Researcher basic information

• 理学(博士), 北海道大学

• https://researchmap.jp/yoko.umeta?lang=en

• 201801020444862016

• 完全WKB解析

• Natural Science, Basic analysis

• Bachelor's degree program, School of Science
• Master's degree program, Graduate School of Science
• Doctoral (PhD) degree program, Graduate School of Science

Research activity information

• Computing holonomic D-modules associated to a family of non-isolated hypersurface singularities via comprehensive Gröbner systems of PBW algebra
  Shinichi Tajima; Katsusuke Nabeshima; Katsuyoshi Ohara; Yoko Umeta
  Mathematics in Computer Science, 17, 1, Mar. 2023, [Peer-reviewed]
  English, Scientific journal
• Algebraic analysis of Siersma’s non-isolated hypersurface singularities
  Shinichi Tajima; Yoko Umeta
  Hokkaido Mathematical Journal, 51, 1, 117, 151, Feb. 2022, [Peer-reviewed]
  English, Scientific journal
• Holonomic D-modules associated with a simple line singularity and vertical monodromy
  Shinichi Tajima; Yoko Umeta
  Funkcialaj Ekvacioj, 64, 1, 17, 48, 2021, [Peer-reviewed]
  English, Scientific journal
• On the Stokes geomatry of a unified family of P_J-hierarchies (J=I,II,IV,34)
  UMETA Yoko
  Publ. Res. Inst. Math. Sci, 55, 1, 79, 107, Jan. 2019, [Peer-reviewed]
  English, Scientific journal
• A certain property of a unified family of P_J-hierarchies (J = I,II,IV,34) with a large parameter
  Yoko Umeta
  RIMS Kokyuroku Bessatsu, B75, 101, 111, 2019, [Peer-reviewed]
  English, International conference proceedings
• General formal solutions for a unified family of P_J-hierarchies (J=I,II,IV,34)
  Yoko Umeta
  Journal of the Mathematical Society of Japan, 71, 3, 979, 1003, 2019, [Peer-reviewed]
  English, Scientific journal
• A unified family of P_J hierarchies (J=I,II,IV,34) with a large parameter
  Yoko Umeta
  RIMS Kokyuroku, 2020, 2020, 92, 96, 京都大学数理解析研究所, 2017
  English, Symposium
• Computing structures of holonomic D-modules associated with a simple line singularity (Several aspects of microlocal analysis)
  Tajima Shinichi; Umeta Yoko
  RIMS Kokyuroku Bessatsu, B, 57, 125, 140, Kyoto University, 2016, [Peer-reviewed]
  English, International conference proceedings
• Instanton-type solutions for the second and the fourth Painleve hierarchies with a large parameter
  Yoko Umeta
  JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 67, 3, 943, 978, Jul. 2015, [Peer-reviewed]
  English, Scientific journal
• Multiple-scale analysis for some class of systems of non-linear differential equations
  Yoko Umeta
  RIMS Kokyuroku Bessatsu, B52, 283, 299, 2014, [Peer-reviewed]
  English, International conference proceedings
• ニュートン非退化孤立特異点と局所コホモロジー類
  梅田 陽子; 田島 慎一
  RIMS Kokyuroku, 1927, 66, 76, 2014
  Japanese, Symposium
• On a construction of general formal solutions of equations of the first Painleve hierarchy I
  Takashi Aoki; Naofumi Honda; Yoko Umeta
  Advances in Mathematics, 235, 496, 524, Mar. 2013, [Peer-reviewed]
  English, Scientific journal
• A relation between instanton-type solutions of P_J(J=I,II,34,IV)-hierarchies with a large parameter
  Yoko Umeta
  RIMS Kokyuroku, 1861, 331, 338, 2013
  English, International conference proceedings
• Instanton-type solutions with free (m+1)-parameters for the m-th member of the first Painleve hierarchy
  Yoko Umeta
  RIMS Kokyuroku Bessatsu, B40, 213, 219, 2013, [Peer-reviewed]
  English, International conference proceedings
• On the number of the turning points of the second kind of the Noumi-Yamada systems with a large parameter
  Takashi Aoki; Naofumi Honda; Yoko Umeta
  RIMS Kokyuroku Bessatsu, B37, 1, 30, 2013, [Peer-reviewed]
  English, International conference proceedings
• On the form of instanton-type solutions for equations of the first Painleve hierarchy by multiple-scale analysis
  Takashi Aoki; Naofumi Honda; Yoko Umeta
  Rend.Sem.Mat.Univ.Politec.Torino, 69, 4, 331, 338, 2011, [Peer-reviewed]
  English, International conference proceedings
• Instanton-type solutions of P_34-hierarchy with a large parameter(accepted)
  Yoko Umeta
  RIMS Kokyuroku Bessatsu, [Peer-reviewed]
  English

