. Takeyama, K. Tasaka

    Compositio Mathematica   Vol. 154 ( 12 ) page： 2701 - 2721   2018.12

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

    DOI： 10.1112/S0010437X18007583

  8. INTERPOLATED SCHUR MULTIPLE ZETA VALUES Reviewed Open Access

    Henrik Bachmann

    Journal of the Australian Mathematical Society   Vol. 104 ( 3 ) page： 289 - 307   2018.6

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

    Inspired by the recent work of M. Nakasuji, O. Phuksuwan and Y. Yamasaki, we combine interpolated multiple zeta values and Schur multiple zeta values into one object, which we call interpolated Schur multiple zeta values. Our main result will be a Jacobi-Trudi formula for a certain class of these new objects. This generalizes an analogous result for Schur multiple zeta values and implies algebraic relations between interpolated multiple zeta values.

    DOI： 10.1017/S1446788717000209

    Scopus

  9. The double shuffle relations for multiple Eisenstein series Reviewed Open Access

    H. Bachmann, K. Tasaka

    Nagoya Mathematical Journal   Vol. 230   page： 180 - 212   2018.6

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

    DOI： 10.1017/nmj.2017.9

    Open Access

  10. THE DOUBLE SHUFFLE RELATIONS FOR MULTIPLE EISENSTEIN SERIES Open Access

    Bachmann Henrik, Tasaka Koji

    NAGOYA MATHEMATICAL JOURNAL   Vol. 230   page： 180 - 212   2018.6

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

    DOI： 10.1017/nmj.2017.9

    Web of Science

  11. Rooted tree maps and the derivation relation for multiple zeta values Reviewed Open Access

    H. Bachmann, T. Tanaka

    International Journal of Number Theory   Vol. 14 ( 10 ) page： 2657 - 2662   2018

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

    Rooted tree maps assign to an element of the Connes-Kreimer Hopf algebra of rooted trees a linear map on the noncommutative polynomial algebra in two letters. Evaluated at any admissible word, these maps induce linear relations between multiple zeta values. In this note, we show that the derivation relations for multiple zeta values are contained in this class of linear relations.

    DOI： 10.1142/S1793042118501592

    Web of Science

  12. On multiple series of Eisenstein type Reviewed

    Henrik Bachmann, Hirofumi Tsumura

    RAMANUJAN JOURNAL   Vol. 42 ( 2 ) page： 479 - 489   2017.2

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

    The aim of this paper is to study certain multiple series which can be regarded as multiple analogues of Eisenstein series. As part of a prior research, the second-named author considered double analogues of Eisenstein series and expressed them as polynomials in terms of ordinary Eisenstein series. This fact was derived from the analytic observation of infinite series involving hyperbolic functions which were based on the study of Cauchy, and also Ramanujan. In this paper, we prove an explicit relation formula among these series. This gives an alternative proof of this fact by using the technique of partial fraction decompositions of multiple series which was introduced by Gangl, Kaneko and Zagier. By the same method, we further show a certain multiple analogue of this fact and give some examples of explicit formulas. Finally we give several remarks about the relation between the results of the present and the previous works for infinite series involving hyperbolic functions.

    DOI： 10.1007/s11139-015-9738-0

    Web of Science

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MISC 4

  1. Finite and symmetric Mordell-Tornheim multiple zeta values

    Henrik Bachmann, Yoshihiro Takeyama, Koji Tasaka

        2020.1

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    We introduce finite and symmetric Mordell-Tornheim type of multiple zeta
    values and give a new approach to the Kaneko-Zagier conjecture stating that the
    finite and symmetric multiple zeta values satisfy the same relations.

    arXiv

  2. Modular forms and q-analogues of modified double zeta values

    H. Bachmann

    preprint     2018

  3. Special values of finite multiple harmonic q-series at roots of unity

    H. Bachmann, Y. Takeyama, K. Tasaka

    preprint     2018

  4. Rooted t​ree maps and the Kawashima relations for multiple zeta values

    H. Bachmann, T. Tanaka

    preprint     2018

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Presentations 13

  1. Numbers, infinite sums and multiple zeta values Invited

    Henrik Bachmann

    17th IAR YLC Seminar, Institute for Advanced Research, Nagoya University  2018.12.25 

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    Language：English   Presentation type：Oral presentation (general)  

  2. Multiple harmonic q-series at roots of unity and their connection to finite & symmetrized multiple zeta values Invited

    Henrik Bachmann

    Algebra seminar, Tohoku University  2018.5 

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    Language：English   Presentation type：Oral presentation (general)  

  3. Multiple harmonic q-series at roots of unity and finite & symmetrized multiple zeta values Invited

    Henrik Bachmann

    Periods in Number Theory, Algebraic Geometry and Physics, HIM, Bonn  2018.1 

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    Language：English   Presentation type：Oral presentation (general)  

  4. Multiple harmonic q-series at primitive roots of unity and finite multiple zeta values Invited

    Henrik Bachmann

    Seminar Aachen-Bonn-Köln-Lille-Siegen on Automorphic Forms, Universität zu Köln  2017.10 

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    Language：English   Presentation type：Oral presentation (general)  

  5. Modular forms and q-analogues of modified double zeta values Invited

    Henrik Bachmann

    解析数論セミナー, Nagoya University  2018.10.11 

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    Language：English   Presentation type：Oral presentation (general)  

  6. Modular forms and q-analogues of modified double zeta values Invited

    Henrik Bachmann

    関西多重ゼータ研究会第４２回, Kyoto Sangyo University  2018.9.29 

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    Language：English   Presentation type：Oral presentation (general)  

  7. Modular forms and q-analogues of modified double zeta values Invited

    Henrik Bachmann

    九大多重ゼータセミナー, Kyushu University  2018.9.14 

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    Language：English   Presentation type：Oral presentation (general)  

