大阿久 俊則 (おおあく としのり)

English page

東京女子大学名誉教授（元数理科学科教授）

専門：代数解析学

著書

  1. 「グレブナー基底の現在」 日比孝之(編) 数学書房 2006年7月発行 (分担執筆).
  2. 「D加群と計算数学」 朝倉書店 （シリーズ：すうがくの風景 5）2002年2月発行. (正誤表)
  3. 「グレブナ基底と線型偏微分方程式系(計算代数解析入門)」 上智大学数学講究録 No.38 (1994年11月). 改訂版PDF (2014年9月)

解説記事

  1. 数式処理と数学--ホロノミックパラダイム. 数理科学 1998年11月号, pp.32-38.
  2. 計算の視点から見たD加群理論. 数学 50巻2号(1998年4月), pp.203-211.

講義録（学部）

  1. 微分積分学I,II
  2. 解析学概論I（多変数関数の微分とその応用）
  3. 解析学概論II（多変数関数の積分）
  4. 複素関数論(2020年度）
  5. 微分方程式入門
  6. 数理モデルと微分方程式
  7. 情報解析学（2023年度後期）講義スライド
  8. 情報解析学I（フーリエ解析とその応用）
  9. 情報解析学II（フーリエ解析と偏微分方程式）
  10. 連続と極限
  11. 環と加群の基礎, 「環と加群の基礎」演習問題, 「環と加群の基礎」演習問題解答,
  12. ガロア理論入門, 「ガロア理論入門」演習問題解答,

講義録（高校生向け授業）

  1. 音と数学

プレプリント

  1. T. Oaku: On various b-functions of specializable D-modules. to appear in RIMS Kokyuroku. PDF
  2. T. Oaku: Bernstein-Sato polynomials and analytic non-equivalence of plane curve singularities. PDF
  3. T. Oaku: Length and multiplicity of the local cohomology with support in a hyperplane arrangement. arXiv published as a part of 'Localization, local cohomology, and the b-function of a D-module with respect to a polynomial' Advanced Studies in Pure Mathematics 77 (2018), pp. 353-398.