• 複素関数論の基礎 (新・数理/工学ライブラリ)
  本多 尚文; 神保 秀一; 梅田 陽子
  数理工学社, 29 Jan. 2024, 4864811075, 168, Japanese, [Joint work]

• A certain problem related to instanton solutions of higher-order Painleve equations
  梅田 陽子
  Recent topics in algebraic analysis, 06 Mar. 2025, Japanese, Oral presentation
• A unified family of PJ-hierarchies (J=I,II,IV,34) with a large parameter
  Yoko Umeta
  Geometric Aspects of Painleve Equations and Related Topics, 09 Sep. 2024, English, Oral presentation
  [Invited]
• Holonomic D-modules associated with a non-isolated hypersurface singularity (joint work with S.Tajima)
  Yoko Umeta
  Recent topics in algebraic analysis, 06 Mar. 2024, Japanese, Oral presentation
• A unified family of PJ-hierarchies (J=I,II,IV,34) with a large parameter
  梅田 陽子
  北大数学 談話会, 21 Dec. 2023, Japanese, Oral presentation
• A unified family of PJ-hierarchies (J=I,II,IV,34) with a large parameter
  Yoko Umeta
  2022年度秋季総合分科会(函数解析分科会特別講演), 13 Sep. 2022, Japanese, Invited oral presentation
  [Invited]
• On a construction of instanton-type solutions from a view point of Multiple-scale analysis
  Yoko Umeta
  Recent topics in algebraic analysis, 20 Feb. 2022, Japanese, Oral presentation
  20 Feb. 2022 - 22 Feb. 2022, [Invited]
• On the Stokes geometry of a unified family of PJ-hierarchies (J=I,II,IV,34)
  UMETA Yoko
  Formal and Analytic Solutions of Partial Differential Equations FASPDE18, 29 Jun. 2018, English, Invited oral presentation
  Padova University, [Invited], [International presentation]
• On the Stokes geometry of a unified family of PJ-hierarchies (J=I,II,IV,34)
  梅田 陽子
  Workshop on Algebraic analysis and Asymptotic analysis, 18 May 2018, English, Oral presentation
  [Invited], [International presentation]
• An introduction to exact WKB analysis
  梅田 陽子
  Bilateral Mini-Workshop of NTNU and Yamaguchi University of Mathematics and its Applications, 25 Dec. 2017, English, Oral presentation
  [International presentation]
• 完全WKB解析による高階パンルヴェ方程式の研究
  梅田 陽子
  山口複素解析セミナー, 15 Dec. 2017, Japanese, Oral presentation
• Lax pairをもつ非線形方程式の完全WKB解析
  梅田 陽子
  第1回岡潔女性数学者セミナー, 02 Dec. 2017, Japanese, Oral presentation
  [Invited], [Domestic Conference]
• Stokes geometry for a unified family of some Painleve hierarchies
  梅田 陽子
  Algebraic Analysis in Yamaguchi - D-module, microlocal analysis, summability-, 17 Nov. 2017, English, Oral presentation
  [International presentation]
• 4つのPainleve階層を含むシステムのストークス幾何
  梅田 陽子
  Workshop on Accessory Parameters, 07 Oct. 2017, Japanese, Oral presentation
  [Domestic Conference]
• 4つのPainleve階層を含むシステムのストークス幾何
  梅田陽子
  東京理科大学理工学部数学科談話会, 27 Jan. 2017, 東京理科大学理工学部数学科, Japanese, Oral presentation
  東京理科大学理工学部数学科, [Domestic Conference]
• ４つのPainleve階層を含むシステムのストークス幾何
  梅田 陽子
  複素解析セミナー 広島大学, 23 Dec. 2016, Japanese, Oral presentation
  [Domestic Conference]
• 4つのPainleve階層を含むシステムのストークス幾何
  梅田陽子
  代数解析奈良研究集会, 25 Nov. 2016, 森藤伸哉, 岡田靖則, 本多尚文, 山崎晋, Japanese, Oral presentation
  奈良女子大学, [Domestic Conference]
• Stokes geometry for a unified family of some Painleve hierarchies
  Yoko Umeta
  New development of microlocal analysis and singular perturbation theory, 03 Oct. 2016, Naofumi Honda, English, Oral presentation
