Details of the Researcher

PHOTO

Saiei Matsubara
Section
Graduate School of Information Sciences
Job title
Associate Professor
Degree

  • 修士（数理科学）（東京大学）

  • 博士（数理科学）（東京大学）

  • 修士（数理科学）（東京大学）

e-Rad No.
70834381

Research History 5

  • 2025/04 - Present
    Tohoku University　Graduate School of Information Sciences Department of Computer and Mathematical Sciences

  • 2022/04 - 2025/03
    Kumamoto University

  • 2019/04 - 2019/12
    Kobe University

  • 2018/04 - 2019/03
    Kobe University

  • 2017/04 - 2018/03
    The University of Tokyo

Education 3

  • The University of Tokyo　Graduate School of Mathematical Sciences

    2015/04 - 2018/03

  • The University of Tokyo　Graduate School of Mathematical Sciences

    2013/03 - 2015/04

  • The University of Tokyo　Faculty of Science

    2011/04 - 2013/03

Research Interests 5

  • rapid decay homology group

  • computational algebraic analysis

  • (co)homology intersection theory

  • GKZ hypergeometric functions

  • system of linear partial differential equations

Research Areas 1

  • Natural sciences / Basic analysis / hypergeometric functions, algebraic analysis

Papers 18

  1. Generalized hypergeometric functions with several variables

    Saiei-Jaeyeong Matsubara-Heo, Toshio Oshima

    Indagationes Mathematicae　2025/03

    Publisher: arXiv

    DOI： 10.1016/j.indag.2024.07.007 　

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    We introduce a hypergoemetirc series with two complex variables, which generalizes Appell's, Lauricella's and Kempé de Fériet's hypergeometric series, and study the system of differential equations that it satisfies. We determine the singularities, the rank and the condition for the reducibility of the system. We give complete local solutions of the system at many singular points of the system and solve the connection problem among these local solutions. Under some assumptions, the system is written as a KZ equation. We determine its spectral type in the direction of coordinates as well as simultaneous eigenspace decompositions of residue matrices. The system may or may not be rigid in the sense of N.~Katz viewed as an ordinary differential equation in some direction. We also show that the system is a special case of Gel'fand-Kapranov-Zelevinsky system. From this point of view, we discuss multivariate generalizations.

  2. Twisted cohomology and likelihood ideals

    Matsubara-Heo, S.-J., Telen, S.

    Advances in Applied Mathematics　165　2025

    Publisher: arXiv

    DOI： 10.1016/j.aam.2024.102832 　

    ISSN： 1090-2074 0196-8858

  3. Restrictions of Pfaffian systems for Feynman integrals Peer-reviewed

    Vsevolod Chestnov, Saiei J. Matsubara-Heo, Henrik J. Munch, Nobuki Takayama

    Journal of High Energy Physics　2023/11/28

    DOI： 10.1007/jhep11(2023)202 　

    ISSN： 1029-8479

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    <jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>This work studies limits of Pfaffian systems, a class of first-order PDEs appearing in the Feynman integral calculus. Such limits appear naturally in the context of scattering amplitudes when there is a separation of scale in a given set of kinematic variables. We model these limits, which are often singular, via <jats:italic>restrictions</jats:italic> of <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \mathcal{D} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>D</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-modules. We thereby develop two different restriction algorithms: one based on gauge transformations, and another relying on the Macaulay matrix. These algorithms output Pfaffian systems containing fewer variables and of smaller rank. We show that it is also possible to retain logarithmic corrections in the limiting variable. The algorithms are showcased in many examples involving Feynman integrals and hypergeometric functions coming from GKZ systems. This work serves as a continuation of [1].</jats:p>

  4. Four lectures on Euler integrals Peer-reviewed

    Saiei-Jaeyeong Matsubara-Heo, Sebastian Mizera, Simon Telen

    SciPost Physics Lecture Notes　2023/10/26

    DOI： 10.21468/scipostphyslectnotes.75 　

    ISSN： 2590-1990

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    <jats:p>These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate the diverse mathematical techniques involved in the study of Euler integrals, including polyhedral geometry, very affine varieties, differential equations, and computational algebra.</jats:p>

  5. Macaulay matrix for Feynman integrals: linear relations and intersection numbers Peer-reviewed

    Vsevolod Chestnov, Federico Gasparotto, Manoj K. Mandal, Pierpaolo Mastrolia, Saiei J. Matsubara-Heo, Henrik J. Munch, Nobuki Takayama

    Journal of High Energy Physics　2022　(9)　2022/09/22

    Publisher: Springer Science and Business Media LLC

    DOI： 10.1007/jhep09(2022)187 　

    ISSN： 1029-8479

    eISSN： 1029-8479

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    Abstract We elaborate on the connection between Gel’fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman Integrals. We propose a novel, more efficient algorithm to compute Macaulay matrices, which are used to derive Pfaffian systems of differential equations. The Pfaffian matrices are then employed to obtain linear relations for $$ \mathcal{A} $$-hypergeometric (Euler) integrals and Feynman integrals, through recurrence relations and through projections by intersection numbers.

