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Wakabayashi Yasuhiro
若林　泰央
Wakabayashi Yasuhiro
若林　泰央
Graduate School of Information Science and Technology　Department of Pure and Applied Mathematics, Associate Professor

keyword moduli，oper，p-curvature，algebraic differential equation，Frobenius-Ehresmann structure，p-adic Teichmüller theory，positive characteristic，dormant oper，algebraic curve，connection，moduli space，vector bundle，arithmetic geometry，algebraic geometry

Research History 8

  1. 2022/10 - Present
    Osaka University　Graduate School of Information Science and Technology Department of Pure and Applied Mathematics　Associate Professor

  2. 2018/04 - 2022/09
    Tokyo Institute of Technology　School of Science　Assistant Professor

  3. 2015/06 - 2018/03
    The University of Tokyo　Graduate School of Mathematical Sciences　Project Assistant Professor

  4. 2015/04 - 2015/05
    Japan Society for the Promotion of Science　Research Fellowship PD (Kyoto University)

  5. 2014/08 - 2015/03
    Kyoto University　Center for the Promotion of Interdisciplinary Education and Research

  6. 2014/04 - 2015/03
    Osaka City University　Advanced Mathematical Institute　Researcher

  7. 2014/04 - 2014/07
    Kyoto University　Research Institute for Mathematical Sciences　Researcher

  8. 2012/04 - 2014/03
    Japan Society for the Promotion of Science　Research Fellowship DC2 (Kyoto Univ. RIMS)

Education 3

  1. Kyoto University　Graduate School of Science　Division of Mathematics

    2011/04 - 2014/03

  2. Kyoto University　Graduate School of Science　Division of Mathematics

    2009/04 - 2011/03

  3. Kyoto University　Faculty of Science

    2005/04 - 2009/03

Committee Memberships 1

  1. The LPP-RIMS AHGT International Research Network　Core member　Other

    2023 - Present

Professional Memberships 1

  1. THE MATHEMATICAL SOCIETY OF JAPAN

Research Areas 1

  1. Natural sciences / Algebra /

Papers 21

  1. Frobenius pull-back of parabolic bundles and dormant opers

    Yasuhiro Wakabayashi

    Proc. Indian Acad. Sci. Math. Sci. accepted　2025　Research paper (scientific journal)

  2. The generic étaleness of the moduli space of dormant so_{2ℓ}-opers

    Yasuhiro Wakabayashi

    J. Geom. Phys. 211 Paper No. 105439, 22pp.　2025/01　Research paper (scientific journal)

  3. Inseparable Gauss maps and dormant opers

    Yasuhiro Wakabayashi

    Math. J. Okayama Univ.　Vol. 67　p. 1-28　2024/10　Research paper (scientific journal)

  4. An upper bound on the generic degree of the generalized Verschiebung for rank two stable bundles

    Yuichiro Hoshi, Yasuhiro Wakabayashi

    Journal of Pure and Applied Algebra　Vol. 228　No. 6　2024/06　Research paper (scientific journal)

  5. Gaudin model modulo p, Tango structures, and dormant Miura opers

    Yasuhiro Wakabayashi

    J. Geom. Phys.　Vol. 200　2024/03　Research paper (scientific journal)

  6. On the category of structure species

    Yasuhiro Wakabayashi

    Palestine Journal of Mathematics　Vol. 13　No. 3　p. 106-124　2024/02　Research paper (scientific journal)

  7. A combinatorial description of the dormant Miura transformation

    Yasuhiro Wakabayashi

    Bull. Iranian Math. Soc.　Vol. 49: 81　2023/12　Research paper (scientific journal)

  8. Frobenius-Ehresmann structures and Cartan geometries in positive characteristic

    Yasuhiro Wakabayashi

    Indag. Math. (N.S.) 34 (2023), no. 3, pp. 488-580.　2023/05

  9. Cyclic étale coverings of generic curves and ordinariness of dormant opers

    Yasuhiro Wakabayashi

    Journal of Algebra　Vol. 623　No. 1　p. 154-192　2023/03　Research paper (scientific journal)

  10. A theory of dormant opers on pointed stable curves

    Yasuhiro Wakabayashi

    Astérisque　Vol. 432　2022/05　Research paper (scientific journal)

  11. Quantization on algebraic curves with Frobenius-projective structure

    Yasuhiro Wakabayashi

    Lett. Math. Phys.　Vol. 112　No. 3　2022/04　Research paper (scientific journal)

  12. Symplectic geometry of p-adic Teichmüller uniformization for ordinary nilpotent indigenous bundles

    Yasuhiro Wakabayashi

    Tunis. J. Math.　Vol. 4　No. 2　p. 203-247　2022/04　Research paper (scientific journal)

  13. An effective version of Belyi's theorem in positive characteristic

    Yasuhiro Wakabayashi

    J. Number Theory　Vol. 231　p. 251-268　2022/04　Research paper (scientific journal)

  14. Categorical representation of superschemes

    Yasuhiro Wakabayashi

    Pure Appl. Math. Q.　Vol. 16　No. 5　p. 1635-1672　2020/10　Research paper (scientific journal)