  RIMS, [International presentation]
• 完全WKB解析とインスタントン解
  梅田 陽子
  岡山大学CORセミナー, 14 Jan. 2016, Japanese, Oral presentation
• ストークス曲線同士の接触の縮退について
  梅田 陽子
  金沢山口数学合同研究集会, 20 Dec. 2015, Japanese, Oral presentation
  [Domestic Conference]
• Instanton-type solutions for a unified family of (P_J)_m(J=I,II,IV,34)
  Yoko Umeta
  Algebraic analysis methods in complex partial differential equations, 11 Dec. 2015, 岡田靖則, English, Oral presentation
  京都大学数理解析研究所, [International presentation]
• Multiple-scale analysis for some class of systems of non-linear differential equations
  梅田 陽子
  広島複素解析セミナー, 27 Nov. 2015, Japanese
• 大きなパラメータを含むパンルヴェ階層のインスタントン解について
  梅田 陽子
  山口大学数理科学談話会, 11 Nov. 2015, Japanese
• Multiple-scale analysis for a unified family of (P_J)_m (J=I,II,IV,34)
  Yoko Umeta
  Algebraic Analysis and Related Topics, 15 Oct. 2015, 本多尚文, English, Oral presentation
  北海道大学, [International presentation]
• Simple line singularities に付随するD加群の局所コホモロジー解とモノドロミー
  梅田 陽子; 田島慎一
  日本数学会, 21 Mar. 2015, Japanese
  [Domestic Conference]
• Simple line singularities に付随するD加群の局所コホモロジー解とモノドロミー
  梅田陽子; 田島慎一
  超幾何研究会2015, 06 Jan. 2015, Japanese, Oral presentation
  [Domestic Conference]
• On the monodromy structure of holonomic D-modules associated with simple line singularities
  梅田 陽子; 田島慎一
  Several aspects of microlocal analysis, 22 Oct. 2014, English, Oral presentation
  [International presentation]
• PI階層のインスタントン解構成法
  梅田 陽子
  関数方程式セミナー 山形大学, 01 Sep. 2014, Japanese
• ニュートン非退化孤立特異点と局所コホモロジー類
  梅田 陽子; 田島慎一
  数式処理研究の新たな発展, 21 Aug. 2014, Japanese, Oral presentation
  [Domestic Conference]
• ニュートン非退化孤立特異点と局所コホモロジー類
  梅田 陽子; 田島慎一
  微分方程式談話会 芝浦工業大学, 18 Aug. 2014, Japanese, Oral presentation
• (PI)mのインスタントン解構成に関する諸問題
  梅田 陽子
  代数解析学と局所凸空間, 19 Feb. 2014, Japanese, Oral presentation
  [Domestic Conference]
• Multiple-scale analysis for Painleve hierarchies with a large parameter
  梅田 陽子
  微分方程式の総合的研究 東京大学, 21 Dec. 2013, Japanese, Invited oral presentation
  [Domestic Conference]
• 大きな変数をもつ高階パンルヴェ方程式のインスタントン解について
  梅田 陽子
  つくば大学解析セミナー, 18 Dec. 2013, Japanese, Oral presentation
• Multiple-scale analysis for Painleve hierarchies with a large parameter
  梅田 陽子
  Recent progress in the domain of Painleve equations: algebraic, asymptotic and topological aspects, 07 Nov. 2013, English, Invited oral presentation
  ストラスブール大学, [Invited], [International presentation]
• Instanton-type solutions of Painleve hierarchies (PJ)m J=I,II,IV,34
  梅田 陽子
  微分方程式の指数解析とその周辺, 18 Oct. 2013, English, Invited oral presentation
  [International presentation]
• On a construction of general formal solutions for the first Painleve hierarchy with a large parameter
  梅田 陽子
  Various Aspects on the Painleve Equations, 28 Nov. 2012, English, Poster presentation
  [International presentation]
• Instanton-type solutions of (P34)m and (PIV)m with a large parameter
  梅田 陽子
  Recent development of microlocal analysis and asymptotic analysis, 25 Oct. 2012, English, Oral presentation
  [International presentation]
• Construction of general formal solutions for equations of the second Painleve hierarchy
  梅田 陽子