  6. An algorithm of computing cohomology intersection number of hypergeometric integrals Peer-reviewed

    Matsubara-Heo, S.-J., Takayama, N.

    Nagoya Mathematical Journal　246　1-17　2022/06

    Publisher: Cambridge University Press ({CUP})

    DOI： 10.1017/nmj.2021.2 　

    ISSN： 0027-7630

    eISSN： 2152-6842

  7. Computing cohomology intersection numbers of GKZ hypergeometric systems

    Saiei-Jaeyeong Matsubara-Heo

    Proceedings of Science, MathemAmplitudes 2019: Intersection Theory & Feynman Integrals (MA2019), 18-20 December 2019, Padova, Italy　2022/02

  8. Localization formulas of cohomology intersection numbers Peer-reviewed

    Saiei-Jaeyeong Matsubara-Heo

    Journal of the Mathematical Society of Japan　1　(1)　1-32　2022/01

    Publisher: Mathematical Society of Japan (Project Euclid)

    DOI： 10.2969/jmsj/87738773 　

    ISSN： 0025-5645

  9. Global Analysis of GG Systems Peer-reviewed

    Matsubara-Heo, S.-J.

    International Mathematics Research Notices　2022　(19)　2022

    Publisher: Oxford University Press (OUP)

    DOI： 10.1093/imrn/rnab144 　

    ISSN： 1687-0247 1073-7928

    eISSN： 1687-0247

  10. Homology and cohomology intersection numbers of GKZ systems Peer-reviewed

    Yoshiaki Goto, Saiei-Jaeyeong Matsubara-Heo

    Indagationes Mathematicae　33　(3)　546-580　2021/12

    Publisher: Elsevier BV

    DOI： 10.1016/j.indag.2021.12.002 　

    ISSN： 0019-3577

  11. A Tree Expansion Formula of a Homology Intersection Number on the Configuration Space M,n Peer-reviewed

    Matsubara-Heo, S.-J.

    Annales Henri Poincare　22　(8)　2831-2852　2021/03

    Publisher: Springer Science and Business Media {LLC}

    DOI： 10.1007/s00023-021-01041-4 　

    ISSN： 1424-0637

    eISSN： 1424-0661

  12. Euler and Laplace integral representations of GKZ hypergeometric functions II Peer-reviewed

    Matsubara-Heo, S.J.

    Proceedings of the Japan Academy Series A: Mathematical Sciences　96　(9)　79-82　2020/11

    Publisher: Project Euclid

    DOI： 10.3792/pjaa.96.015 　

    ISSN： 0386-2194

  13. Algorithms for Pfaffian Systems and Cohomology Intersection Numbers of Hypergeometric Integrals Peer-reviewed

    Saiei-Jaeyeong Matsubara-Heo, Nobuki Takayama

    Lecture Notes in Computer Science　73-84　2020

    Publisher: Springer International Publishing

    DOI： 10.1007/978-3-030-52200-1_7 　

    ISSN： 0302-9743

    eISSN： 1611-3349

  14. Euler and Laplace integral representations of GKZ hypergeometric functions I Peer-reviewed

    MATSUBARA-HEO, S.J.

    Proceedings of the Japan Academy Series A: Mathematical Sciences　96　(9)　75-78　2020

    Publisher: Project Euclid

    DOI： 10.3792/pjaa.96.014 　

    ISSN： 0386-2194

  15. On mellin–barnes integral representations for GKZ hypergeometric functions Peer-reviewed

    Matsubara-Heo, S.-J.

    Kyushu Journal of Mathematics　74　(1)　109-125　2020

    Publisher: Faculty of Mathematics, Kyushu University

    DOI： 10.2206/kyushujm.74.109 　

    ISSN： 1340-6116

  16. Intersection theory for Euler integral representations of GKZ hypergeometric functions: Appell’s F1 case Invited

    Saiei-Jaeyeong Matsubara-Heo

    Complex Differential and Difference Equations　283-296　2019/11/18

    Publisher: De Gruyter

    DOI： 10.1515/9783110611427-009 　

  17. On the rapid decay homology of F. Pham Peer-reviewed

    Saiei-Jaeyeong Matsubara-Heo

    RIMS Kokyuroku Bessatsu　75　2019

  18. Residue current approach to Ehrenpreis–Malgrange type theorem for linear differential equations with constant coefficients and commensurate time lags Peer-reviewed

    Saiei-Jaeyeong Matsubara-Heo

    Advances in Mathematics　331　170-208　2018/06/20

    Publisher: Academic Press Inc.

