Updated on 2026/04/18

写真b

 
INAYAMA,TAKAHIRO
 
*Items subject to periodic update by Rikkyo University (The rest are reprinted from information registered on researchmap.)
Affiliation*
College of Science Department of Mathematics
Title*
Assistant Professor
Degree
Ph.D. (Mathematical Sciences) （ 9 2020   The University of Tokyo ）
Contact information
Mail Address
Campus Career*
  • 4 2026 - Present 
    College of Science   Department of Mathematics   Assistant Professor
 

Research Areas

  • Natural Science / Geometry  / complex geometry

  • Natural Science / Basic analysis  / 複素解析学

Research History

  • 4 2026 - Present 
    Rikkyo University   College of Science Department of Mathematics

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  • 4 2021 - 3 2026 
    Tokyo University of Science   Faculty of Science and Technology Mathematics   Assistant Professor

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    Country：Japan

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  • 10 2020 - 3 2021 
    The University of Tokyo   Graduate School of Mathematical Sciences

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    Country：Japan

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  • 4 2018 - 9 2020 
    The University of Tokyo   Graduate School of Mathematical Sciences

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    Country：Japan

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Education

  • 4 2018 - 9 2020 
    The University of Tokyo   Graduate School of Mathematical Sciences

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    Country： Japan

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  • 4 2016 - 3 2018 
    The University of Tokyo   Graduate School of Mathematical Sciences

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    Country： Japan

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  • 4 2014 - 3 2016 
    The University of Tokyo   Faculty of Science   Department of Mathematics

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    Country： Japan

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  • 4 2012 - 3 2014 
    The University of Tokyo   College of Arts and Sciences

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    Country： Japan

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Awards

  • 3 2021  
    東京大学大学院数理科学研究科  研究科長賞 (博士課程) 

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  • 3 2018  
    東京大学大学院数理科学研究科  研究科長賞 (修士課程) 

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Papers

  • Nakano positivity of singular Hermitian metrics: Approximations and applications Peer-reviewed

    Takahiro Inayama, Shin-ichi Matsumura

    Journal of Functional Analysis   1 2026

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

    DOI： 10.1016/j.jfa.2025.111206

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  • L^2-extension indices, sharper estimates and curvature positivity Peer-reviewed

    Takahiro Inayama

    Annales de l'Institut Fourier   1 - 29   22 9 2025

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

    In this paper, we introduce a new concept of -extension indices. This index is a function that gives the minimum constant with respect to the -estimate of an Ohsawa–Takegoshi-type extension at each point. By using this notion, we propose a new way to study the positivity of curvature. We prove that there is an equivalence between how sharp the -extension is and how positive the curvature is. New examples of sharper -extensions are also systematically given. As applications, we use the -extension index to study Prékopa-type theorems and to study the positivity of a certain direct image sheaf. We also provide new characterizations of pluriharmonicity and curvature flatness.

    DOI： 10.5802/aif.3738

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  • Pseudonorms on direct images of pluricanonical bundles Peer-reviewed

    Takahiro Inayama

    Journal of Functional Analysis284 ( 12 ) 109916 - 109916   6 2023

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

    DOI： 10.1016/j.jfa.2023.109916

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  • A note on characterizing pluriharmonic functions via the Ohsawa--Takegoshi extension theorem Peer-reviewed

    Takahiro Inayama

    J. Math. Sci. Univ. Tokyo30 ( 3 ) 365 - 369   2023

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

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  • SINGULAR HERMITIAN METRICS WITH ISOLATED SINGULARITIES Peer-reviewed

    TAKAHIRO INAYAMA

    Nagoya Mathematical Journal248   980 - 989   10 6 2022

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Cambridge University Press (CUP)  

    Abstract

    In this paper, we study the coherence of a higher rank analogue of a multiplier ideal sheaf. Key tools of the study are Hörmander’s $L^2$-estimate and a singular version of a Demailly–Skoda-type result.

    DOI： 10.1017/nmj.2022.16

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  • Nakano positivity of singular Hermitian metrics and vanishing theorems \n of Demailly–Nadel–Nakano type Peer-reviewed

    Takahiro Inayama

    Algebraic Geometry9 ( 1 ) 69 - 92   1 1 2022

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Foundation Compositio Mathematica  

    In this article, we propose a general definition of Nakano semi-positivity of singular Hermitian metrics on holomorphic vector bundles. By using this positivity notion, we establish $L^2$-estimates for holomorphic vector bundles with Nakano positive singular Hermitian metrics. We also show vanishing theorems, which generalize both Nakano type and Demailly-Nadel type vanishing theorems.

    DOI： 10.14231/ag-2022-003

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  • Optimal $$L^2$$-Extensions on Tube Domains and a Simple Proof of Prékopa’s Theorem

    Takahiro Inayama

    The Journal of Geometric Analysis32 ( 1 )   10 12 2021

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

    DOI： 10.1007/s12220-021-00796-w

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    Other Link： https://link.springer.com/article/10.1007/s12220-021-00796-w/fulltext.html

  • A remark on characterizations of Griffiths positivity through asymptotic conditions Peer-reviewed

    Genki Hosono, Takahiro Inayama

    International Journal of Mathematics32 ( 11 ) 2150087 - 2150087   10 2021

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：World Scientific Pub Co Pte Ltd  

    In this paper, we study characterizations of Griffiths semi-positivity through [Formula: see text]-estimates of the [Formula: see text]-equation and [Formula: see text]-extension theorems for symmetric powers of a holomorphic vector bundle. We also investigate several versions of the converse of the Demailly–Skoda theorem.