  関数方程式分科会, 日本数学会, 18 Sep. 2012, Japanese, Oral presentation
  [Domestic Conference]
• On a construction of instanton-type solutions for the second Painleve hierarchy
  梅田 陽子
  Recent development of microlocal analysis for the theory of asymptotic analysis, 18 Nov. 2011, English, Oral presentation
  [International presentation]
• On the exact WKB analysis and instanton-type solutions
  梅田 陽子
  GF2011 International Conference on Generalized Functions, 19 Apr. 2011, English, Oral presentation
  [International presentation]
• An introduction to WKB analysis I - IV
  梅田 陽子
  Workshops, GTAnalysis WKB et D-modules, 24 Nov. 2010, English
  [International presentation]
• Multiple-scale analysis for Painleve hierarchies with a large parameter
  梅田 陽子
  Recent Developments in Resurgence Theory and Related Topics, 01 Jul. 2010, English, Oral presentation
  [International presentation]
• Multiple-scale analysis for Painleve hierarchies with a large parameter
  梅田 陽子
  第11回北東数学解析研究集会, 02 Feb. 2010, English, Poster presentation
  [International presentation]
• A construction of instanton-type solutions for Painleve hierarchy by using multiple-scale analysis
  梅田 陽子
  Microlocal Analysis and Related Topics, 22 Oct. 2009, English, Oral presentation
  [International presentation]
• On a consturction of instanton-type solutions for Painleve hierarchy from a view point of multiple scale analysis
  青木貴史; 梅田 陽子; 本多尚文
  関数方程式分科会, 日本数学会, 24 Sep. 2009, Japanese, Oral presentation
  [Domestic Conference]
• Multiple-scale analysis for the first Painleve hierarchy
  梅田 陽子
  New Development of Asymptotic Analysis and Dynamical Systems, 15 Jun. 2009, English, Oral presentation
  [International presentation]
• On the solid or dotted line condition for degenerate Stokes geometry
  梅田 陽子
  Foundations of exact WKB analysis and resurgence theory, 15 Dec. 2008, English, Oral presentation
  [International presentation]
• On the solid or dotted line condition for degenerate Stokes geometry
  梅田 陽子
  Workshop on New approach to analytic equations-transformation theory, singular solutions and Stokes problem, 18 Sep. 2008, English, Oral presentation
  [International presentation]
• ストークス曲線同士の接触の縮退をもつストークス幾何について
  梅田 陽子
  稚内表現論セミナー/ 数理科学系談話会, 03 Jul. 2008, Japanese, Oral presentation
• On the number of the turning points of the second kind of the Noumi-Yamada system
  梅田 陽子
  完全WKB解析と超局所解析, 27 May 2008, Japanese, Oral presentation
  [Domestic Conference]
• 野海山田方程式のStokes幾何について
  梅田 陽子
  PDEセミナー 北海道大学, 28 Apr. 2008, Japanese
• 野海山田方程式NY奇数系のなす代数多様体について
  梅田 陽子
  関数方程式分科会, 日本数学会, 23 Mar. 2008, Japanese, Oral presentation
  [Domestic Conference]
• On the solid or dotted line condition for the degenerate Stokes geometry
  梅田 陽子
  関数方程式分科会, 日本数学会, 23 Mar. 2008, Japanese, Oral presentation
  [Domestic Conference]
• On the turning point of the second kind of the Noumi-Yamada system NY_(2m+1)
  梅田 陽子
  第9回北東数学解析研究集会, 21 Feb. 2008, English, Poster presentation
  [International presentation]
• 野海山田方程式NY奇数系の第2種変わり点について
  梅田 陽子
  COE Conference for Young Researchers, 12 Feb. 2008, Japanese, Oral presentation
  [Domestic Conference]