発表論文

  1. T. Oaku: An algorithmic study on the integration of holonomic hyperfunctions --oscillatory integrals and a phase space integral associated with a Feynman diagram. RIMS Kokyuroku Bessatsu B75 (2019), pp. 41-60. PDF
  2. T. Oaku: An attempt to compute holonomic systems for Feynman integrals in two-dimensional space-time. RIMS Kokyuroku, Kyoto Univ., Vol. 2101, pp. 77-90, 2019. PDF
  3. T. Oaku: Localization, local cohomology, and the b-function of a D-module with respect to a polynomial. Advanced Studies in Pure Mathematics 77 (2018), pp. 353-398. PDF
  4. T. Oaku: Algorithms for D-modules, integration, and generalized functions with applications to statistics. Advanced Studies in Pure Mathematics 77 (2018), pp. 253-352. PDF
  5. T. Oaku: Operational calculus for holonomic distributions in the framework of D-module theory. RIMS Kokyuroku Bessatsu B61 (2017), pp. 123--140. arXiv PDF file
  6. T. Oaku: Annihilators of Laurent coefficients of the complex power for normal crossing singularity. RIMS Kokyuroku Bessatsu B57 (2016), pp. 79--84. arXiv PDF file
  7. N. Marumo, T. Oaku, A. Takemura: Properties of powers of functions satisfying second-order linear differential equations with applications to statistics. Japan Journal of Industrial and Applied Mathematics: Volume 32, Issue 2 (2015), 553-572. Preprint:arXiv
  8. T. Oaku: Annihilators of distributions associated with algebraic local cohomology of a hypersurface. Complex Variables and Elliptic Equations 59 (2014), 1533-1546. PDF
  9. T. Oaku: Algorithms for integrals of holonomic functions over domains defined by polynomial inequalities. Journal of Symbolic Computation 50 (2013), 1--27. http://dx.doi.org/10.1016/j.jsc.2012.05.004. arXiv:1108.4853v2[cs.SC] PDF file Errata
  10. T. Oaku: An algorithm to compute the differential equations for the logarithm of a polynomial. In Proceedings of the 37th International Conference on Symbolic and Algebraic Computation (ISSAC 2012), pages 273--280. ACM Press, 2012. arXiv:1201.3198v1[cs.SC] PDF file
  11. R. Bahloul, T. Oaku: Local Bernstein-Sato ideals: algorithm and examples. J. Symbolic Computation 45 (2010), 46-59. arXiv:0806.4869 PDF file
  12. T. Oaku: Regular b-functions of D-modules. J. Pure and Applied Algebra 213 (2009), 1545-1557. PDF file
  13. M. Granger, T. Oaku, N. Takayama: Tangent cone algorithm for homogenized differential operators. J. Symbolic Computation 39 (2005), 417-431. PDF file
  14. M. Granger, T. Oaku: Minimal filtered free resolutions for analytic D-modules. J. Pure and Applied Algebra 191 (2004), 157-180. PDF file
  15. T. Oaku, Y.Shiraki, N.Takayama: Algebraic algorithms for D-modules and numerical analysis. Computer mathematics (Proceedings of ASCM 2003), 23--39, Lecture Notes Ser. Comput., 10, World Sci. Publ., River Edge, NJ, 2003. PDF file .
  16. T. Oaku: Minimal free resolutions of analytic D-modules. Proceedings of the 10th International Conference on Complex Analysis, Pusan, Korea, 2002, pp. 145-151. PDF file
  17. T. Oaku, N. Takayama: Minimal free resolutions of homogenized D-modules. J. Symbolic Computation 32 (2001), 575-595. PDF file
  18. T. Oaku, N. Takayama, H. Tsai: Polynomial and rational solutions of holonomic systems. J. Pure and Applied Algebra 164 (2001), 199-220. arXiv:math/0001064
  19. T. Oaku, N. Takayama: Algorithms for D-modules --restriction, tensor product, localization, and local cohomology groups. J. Pure and Applied Algebra 156 (2001), 267-308. PDF file
  20. T. Oaku, N. Takayama, U. Walther: A localization algorithm for D-modules. J. Symbolic Computation 29 (2000), 721-728. arXiv:math/9811030
  21. T. Oaku, N. Takayama: An algorithm for de Rham cohomology groups of the complement of an affine variety. J. Pure and Applied Algebra 139 (1999), 201-233. . arXiv:math/9801114
  22. T. Oaku, S. Yamazaki: Higher-codimensional boundary value problems and F-mild microfunctions --Local and microlocal uniqueness--. Publication of the Research Institute for Mathematical Sciences, Kyoto Univ. 34 (1998), 383-437 .
  23. T. Oaku: Algorithms for b-functions, restrictions, and algebraic local cohomology groups of D-modules. Advances in Applied Math. 19 (1997), 61-105. PDF file Errata
  24. T. Oaku: Algorithms for the b-function and D-modules associated with a polynomial. J. Pure Appl. Algebra 117 & 118 (1997), 495-518. PDF file
  25. T. Oaku: An algorithm of computing b-functions. Duke Math. J. 87 (1997), 115-132. PDF file
  26. T. Oaku: Groebner bases for D-modules on a non-singluar affine algebraic variety. Tohoku Math. J. 48 (1996), 575-600.
  27. T. Oaku: Algorithmic methods for Fuchsian systems of linear partial differential equations. J. Math. Soc. Japan 47 (1995), 297-328 .
  28. T. Oaku, T. Shimoyama: A Groebner basis method for modules over rings of differential operators. J. Symbolic Computation 18 (1994), 223-248.
  29. T. Oaku: Computation of the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients. Japan J. Indust. Appl. Math. 11 (1994), 485-497. PDF
  30. T. Oaku: Boundary value problem for Fuchsian partial differential equations and reflection of singularities. Banach Center Publications 27 (1992), 337-348. PDF
  31. T. Oaku: Some remarks on local solvability of Fuchsian partial differential equations for hyperfunctions. Yokohama Math. J. 37 (1989), 139-143. PDF
  32. T. Oaku: Local solvability of Fuchsian elliptic equations for hyperfunctions. Yokohama Math. J. 36 (1988), 109-114. PDF
  33. T. Oaku: Higher codimensional boundary value problem and F-mild hyperfunctions. In: Algebraic Analysis, eds M. Kashiwara, T. Kawai, Academic Press, 1988, pp. 571-586.
  34. T. Oaku: Removable singularities of solutions of linear partial differential equations : Systems and Fuchsian equations. J. Fac. Sci. Univ. Tokyo 33 (1986), 403-428. doi/10.15083/00039504
  35. T. Oaku: Boundary value problems for systems of linear partial differential equations and propagation of micro-analyticity. J. Fac. Sci. Univ. Tokyo 33 (1986), 175-232. doi/10.15083/00039506
  36. T. Oaku: Microlocal boundary value problem for Fuchsian operators, I. -F-mild microfunctions and uniqueness theorem. J. Fac. Sci. Univ. Tokyo 32 (1985), 287-317. doi/10.15083/00039518
  37. T. Oaku: F-mild hyperfunctions and Fuchsian partial differential equations. Advanced Studies in Pure Mathematics 4 (1984), 223-242. PDF
  38. T. Oaku: Analytic hypo-ellipticity and propagation of regularity for a system of microdifferential equations with non-involutory characteristics. Math. Ann. 269 (1984), 145-168. DigiZeitschriften
  39. T. Oaku: A canonical form of a system of microdifferential equations with non-involutory characteristics and branching of singularities. Inventiones Math. 65 (1982), 491-525. DigiZeitschriften
  40. T. Oaku: Micro-local Cauchy problems and local boundary value problems. Proc. Japan Acad. 55 (1979), 136-140. PDF

