Updated on 2026/05/16
Ph.D. （ 2015.12 ）
Number Theory
Multiple zeta values
Modular forms
Natural Science / Algebra
Natural Science / Mathematical physics and basic theory / Number theory
Nagoya University Graduate School of Mathematics
2022.10
Nagoya University Graduate School of Mathematics Designated Associate Professor (Global 30 International Program)
2019.10 - 2022.12
Nagoya University Institute for Advanced Research & Graduate School of Mathematics Assistant professor (YLC)
2017.4 - 2019.9
Max-Planck Institute for Mathematics (Bonn/Germany) Guest Scientist
2017.4 - 2018.3
Nagoya University Graduate School of Mathematics JSPS Postdoctoral fellow
2016.4 - 2017.3
Formal multiple Eisenstein series and their derivations Reviewed International journal Open Access
Henrik Bachmann, Jan-Willem van Ittersum
Advances in Mathematics Vol. 487 page： 110739 - 110739 2026
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
On a conjecture of Zhao related to standard relations among cyclotomic multiple zeta values Reviewed International journal Open Access
Henrik Bachmann, Khalef Yaddaden
Journal of Algebra Vol. 688 page： 21 - 58 2026
Realizations of the formal double Eisenstein space Reviewed International journal
Henrik Bachmann, Ulf Kuhn, Nils Matthes
Tohoku Mathematical Journal 2025
Partitions, multiple zeta values and the q-bracket Reviewed International journal Open Access
Henrik Bachmann, Jan-Willem van Ittersum
Selecta Mathematica Vol. 30 ( 3 ) 2024
MacMahon's sums-of-divisors and their connection to multiple Eisenstein series Reviewed International journal
Henrik Bachmann
Research in Number Theory Vol. 10 ( 2 ) page： 50 - 50 2024
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
Combinatorial multiple Eisenstein series Reviewed International journal Open Access
Henrik Bachmann, Annika Burmester
Research in the Mathematical Sciences Vol. 10 ( 3 ) page： 35 - 35 2023
Finite and symmetric Mordell-Tornheim multiple zeta values Reviewed International journal
Henrik Bachmann, Yoshihiro Takeyama, Koji Tasaka
Journal of the Mathematical Society of Japan Vol. 73 ( 4 ) page： 1129 - 1158 2021.10
Modular forms and q-analogues of modified double zeta values Reviewed International journal Open Access
Henrik Bachmann
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg Vol. 90 ( 2 ) page： 201 - 213 2020.10
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
Special values of finite multiple harmonic q-series at roots of unity Reviewed International journal
Henrik Bachmann, Yoshihiro Takeyama, Koji Tasaka
Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) Vol. 2 (IRMA Lectures in Mathematics and Theoretical Physics 31) Vol. 31 page： 1 - 18 2020
Multiple Eisenstein series and q-analogues of multiple zeta values Reviewed International journal
Henrik Bachmann
Periods in Quantum Field Theory and Arithmetic (Springer Proceedings in Mathematics & Statistics 314) Vol. 314 page： 173 - 235 2020
A dimension conjecture for q-analogues of multiple zeta values Reviewed International journal
Henrik Bachmann, Ulf Kuhn
Periods in Quantum Field Theory and Arithmetic (Springer Proceedings in Mathematics & Statistics 314) Vol. 314 page： 237 - 258 2020
Rooted tree maps and the Kawashima relations for multiple zeta values Reviewed International journal Open Access
Henrik Bachmann, Tatsushi Tanaka
Kyushu Journal of Mathematics Vol. 74 ( 1 ) page： 169 - 176 2020
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
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
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
Cyclotomic analogues of finite multiple zeta values Reviewed Open Access
H. Bachmann, Y. Takeyama, K. Tasaka
Compositio Mathematica Vol. 154 ( 12 ) page： 2701 - 2721 2018.12
INTERPOLATED SCHUR MULTIPLE ZETA VALUES Reviewed Open Access
Henrik Bachmann
Journal of the Australian Mathematical Society Vol. 104 ( 3 ) page： 289 - 307 2018.6
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
THE DOUBLE SHUFFLE RELATIONS FOR MULTIPLE EISENSTEIN SERIES Open Access
Bachmann Henrik, Tasaka Koji
NAGOYA MATHEMATICAL JOURNAL Vol. 230 page： 180 - 212 2018.6
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