  15. Moduli of Tango structures and dormant Miura opers

    Yasuhiro Wakabayashi

    Mosc. Math. J.　Vol. 20　No. 3　p. 575-636　2020/10　Research paper (scientific journal)

  16. Spin networks, Ehrhart quasi-polynomials, and combinatorics of dormant indigenous bundles

    Yasuhiro Wakabayashi

    Kyoto J. Math.　Vol. 59　No. 3　p. 649-684　2019/10　Research paper (scientific journal)

  17. On the ordinariness of dormant GL(n)-opers

    Yasuhiro Wakabayashi

    RIMS Kôkyûroku Bessatsu　Vol. B72　p. 161-180　2018/10　Research paper (conference, symposium, etc.)

  18. Counting dormant opers on a pointed stable curve

    Yasuhiro Wakabayashi

    RIMS Kôkyûroku Bessatsu　Vol. B64　2017/10　Research paper (conference, symposium, etc.)

  19. Duality for dormant opers

    Yasuhiro Wakabayashi

    J. Math. Sci. Univ. Tokyo　Vol. 24　No. 3　p. 271-320　2017/10　Research paper (scientific journal)

  20. On the cuspidalization problem for hyperbolic curves over finite fields

    Yasuhiro Wakabayashi

    Kyoto J. Math.　Vol. 56　No. 1　p. 125-164　2016/10　Research paper (scientific journal)

  21. An explicit formula for the generic number of dormant indigenous bundles

    Yasuhiro Wakabayashi

    Publ. Res. Inst. Math. Sci.　Vol. 50　No. 3　p. 383-409　2014/01　Research paper (scientific journal)

Misc. 21

  1. 書評『マニン 数学・物理論集 隠喩としての数学』（ユーリ・I・マニン著, 橋本義武訳, 朝倉書店, 2024年）

    若林 泰央

    数学通信（日本数学会編集）　Vol. 30　No. 1　p. 111-113　2025/05　Book review, literature introduction, etc.

  2. The moduli space of dormant opers on elliptic curves

    Naoka Karube, Yasuhiro Wakabayashi

    Preprint, arXiv:2504.00418v1 [math.AG]　2025/04

  3. Complete flags on flat vector bundles in positive characteristic

    Yohei Morita, Yasuhiro Wakabayashi

    Preprint, arXiv:2503.13750v1 [math.AG]　2025/03

  4. Book review: "Foundations of p-adic Teichmuller theory" (S. Mochizuki, AMS/IP Stud. Adv. Math.,11)

    Y. Wakabayashi

    Vol. 76　No. 4　p. 425-431　2024/10　Book review, literature introduction, etc.

  5. Projective structures in positive characteristic and their quantum field theory

    Yasuhiro Wakabayashi

    2024/09

  6. Arithmetic liftings and 2d TQFT for dormant opers of higher level

    Yasuhiro Wakabayashi

    Preprint, arXiv:2209.08528v2 [math.AG]　2024/08

  7. Projective and affine structures in positive characteristic II: Classifications for Abelian varieties, curve, and surfaces

    Yasuhiro Wakabayashi

    2024

  8. Projective and affine structures in positive characteristic I: Chern class formulae and characterizations of projective spaces

    2024

  9. On projective structures in positive characteristic

    Yasuhiro Wakabayashi

    2023/10

  10. Infinitesimal deformations of opers in positive characteristic and the de Rham cohomology of symmetric products

    Yasuhiro Wakabayashi

    Preprint, arXiv:2309.11750 [math.AG]　2023/09

  11. Holonomic D-modules of arithmetic type and middle convolution

    Yasuhiro Wakabayashi

    Preprint, arXiv:2309.12199 [math.AG]　2023/09

  12. Opers with real monodromy and Eichler-Shimura isomorphism

    Yasuhiro Wakabayashi

    Preprint, arXiv:2309.12203 [math.CV]　2023/09

  13. What is a Frobenius-projective structure?

    Yasuhiro Wakabayashi

    p. 29-36　2022/01　Article, review, commentary, editorial, etc. (scientific journal)

  14. Differential modules and dormant opers of higher level

    Yasuhiro Wakabayashi

    Preprint, arXiv:2201.11266 [math.AG]　2022

  15. Frobenius projective and affine geometry of varieties in positive characteristic

    Yasuhiro Wakabayashi

    Preprint, arXiv:2011.04846 [math.AG]　2020

  16. 協同組合の数理解析

    蕭冬遠, 張龍傑, 中安淳, 若林泰央

    数理科学実践研究レター　2018/07　Rapid communication, short report, research note, etc. (bulletin of university, research institution)