講演スライド

  1. 大阿久俊則 代数解析学の考え方とその応用--微分方程式と超関数と確率分布 東京女子大学連続講演会「神秘的な数学の世界」2023年11月1日
  2. T. Oaku: A naive approach to microlocal analysis of Feynman amplitudes. Recent topics in algebraic analysis, February 21, 2022, Chiba University.
  3. T. Oaku: Computation of holonomic systems for Feynman amplitudes associated with some simple diagrams. The Mathematics of Linear Relations between Feynman Integrals Mainz Institute for Theoretical Physics, March 18-22, 2019.
  4. T. Oaku: On various b-functions of specializable D-modules RIMS共同研究（公開型）「代数解析学の諸問題ー超局所解析及び漸近解析」，京都大学数理解析研究所，2018年10月15日~19日．
  5. T. Oaku: An attempt to compute holonomic systems for Feynman integrals in two-dimensional space-time. RIMS共同研究（公開型）「超局所解析と漸近解析」，京都大学数理解析研究所，2017年10月16日~20日．
  6. T. Oaku: An algorithmic study on the intgration of holonomic distributions. New development of microlocal analysis and singular perturbation theory, RIMS, Kyoto University, October 3-7, 2016.
  7. T. Oaku: Some algorithmic problems for holonomic distributions. Microlocal Analysis and Singular Perturbation Theory, RIMS, Kyoto University, October 5-9, 2015.
  8. T. Oaku: Algorithms for D-modules, integration, and generalized functions. The 8th Mathematical Society of Japan Seasonal Institute "Current Trends on Groebner Bases -The 50th Anniversary of Groebner Bases-", Hotel Nikko Osaka, Osaka, Japan, July 1-10, 2015. chapter 1 , chapter 2 , chapter 3 , chapter 4 , chapter 5
  9. T. Oaku: Some D-module theoretic aspects of the local cohomology of a polynomial ring. The 8th Mathematical Society of Japan Seasonal Institute "Current Trends on Groebner Bases -The 50th Anniversary of Groebner Bases-", Hotel Nikko Osaka, Osaka, Japan, July 1-10, 2015.
  10. T. Oaku: Algebraic and algorithmic study of some generalized functions associated with a real polynomial (or a real analytic function) Seminar at the department of algebra, the University of Sevilla, Spain, September, 2014.
  11. T. Oaku: Algorithms for D-modules applied to generalized functions. Summer school "Algebra, Algorithms and Algebraic Analysis", Rolduc Abbey, the Netherlands, September 2-6, 2013.
  12. T. Oaku: An algorithm to compute the differential equations for the logarithm of a polynomial. the 37th International Conference on Symbolic and Algebraic Computation (ISSAC 2012), Grenoble, July 2012.

Risa/Asir プログラム

e-mail: oaku at lab.twcu.ac.jp