• 基礎数学演習Ｄ, 2024年, 学士課程, 理学部
• 基礎数学Ｄ, 2024年, 学士課程, 理学部
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• Algebraic analysis of deformations of non-isolated singularities, computational complex analysis and algorithms
  Grants-in-Aid for Scientific Research
  01 Apr. 2022 - 31 Mar. 2027
  田島 慎一; 小原 功任; 鍋島 克輔; 渋田 敬史; 梅田 陽子
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Niigata University, 22K03334
• 高階パンルヴェ方程式のStokes幾何とインスタントン解の構造解析
  科学研究費助成事業
  Apr. 2020 - Mar. 2024
  梅田陽子
  日本学術振興会, 基盤研究(C), Competitive research funding
• Algebraic aanalysis of non-isolated singularities and computational complex analysis algorithms
  Grants-in-Aid for Scientific Research
  01 Apr. 2018 - 31 Mar. 2022
  Tajima Shinichi
  By utilizing the theory of algebraic analysis and the method of computer algebra, we construct a new framework for analyzing complex analytic properties of singularities. We invent new algorithms for computing several complex analytic invariant of singularities. We also implement resulting algorithms in a computer algebra system. Using these new device, we study singularities.
  Based on the theory of comprehensive Groebner systems on the Poincare-Birkhoff-Witt algebra, we construct an algorithm for computing holonomic D-modules associated to a non-isolated hypersurface singularities. For some typical cases, we investigate the structure of holonomic D-modules in an explicit manner. We apply these result to the study of non-isolated hypersurface singularities.
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Niigata University, 18K03320
• Computational complex analysis and algebraic analysis of singularities
  Grants-in-Aid for Scientific Research
  01 Apr. 2015 - 31 Mar. 2018
  Tajima Shinichi; Oaku Toshinori; Shibuta Takafumi; Umeta Yoko
  Based on the theory of algebraic analysis and computer algebra, complex analytic aspects of singularities are considered. Main results of our study are (i) an extended ideal membership algorithm in a ring of convergent power series. (ii) algorithms for computing integral numbers, and generalized integral dependence relations of an ideal in a local ring, (iii) algorithms for computing logarithmic vector fields and Bruce-Roberts Milnor numbers, (iv) an algorithm for computing b-functions and relevant holonomic D-modules associated to a hypersurface, (v) an algorithm for computing generic Le numbers.
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), University of Tsukuba, 15K04891
• Algebraic analysis of parametric Stokes phenomena
  Grants-in-Aid for Scientific Research
  01 Apr. 2014 - 31 Mar. 2018
  AOKI TAKASHI; HONDA Naofumi; KAWAI Takahiro; TAKEI Yoshitsugu; YAMAZAKI Susumu; KOIKE Tatsuya; UMETA Yoko
  Introducing a large parameter in the 3 parameters contained in the Gauss hypergeometric differential equation, we can construct the WKB solutions which are formal solutions to the equation. The construction is done algebraically and elementarily, however, these formal solutions are divergent in general and do not have analytic sense. We may apply the Borel resummation method to the formal solutions and can construct analytic solutions and bases of the solution space. On the other hand, the Gauss hypergeometric differential equation has standard bases of solutions expressed by the hypergeometric function. In this research, we have obtained linear relations between these two classes of bases. As an application, asymptotic expansion formulas with respect to the large parameter of the Gauss hypergeometric function have been obtained. At the same time, we have some formulas which describe the parametric Stokes phenomena of the WKB solutions.
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Kindai University, 26400126
• パンルヴェ階層の完全WKB解析
  若手研究B
  Apr. 2015 - Mar. 2018
  梅田 陽子
  Principal investigator, Competitive research funding