    DOI： 10.1016/j.aim.2018.04.004 　

    ISSN： 1090-2082 0001-8708

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Books and Other Publications 2

  1. 数理科学 2024年3月号 Ｎｏ.729

    高山 信毅, 松原 宰栄

    2024/03

  2. 数理科学 2023年8月号 No.722

    サイエンス社　2023/08

Presentations 66

  1. Generalized hypergeometric functions with several variables

  2. Hypergeometric study of Feynman (Euler) integrals Invited

    Saiei-Jaeyeong Matsubara-Heo

    Positive Geometry in Particle Physics and Cosmology, Max Planck Institute for Mathematics in the Sciences

  3. Non-rigid and globally analyzable hypergeometric system Invited

    Saiei-Jaeyeong Matsubara-Heo

  4. 代数方程式系と超幾何系 Invited

    松原 宰栄

    日本数学会2023年度秋季総合分科会・無限可積分系セッション

  5. Towards Algebraic Analysis of Hypergeometric Systems

    Saiei-Jaeyeong Matsubara-Heo

    ICIAM10

  6. Twisted Cohomology and Likelihood Ideals

  7. The signature of the invariant hermitian form for a regular holonomic GKZ system

    松原宰栄, 後藤良彰

    日本数学会年会　2023/03/15

  8. Twisted Cohomology and Likelihood Ideals Invited

    松原宰栄

    代数解析日大研究集会　2023/03/08

  9. Twisted Cohomology and Likelihood Ideals

    2023/01/06

  10. Hypergeometric system of contingency table Invited

    2022/10/06

  11. Euler積分をめぐって

    松原宰栄

    函数方程式論サマーセミナー2022　2022/08/12

  12. Restrictions of integrable connection and hypergeometric system of contingency table Invited

    Seminar on Nonlinear Algebra at MPIMiS　2022/06/09

  13. 分割表の超幾何系について Invited

    松原宰栄

    モデリングとシミュレーションのための計算代数2022　2022/03

  14. 分割表の超幾何函数について Invited

    松原宰栄

    代数解析千葉研究集会　2022/02/21

  15. Cohomology intersection numbers and computational algebra 1,2 Invited

    Saiei-Jaeyeong Matsubara-Heo

    2021/02/12

  16. Combinatorics of a point configuration space on Riemann sphere and homology intersection numbers

    Saiei-Jaeyeong Matsubara-Heo

    2021/01/06

  17. Combinatorics of a point configuration space on Riemann sphere and homology intersection numbers Invited

    Saiei-Jaeyeong Matsubara-Heo

    2020/12/17

  18. The secondary structure in the intersection theory of GKZ system Invited

    Saiei-Jaeyeong Matsubara-Heo

    2020/11/07

  19. Computing cohomology intersection numbers of GKZ systems Invited

    Saiei-Jaeyeong Matsubara-Heo

    2020/10/01

  20. Signature of the monodromy invariant hermitian form of GKZ system Invited

    Saiei-Jaeyeong Matsubara-Heo

    2020/07/24

  21. Computing cohomology intersection numbers of GKZ systems

    Saiei-Jaeyeong Matsubara-Heo

  22. Intersection numbers of Euler-Laplace integrals Invited

    Saiei-Jaeyeong Matsubara-Heo

    2020/02/18

  23. Boundary value problem GG systems and global analysis Invited

    Saiei-Jaeyeong Matsubara-Heo

    2020/01/31

  24. On a confluence of secondary fan

    Saiei-Jaeyeong Matsubara-Heo

  25. Computing cohomology intersection numbers of GKZ hypergeometric systems Invited

    Saiei-Jaeyeong Matsubara-Heo

  26. Evaluating cohomology intersection numbers from twisted period relations Invited

    Saiei-Jaeyeong Matsubara-Heo

    2019/09/25

  27. Computing cohomology intersection numbers of hypergeometric integrals Invited

    Saiei-Jaeyeong Matsubara-Heo

    2019/09/18

  28. Boundary value problem and GKZ systems

    Saiei-Jaeyeong Matsubara-Heo

  29. Boundary value problem of GKZ systems and monodromy invariant subspaces

    Saiei-Jaeyeong Matsubara-Heo

  30. Connection problem of GKZ hypergeometric functions

    Saiei-Jaeyeong Matsubara-Heo

  31. Connection problem of regular holonomic GKZ hypergeometric functions Invited

    Saiei-Jaeyeong Matsubara-Heo

    2019/05/22

  32. Integral representations of GKZ hypergeometric functions: Gauss-Manin connection, intersection theory, and quadratic relations Invited