On multiple series of Eisenstein type Reviewed
Henrik Bachmann, Hirofumi Tsumura
RAMANUJAN JOURNAL Vol. 42 ( 2 ) page： 479 - 489 2017.2
The algebra of multiple divisor functions and applications to multiple zeta values Reviewed International journal
Henrik Bachmann, Ulf Kuhn
The Ramanujan Journal Vol. 40 ( 3 ) page： 605 - 648 2016.7
Finite and symmetric Mordell-Tornheim multiple zeta values
Henrik Bachmann, Yoshihiro Takeyama, Koji Tasaka
2020.1
Modular forms and q-analogues of modified double zeta values
H. Bachmann
preprint 2018
Special values of finite multiple harmonic q-series at roots of unity
H. Bachmann, Y. Takeyama, K. Tasaka
preprint 2018
Rooted tree maps and the Kawashima relations for multiple zeta values
H. Bachmann, T. Tanaka
preprint 2018
Formal finite multiple zeta values Invited International conference
Henrik Bachmann
Meeting in the Middle: Conference on characteristic 0 and characteristic p multiple zeta values, Hawaii University 2026.3
Variants of Multiple Eisenstein Series Invited
Henrik Bachmann
Japan-India Workshop on L-functions and multiple zeta functions, Sophia University 2026.3
Relations and derivatives for multiple Eisenstein series Invited International conference
Henrik Bachmann
Multiple zeta values and modular forms, Mathematisches Forschungsinstitut Oberwolfach 2026.2
Multiple Zeta Values and Multiple Eisenstein Series Invited
Henrik Bachmann
都立大整数論セミナー, Tokyo Metropolitan University 2025.12
Recent developments for multiple Eisenstein series Invited
Henrik Bachmann
多重ゼータ値の諸相 (Various Aspects of Multiple Zeta Values), RIMS, Kyoto 2025.9
Recent developments for multiple Eisenstein series Invited International conference
Henrik Bachmann
Elliptics and Beyond 25, Bethe Center for Theoretical Physics, Bonn 2025.9
Multiple zeta values and modular forms Invited International conference
Henrik Bachmann
Algebra, Geometry, and Mathematical Physics Seminar, University of Amsterdam 2025.9
sl_2 代数と多重アイゼンシュタイン級数について Invited
Henrik Bachmann
第70回 代数学シンポジウム, Kyushu University 2025.8
Flexion Units Invited
Henrik Bachmann
Kagoshima Mould Seminar, Kagoshima University 2025.8
sl2-algebras and multiple Eisenstein series Invited International conference
Henrik Bachmann
4th International Workshop on Multiple Zeta Values and Related Fields, Tongji University, Shanghai 2025.7
sl2-algebras and multiple Eisenstein series Invited International conference
Henrik Bachmann
HKU Number Theory Days 2025, The University of Hong Kong 2025.6
Recent developments and 12 open problems on multiple Eisenstein series Invited
Henrik Bachmann
Seminar on multiple Eisenstein series, Tohoku University 2024.12
Finite multiple zeta values and their variants Invited International conference
Henrik Bachmann
Beyond multiple zeta values, Universität Hamburg 2024.8
Formal multiple zeta values and their variants Invited International conference
Henrik Bachmann
多重zeta值与L-函数相关领域 研讨会 2024, Anhui Normal University 2024.6
q-analogues of multiple zeta values and polynomial functions on partitions Invited
Henrik Bachmann
q級数とその周辺, Osaka Institute of Technology 2024.3
Derivations for quasi-shuffle algebras Invited
Henrik Bachmann
第18回多重ゼータ研究集会, Kindai University 2024.2
Numbers, infinite sums and why Japan is a great place for certain number theorists Invited
Henrik Bachmann
12th JSPS Club Meeting in Japan, Nagoya University 2023.12
Formal multiple Eisenstein series and their derivations Invited
Henrik Bachmann
Algebraic Number Theory and Related Topics 2023, RIMS, Kyoto 2023.12
Formalization of multiple Eisenstein series Invited
Henrik Bachmann
Lecture series, Kyushu University (jointly with Annika Burmester) 2023.6
Formal quasimodular forms and formal multiple Eisenstein series Invited International conference
Henrik Bachmann
Modular forms in number theory and beyond, Bielefeld University 2022.8
The zoo of multiple Eisenstein series Invited
Henrik Bachmann
多重ゼータ値の諸相, RIMS Kyoto 2022.5
Combinatorial multiple Eisenstein series & polynomial functions on partitions Invited
Henrik Bachmann
Lecture series, Kyushu University 2022.4
Connecting modular forms and multiple zeta values via combinatorial multiple Eisenstein series Invited International conference