  8. Modular forms and multiple zeta values Invited

    Henrik Bachmann

    33rd Automorphic Forms Workshop, Duquesne University, Pittsburgh  2019.3.7 

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    Language：English   Presentation type：Oral presentation (general)  

  9. Interpolated Schur multiple zeta values Invited

    Henrik Bachmann

    解析数論セミナー, Nagoya University  2017.1 

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    Language：English   Presentation type：Oral presentation (general)  

  10. Derivatives of q-analogues of multiple zeta values Invited

    Henrik Bachmann

    Multiple zeta values research meeting,Kindai University  2017.2 

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    Language：English   Presentation type：Oral presentation (general)  

  11. Cyclotomic analogues of finite multiple zeta values Invited

    Henrik Bachmann

    The 10th Young Mathematicians Conference on Zeta Functions, Nagoya University  2017.2 

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    Language：English   Presentation type：Oral presentation (general)  

  12. Checkerboard style Schur multiple zeta values Invited

    Henrik Bachmann

    解析数論セミナー, Nagoya Unversity  2018.4 

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    Language：English   Presentation type：Oral presentation (general)  

  13. A simultaneous q-analogue of finite and symmetrized multiple zeta values Invited International conference

    Henrik Bachmann

    CARMA (Algebraic Combinatorics, Resurgence, Moulds and Applications), CIRM, Luminy  2017.6 

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    Language：English   Presentation type：Oral presentation (general)  

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KAKENHI (Grants-in-Aid for Scientific Research) 4

  1. Connections of (quasi)modular forms to multiple zeta values and their finite analogues

    Grant number：23K03030  2023.4 - 2026.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Authorship：Principal investigator 

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

  2. Generalizations of the double shuffle relations for multiple zeta values and the connections to modular forms

    Grant number：21K13771  2021.4 - 2023.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Early-Career Scientists

    Bachmann Henrik

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    Authorship：Principal investigator 

    Grant amount：\2210000 （ Direct Cost: \1700000 、 Indirect Cost：\510000 ）

    In this research project a generalization of the classical double shuffle relations of multiple zeta values were introduced and studied. This
    new set of equations are motivated by multiple Eisenstein series introduced by Gangl-Kaneko-Zagier. It is defined by using the notion of
    bimoulds and they are given by those bimoulds which are symmetril and swap invariant.

  3. q-analogues of multiple zeta values and their applications in geometry

    Grant number：19K14499  2019.4 - 2023.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Early-Career Scientists

    Bachmann Henrik

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    Authorship：Principal investigator 

    Grant amount：\2080000 （ Direct Cost: \1600000 、 Indirect Cost：\480000 ）

    In the project "q-analogues of multiple zeta values and their applications in geometry" the connection of q-analogues and the study of a more broader class of q-series were studied. For this we (j.w. with Jan-Willem van Ittersum) introduced the notion of polynomial functions on partitions. The main result is that all these functions, which are given by the q-bracket of certain polynomials, are always give rise to qanalogues of multiple zeta values. In particular, we calculated the limit as q goes to 1. As an application we showed how these connections give rise to relations among multiple zeta values. In another project (j.w. Ulf Kuehn and Nils Matthes) we introduced the notion of the formal double Eisenstein space. This space can be seen as a generalization of the formal double zeta space introduced by Gangl-Kaneko-Zagier. We showed that any power series satisfying the Fay-idendity give rise to a realization of this space.

  4. 多重ゼータ値と多重Ｅｉｓｅｎｓｔｅｉｎ級数の代数的， 幾何的な研究

    Grant number：16F16021  2016.4 - 2018.3

    日本学術振興会  科学研究費助成事業  特別研究員奨励費

    古庄 英和, BACHMANN HENRIK

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    多重ゼータ値とはここ四半世紀で研究が盛んになった研究対象であり、多重Eisenstein級数とはGangl, Kaneko Zagier (2006)により導入された二重Eisenstein級数を一般化した級数のことである。Bachamann氏は外国人特別研究員として採用されていた１年間、国内のさまざまなセミナー、研究集会に足繁く出向き国内の若手の研究者たちと複数の共同研究を同時進行で行い、この多重ゼータ値と多重Eisenstein級数について精力的に研究を続けてきた。主だった業績として以下の４つが挙げられる：
    1).多重Eisenstein級数の微分に関する研究：多重Eisenstein級数は、depthが1,2,3の場合において多重Eisenstein級数に関連するある種のq級数が微分作用素で閉じていることを計算により示した。
    2).補間Schur多重ゼータ値の研究：多重ゼータ値や多重ゼータスター値を一般化した補間多重ゼータ値という多項式とYoung図形より構成されるSchur多重ゼータ値が知られている。これら二者をつなげる補間Schur多重ゼータ値という多項式を導入し基本的な性質を導いた。
    3).円分的有限多重ゼータ値の研究：円分的有限多重ゼータ値を導入して、これの基本的な代数的構造の基本的性質、特殊値、有限多重ゼータ値のq類似とのつながりについての結果を得た。
    4).Schur多重ゼータ値の和公式の類似の研究：多重ゼータ値や多重ゼータスター値と同様にSchur多重ゼータ値に対しても和公式の類似が成り立つことを示した。

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Social Contribution 2

  1. Studium Generale

    Role(s)：Lecturer

    Nagoya University  Numbers, infinite sums and their appearences in daily life  2018.12

  2. JSPS Science Dialogue

    Role(s)：Presenter,　Lecturer

    Iwate Prefectural Mizusawa High School & Japan Society for the Promotion of Science  "Hamburgers, Numbers and infinite Series"  2016.11

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