    Saiei-Jaeyeong Matsubara-Heo

    2019/05/10

  33. On Laplace-Gauss-Manin connection associated to GKZ system Invited

    Saiei-Jaeyeong Matsubara-Heo

    2019/03/07

  34. Connection problem of GKZ hypergeometric functions Invited

    Saiei-Jaeyeong Matsubara-Heo

    2019/03/04

  35. On a twisted homology group

    Saiei-Jaeyeong Matsubara-Heo

    2019/02/18

  36. Connection problem of GKZ hypergeometric functions Invited

    Saiei-Jaeyeong Matsubara-Heo

    2018/12/27

  37. Quadratic relations of GKZ hypergeometric functions I, II Invited

    Saiei-Jaeyeong Matsubara-Heo

    2018/12/18

  38. Euler integral representations of regular holonomic GKZ hypergeometric functions: integration cycles, intersection theory and quadratic relation Invited

    Saiei-Jaeyeong Matsubara-Heo

    2018/10/23

  39. Integral representations of GKZ hypergeometric systems Invited

    Saiei-Jaeyeong Matsubara-Heo

    2018/09/18

  40. Intersection theory for Euler integral representations of GKZ hypergeometric functions

    Saiei-Jaeyeong Matsubara-Heo

    2018/09/10

  41. Intersection theory of regular holonomic GKZ hypergeometric systems

    Saiei-Jaeyeong Matsubara-Heo

    2018/08/07

  42. Integral representations of GKZ hypergeometric functions

    Saiei-Jaeyeong Matsubara-Heo

    2018/08/03

  43. GKZ hypergeometric systems, twisted Laplace-Gauss-Manin connections, series representations, and integration cycles

    Saiei-Jaeyeong Matsubara-Heo

    2018/06/20

  44. Integral representations of GKZ systems Invited

    Saiei-Jaeyeong Matsubara-Heo

    2018/05/26

  45. On Euler integral representations of GKZ hypergeometric functions and a construction of a basis of cycles

    Saiei-Jaeyeong Matsubara-Heo

    2018/03/14

  46. On a duality between series and integral representations of GKZ hypergeometric functions Invited

    Saiei-Jaeyeong Matsubara-Heo

    2018/02/19

  47. Residue trick for integral representations of GKZ hypergeometric equations Invited

    Saiei-Jaeyeong Matsubara-Heo

    2017/11/17

  48. On Laplace and Residue integral representations of GKZ hypergeometric functions

    Saiei-Jaeyeong Matsubara-Heo

    2017/10/16

  49. On series and integral representations of GKZ hypergeometric functions

    Saiei-Jaeyeong Matsubara-Heo

    2017/10/06

  50. On Mellin-Barnes integral representations of A-hypergeometric functions

    Saiei-Jaeyeong Matsubara-Heo

    2017/08/01

  51. On Mellin-Barnes integral representations of irregular GKZ hypergeometric functions Invited

    Saiei-Jaeyeong Matsubara-Heo

    2017/07/05

  52. Comparison of rapid decay homology theories and construction of solution basis of irregular connections of hypergeometric type Invited

    Saiei-Jaeyeong Matsubara-Heo

    2017/01/17

  53. Ordinary and relative Laplace-Gauss-Manin systems and their cycles Invited

    Saiei-Jaeyeong Matsubara-Heo

    2016/11/25

  54. On the rapid decay homology of F.Pham Invited

    Saiei-Jaeyeong Matsubara-Heo

    2016/10/03

  55. Rapid decay homology of F.Pham and its relative variant

    Saiei-Jaeyeong Matsubara-Heo

    2016/08/22

  56. On the rapid decay homology of F. Pham

    Saiei-Jaeyeong Matsubara-Heo

    2016/08/02

  57. On microlocal analysis of Gauss-Manin connections for boundary singularities Invited

    Saiei-Jaeyeong Matsubara-Heo

    2016/04/26

  58. On microlocal analysis of Gauss-Manin systems for boundary singularities Invited

    Saiei-Jaeyeong Matsubara-Heo

    2016/03/03

  59. On D. Barlet’s integration currents

    Saiei-Jaeyeong Matsubara-Heo

    2016/01/23

  60. On Ehrenpreis' fundamental principle for difference-differential systems 2

    Saiei-Jaeyeong Matsubara-Heo

    2015/08/05

  61. Residue current techniques applied for Malgrange-Ehrenpreis type theorems of D$\Delta$equations

    Saiei-Jaeyeong Matsubara-Heo

    2015/06/18

  62. On residue currents and a general theory systems of linear delay-differential systems with constant coefficients Invited