    DOI： 10.1142/s0129167x21500877

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  • A converse of Hörmander’s L2-estimate and new positivity notions for vector bundles Peer-reviewed

    Genki Hosono, Takahiro Inayama

    Science China Mathematics64 ( 8 ) 1745 - 1756   8 2021

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

    DOI： 10.1007/s11425-019-1654-9

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    Other Link： https://link.springer.com/article/10.1007/s11425-019-1654-9/fulltext.html

  • From Hörmander’s L 2 -estimates to partial positivity Peer-reviewed

    Takahiro Inayama

    Comptes Rendus. Mathématique359 ( 2 ) 169 - 179   17 3 2021

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Cellule MathDoc/CEDRAM  

    In this article, using a twisted version of H\"ormander's $L^2$-estimate, we give new characterizations of notions of partial positivity, which are uniform $q$-positivity and RC-positivity. We also discuss the definition of uniform $q$-positivity for singular Hermitian metrics.

    DOI： 10.5802/crmath.168

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  • L2 Estimates and Vanishing Theorems for Holomorphic Vector Bundles Equipped with Singular Hermitian Metrics Peer-reviewed

    Takahiro Inayama

    Michigan Mathematical Journal69 ( 1 )   1 3 2020

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Michigan Mathematical Journal  

    DOI： 10.1307/mmj/1573700740

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  • Curvature Currents and Chern Forms of Singular Hermitian Metrics on Holomorphic Vector Bundles Peer-reviewed

    Takahiro Inayama

    The Journal of Geometric Analysis30 ( 1 ) 910 - 935   1 2020

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

    DOI： 10.1007/s12220-019-00164-9

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    Other Link： http://link.springer.com/article/10.1007/s12220-019-00164-9/fulltext.html

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Misc.

  • Singular Nakano positivity of direct image sheaves of adjoint bundles

    Takahiro Inayama, Shin-ichi Matsumura, Yuta Watanabe

    arXiv:2407.11412   7 2024

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  • 液滴の分裂にまつわる数理 Peer-reviewed

    稲山 貴大

    数理科学実践研究レターLMSR 2020-9   9 2020

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Professional Memberships

  • 4 2018 - Present 
    日本数学会

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Research Projects

  • L2評価法及びL2拡張定理に基づく複素解析幾何学の新展開

    日本学術振興会  科学研究費助成事業 

    稲山貴大

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    4 2023 - 3 2028

    Grant number：23K12978

    Authorship：Principal investigator 

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  • Studies on singular Hermitian metrics via L2 theoretic methods and their applications to algebraic geometry

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Research Activity Start-up 

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    8 2021 - 3 2024

    Grant number：21K20336

    Grant amount：\3120000 （ Direct Cost: \2400000 、 Indirect Cost：\720000 ）

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  • ベクトル束の特異エルミート計量と相対随伴束の順像層の正値性の研究

    日本学術振興会  科学研究費助成事業 特別研究員奨励費 

    稲山 貴大

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    4 2018 - 3 2021

    Grant number：18J22119

    Grant amount：\2200000 （ Direct Cost: \2200000 ）

    本研究の目的は、正則ベクトル束上の特異エルミート計量の正値性を調べること、及びそれを応用して相対随伴束の順像層の正値性を解明することである。本年度は以下の研究成果を得た。
    (1)ヘルマンダー型の評価式の研究：Griffiths正値な特異エルミート計量を持つベクトル束係数のヘルマンダー型の評価式を得た。かつては計量の滑らかさに一定の条件を設けていたが、本年度はその仮定を外すことに成功し、一般的な設定で上記の評価式を得た。また、これを応用してある種のコホモロジーの消滅定理を得た。これはGriffithsの消滅定理の特異エルミート計量への一般化に相当する。
    (2)相対多重標準束の順像層に入る擬ノルムの研究：複素多様体間の射に対し、相対多重標準束の順像層にはベルグマン核計量の類似により標準擬ノルムが定まる。報告者はある幾何学的な設定の下で、Stein射の正則構造がこの標準擬ノルムによって定まることを示した。このような研究はRoydenによるコンパクトリーマン面のタイヒミュラー理論の研究に端を発し、代数幾何学ではYauの擬ノルム計画とも呼ばれている。報告者は近年Deng-Wang-Zhang-Zhouによって得られていた複素ユークリッド空間内の有界超凸領域に関する上記タイプの結果を一般化し、大沢-竹腰の拡張定理のあるバージョンを用いることで上記の結果を得ることに成功した。またStein射が複素ユークリッド空間内の有界擬凸領域からの射影で得られる特別な場合については、大沢-竹腰の拡張定理を用いない簡明な証明方法を与えた。

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