  17. l-adic cohomological field theory for dormant opers

    Yasuhiro Wakabayashi

    2017　Article, review, commentary, editorial, etc. (scientific journal)

  18. Topological quantum field theory for dormant opers

    Yasuhiro Wakabayashi

    Preprint, arXiv:1709.04235 [math.AG]　2017

  19. Moduli of log twisted N=1 SUSY curves

    Yasuhiro Wakabayashi

    Preprint, arXiv:1602.07059 [math.AG]　2016

  20. The symplectic nature of the space of dormant indigenous bundles on algebraic curves

    Yasuhiro Wakabayashi

    Preprint, arXiv:1411.1197 [math.AG]　2014

  21. On the cuspidalization problem for hyperbolic curves over finite fields

    Yasuhiro Wakabayashi

    p. 229-238　2011　Article, review, commentary, editorial, etc. (scientific journal)

Publications 1

  1. A theory of dormant opers on pointed stable curves

    Yasuhiro Wakabayashi

    Astérisque 432, Société Mathématique de France　2022/05　Scholarly book

    ISBN: 9782856299562

Presentations 25

  1. p-adic Teichmuller theory (Chapter VI)

    Y. Wakabayashi

    2025/03/13

  2. Diagonal reduction/lifting (Chapter V)

    Y. Wakabayashi

    2025/03/13

  3. Counting dormant opers (Chaper IV)

    Y. Wakabayashi

    2025/03/12

  4. p-Hitchin map (Chapter III)

    Y. Wakabayashi

    2025/03/12

  5. Moduli space of opers (Chapter II)

    Y. Wakabayashi

    2025/03/11

  6. Projective structures (Chapter I)

    Y. Wakabayashi

    2025/03/11

  7. On some arithmetic properties of connections and holonomic D-modules

    Yasuhiro Wakabayashi

    2024/12/20

  8. 正標数の射影構造およびその位相的場の理論について

    若林 泰央

    研究集会「リーマン面に関連する位相幾何学」　2024/09/15

  9. 線形微分方程式の数論的持ち上げと位相的場の理論

    若林 泰央

    野田代数幾何学・数論幾何学シンポジウム　2024/09/12

  10. p曲率に関するいくつかの予想について

    Yasuhiro Wakabayashi

    2024/09/11

  11. Arithmetic liftings and 2d TQFT for differential equations in positive characteristic

    Yasuhiro Wakabayashi

    Moduli Space and Arithmetic　2024/09/09

  12. Topological quantum field theory for differential equations in characteristic p^N

    Yasuhiro Wakabayashi

    Low dimensional topology and number theory XV　2024/03/06

  13. Opers with real monodromy and Eichler-Shimura isomorphism

    Yasuhiro Wakabayashi

    2024/01/15

  14. On projective structures in positive characteristic

    Yasuhiro Wakabayashi

    2023/10/20

  15. p-adic Teichmüller theory and the counting problem of dormant opers

    Yasuhiro Wakabayashi

    Arithmetic & Homotopical Galois Theory　2023/03/23

  16. Dormant opers and canonical diagonal liftings

    Yasuhiro Wakabayashi

    Algebra and Number Theory Seminar, Univ. of Arizona　2023/03/15

  17. What is p-adic Teichmuller theory?

    Yasuhiro Wakabayashi

    2022/11/30

  18. On arithmetic liftings of differential equations, or related enumerative geometry

    Yasuhiro Wakabayashi

    2022/10

  19. What is a Frobenius-projective structure?

    Yasuhiro Wakabayashi

    2021/10

  20. Introduction to p-adic Teichmüller theory

    Yasuhiro Wakabayashi

    Promenade in Inter-Universal Teichmuller Theory　2021/04

  21. Frobenius-projective structures on higher dimensional varieties

    Yasuhiro Wakabayashi

    2nd Kyoto-Hefei Workshop on Arithmetic Geometry　2020/08

  22. The Gaudin model and pathology in positive characteristic

    Yasuhiro Wakabayashi

    The 6th Uppsala University-Tokyo Tech Joint Symposium　2019/11

  23. Symplectic geometry of p-adic Teichmüller uniformization

    Yasuhiro Wakabayashi

    The 8th East Asia Number Theory Conference　2019/08

  24. Enumerative geometry of dormant opers

    Yasuhiro Wakabayashi

    Representation Theory and D-modules　2019/06

  25. Symplectic aspect of the p-adic Teichmüller uniformization

    Yasuhiro Wakabayashi

    p-adic cohomology and arithmetic geometry 2018　2018/11

Social Activities 5

  • モジュライ空間ってなに？カタチが織りなす関係の世界

    フロムページ　夢ナビ 学問図鑑@阪大

    2025/04 -

  • 「数える」にひそむ現代数学

    大阪大学 いちょう祭 IST一日体験教室プログラム

    2024/05/03 -

  • 数学者に遠慮なく研究の話をしてくださいと言ったら【学術対談】

    YouTube 予備校のノリで学ぶ「大学の数学・物理」

    2023/03 -

  • p進タイヒミューラー理論とその周辺

    株式会社すうがくぶんか　現代数学レクチャーシリーズ 第7回

    2022/02 -

  • p進タイヒミューラー理論 －失われたカタチを求めて－

    株式会社すうがくぶんか・東京工業大学理学院　現代数学レクチャーシリーズ

    2021/09 -