    Saiei-Jaeyeong Matsubara-Heo

    2015/04/21

  63. residue current techniques applied for Malgrange-Ehrenpreis type theorems of D$\Delta$ equations Invited

    Saiei-Jaeyeong Matsubara-Heo

    2015/03/06

  64. On a general theory of linear delay-differential systems

    Saiei-Jaeyeong Matsubara-Heo

    2015/01/31

  65. On Ehrenpreis' fundamental principle for difference-differential systems

    Saiei-Jaeyeong Matsubara-Heo

    2014/09/08

  66. On Ehrenpreis' fundamental principle for difference-differential systems

    Saiei-Jaeyeong Matsubara-Heo

    2014/08/05

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Research Projects 4

  1. Global analysis of GKZ systems and new development of intersection theory

    Offer Organization: Japan Society for the Promotion of Science

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

    Category: Grant-in-Aid for Early-Career Scientists

    Institution: Kumamoto University

    2022/04/01 - 2026/03/31

  2. Studies on integral representations of GKZ hypergeometric functions

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows

    Category: Grant-in-Aid for JSPS Fellows

    Institution: Kobe University

    2019/04/25 - 2022/03/31

  3. Studies on integral representations of GKZ hypergeometric functions

    Offer Organization: Japan Society for the Promotion of Science

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

    Category: Grant-in-Aid for Early-Career Scientists

    Institution: Kobe University

    2019/04/01 - 2022/03/31

  4. Ｇａｕｓｓ－Ｍａｎｉｎ系の代数解析学の深化

    松原 宰栄

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業 特別研究員奨励費

    Category: 特別研究員奨励費

    2017/04/26 - 2019/03/31

    More details Close

    1.Euler-Laplace積分表示と交点理論:Euler型積分表示とLaplace型積分表示の補間に当たる積分表示として以前申請者が導入したEuler-Laplace型積分表示がある。この積分表示はとあるD加群の順像(Laplace-Gauss-Manin系)として記述されることが昨年度までにわかっていた。本年度はLaplace-Gauss-Manin系の生成元を記述し、この応用としてLaplace-Gauss-Manin系に付随する急減少ホモロジー群とGKZ系の解空間の同型対応を確立した。その際のコンパクト化にはA.Esterov, A.G.Khovanski,松井優、竹内潔らのtoric compact化をより一般化した構成を用いる。また、昨年度に構成したEuler型積分表示に付随した積分サイクルの基底は交点理論的に良い性質を持つことが確認された。積分サイクルの基底は正則三角形分割Tによって構成されるが、特にTが単模の場合には交点行列が完全に決定される。これをねじれ周期関係式に適用し、Aomoto-Gelfand超幾何函数の二次関係式の閉じた公式を得た。上述の成果はarXiv:1904.00565にまとめられている。 2.Cohomology交点数を計算するアルゴリズム:神戸大学の高山信毅氏との共同研究により、1の研究に基づきcohomology交点数を計算するアルゴリズムを考案した。このアルゴリズムは、cohomology交点数をあるPfaff系の有理函数解として定数倍を除いて特徴付け、1の結果を応用して定数倍を決定するという手順を踏む。このアルゴリズムの応用として、志賀弘典氏、成宮氏らにより議論されたK3曲面の族の周期積分に付随した超幾何函数の二次関係式を得た。この成果はarXiv:1904.01253にまとめられている。

Teaching Experience 4

  1. Functional Analysis I　Kobe University

  2. Linear Algebra III,IV　Kobe University

  3. Linear Algebra I,II　Kobe University

  4. Linear Algebra III,IV　Kobe University

Works 2

  1. TCLI.jl

    Simon Telen, Saiei-Jaeyeong Matsubara-Heo

    2024/01 - Present

    Type: Software

  2. mt_gkz.rr, a Risa/Asir package for computing cohomology intersection numbers of GKZ hypergeometric systems

    Saiei-Jaeyeong Matsubara-Heo, Nobuki Takayama

    2021/02 - Present

    Type: Software