Henrik Bachmann
Seminar arithmetische Geometrie und Zahlentheorie, Universität Hamburg (Online) 2022.1
Finite multiple zeta values Invited International conference
Henrik Bachmann
Geometry, Arithmetic and Differential Equations of Periods (GADEPs), Online 2021.10
多重ゼータ値のq類似および形式的な二重アイゼンシュタイン空間の実現 Invited
Henrik Bachmann
解析数論セミナー, Nagoya University (Online) 2021.7
Formal multiple Eisenstein series and formal multiple zeta values Invited
Henrik Bachmann
関西多重ゼータ研究会第54回 (Online) 2021.5
Formal multiple Eisenstein series Invited International conference
Henrik Bachmann
Seminar arithmetische Geometrie und Zahlentheorie, Universität Hamburg (Online) 2021.5
Formal quasi-modular forms Invited
Henrik Bachmann
2021 Waseda number theory Conference (Online) 2021.3
A variant of the double shuffle relations and quasi modular forms Invited
Henrik Bachmann
ACPMS Seminar (Online) 2020.12
多重ゼータ値とそのモジュラー形式との関係 Invited
Henrik Bachmann
2020年度第3回多元数理談話会 (Online), Nagoya University 2020.12
Multiple Eisenstein series and their Fourier coefficients Invited
Henrik Bachmann
九大多重ゼータセミナー (Online), Kyushu University 2020.5
q-double zeta values and modular forms Invited
Henrik Bachmann
Japan-Taiwan joint workshop on multiple zeta values, 沖縄県青年会館, Naha, Okinawa 2020.2
Combinatorial multiple Eisenstein series Invited
Henrik Bachmann
第13回多重ゼータ研究集会, Kindai University, Osaka 2020.2
Generalized double shuffle equations for (q-)multiple zeta values Invited
Henrik Bachmann
九大多重ゼータセミナー, Kyushu University, Fukuoka 2020.1
有限多重調和q級数の1のベキ根での値と有限および対称多重ゼータ値
Henrik Bachmann
日本数学会2019年度秋季総合分科会, 金沢大学 2019.9
Generalized double shuffle equations in depth two and quasi modular forms Invited
Henrik Bachmann
解析数論セミナー, Nagoya University 2019.9
Multiple harmonic q-series at roots of unity and their connection to finite & symmetric multiple zeta values Invited International conference
Henrik Bachmann
Research seminar, Oxford University 2019.8
Sum/Some formulas for Schur multiple zeta values Invited
Henrik Bachmann
多重ゼータ研究集会, Kyushu University, Fukuoka 2019.6
Multiple harmonic q-series at roots of unity and their connection to finite & symmetric multiple zeta values Invited
Henrik Bachmann
愛媛大学代数セミナー (Ehime Algebra Seminar), Ehime University, Matsuyama 2019.4
Cyclotomic analogues of finite multiple zeta values Invited
Henrik Bachmann
The 10th Young Mathematicians Conference on Zeta Functions, Nagoya University 2017.2
Checkerboard style Schur multiple zeta values Invited
Henrik Bachmann
解析数論セミナー, Nagoya Unversity 2018.4
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
Derivatives of q-analogues of multiple zeta values Invited
Henrik Bachmann
Multiple zeta values research meeting,Kindai University 2017.2
Numbers, infinite sums and multiple zeta values Invited
Henrik Bachmann
17th IAR YLC Seminar, Institute for Advanced Research, Nagoya University 2018.12.25
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
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
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
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
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
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
Modular forms and multiple zeta values Invited
Henrik Bachmann
33rd Automorphic Forms Workshop, Duquesne University, Pittsburgh 2019.3.7
Interpolated Schur multiple zeta values Invited
Henrik Bachmann
解析数論セミナー, Nagoya University 2017.1
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)
Authorship：Principal investigator
Grant amount：\3640000 （ Direct Cost: \2800000 、 Indirect Cost：\840000 ）
Grant number：21K13771 2021.4 - 2023.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Early-Career Scientists
Bachmann Henrik
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.
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
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.
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
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。
Studium Generale
Role(s)：Lecturer
Nagoya University Numbers, infinite sums and their appearences in daily life 2018.12
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
