Researcher Database
Last Updated :2024/07/25
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Profile and Settings
Affiliation
Profile and Settings
Name (Japanese)
UmetaName (Kana)
YokoName
201801020444862016
Affiliation
Achievement
Research Interests
Research Areas
Research Experience
- 2023/04 - Today Hokkaido University Faculty of Science Department of Mathematics
- 2018/04 - 2023/03 Josai University
- 2016/04 - 2018/03 Yamaguchi University
- 2015/10 - 2016/03 Yamaguchi University
- 2013/04 - 2015/09 Tokyo University of Science Faculty of Science and Technology
Published Papers
- Shinichi Tajima, Katsusuke Nabeshima, Katsuyoshi Ohara, Yoko UmetaMathematics in Computer Science 17 (1) 2023/03 [Refereed]
- Algebraic analysis of Siersma’s non-isolated hypersurface singularitiesShinichi Tajima, Yoko UmetaHokkaido Mathematical Journal 51 (1) 117 - 151 2022/02 [Refereed][Not invited]
- Holonomic D-modules associated with a simple line singularity and vertical monodromyShinichi Tajima, Yoko UmetaFunkcialaj Ekvacioj 64 (1) 17 - 48 2021 [Refereed]
- On the Stokes geomatry of a unified family of P_J-hierarchies (J=I,II,IV,34)UMETA YokoPubl. Res. Inst. Math. Sci 55 (1) 79 - 107 2019/01 [Refereed][Not invited]
- A certain property of a unified family of P_J-hierarchies (J = I,II,IV,34) with a large parameterYoko UmetaRIMS Kokyuroku Bessatsu B75 101 - 111 2019 [Refereed][Not invited]
- General formal solutions for a unified family of P_J-hierarchies (J=I,II,IV,34)Yoko UmetaJournal of the Mathematical Society of Japan 71 (3) 979 - 1003 2019 [Refereed][Not invited]
- Yoko UmetaRIMS Kokyuroku 京都大学数理解析研究所 2020 (2020) 92 - 96 1880-2818 2017 [Not refereed][Not invited]
- Tajima Shinichi, Umeta YokoRIMS Kokyuroku Bessatsu 京都大学 B (57) 125 - 140 1881-6193 2016 [Refereed][Not invited]
- Yoko UmetaJOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 67 (3) 943 - 978 0025-5645 2015/07 [Refereed][Not invited]
A construction of general formal solutions for members (P-J)(m) = (J = II, IV) of the second and the fourth Painleve hierarchies with a large parameter is discussed. We also investigate a relation between formal solutions of (P-J)(m) (J = II, IV). - Multiple-scale analysis for some class of systems of non-linear differential equationsYoko UmetaRIMS Kokyuroku Bessatsu B52 283 - 299 2014 [Refereed][Not invited]
- 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 [Not refereed][Not invited]
- Takashi Aoki, Naofumi Honda, Yoko UmetaAdvances in Mathematics 235 496 - 524 2013/03 [Refereed][Not invited]
- A relation between instanton-type solutions of P_J(J=I,II,34,IV)-hierarchies with a large parameterYoko UmetaRIMS Kokyuroku 1861 331 - 338 2013 [Not refereed][Not invited]
- Instanton-type solutions with free (m+1)-parameters for the m-th member of the first Painleve hierarchyYoko UmetaRIMS Kokyuroku Bessatsu B40 213 - 219 2013 [Refereed][Not invited]
- On the number of the turning points of the second kind of the Noumi-Yamada systems with a large parameterTakashi Aoki, Naofumi Honda, Yoko UmetaRIMS Kokyuroku Bessatsu B37 1 - 30 2013 [Refereed][Not invited]
- On the form of instanton-type solutions for equations of the first Painleve hierarchy by multiple-scale analysisTakashi Aoki, Naofumi Honda, Yoko UmetaRend.Sem.Mat.Univ.Politec.Torino 69 (4) 331 - 338 2011 [Refereed][Not invited]
- Instanton-type solutions of P_34-hierarchy with a large parameter(accepted)Yoko UmetaRIMS Kokyuroku Bessatsu [Refereed][Not invited]
Presentations
- A unified family of PJ-hierarchies (J=I,II,IV,34) with a large parameter [Invited]Yoko Umeta2022年度秋季総合分科会(函数解析分科会特別講演) 2022/09
- On a construction of instanton-type solutions from a view point of Multiple-scale analysis [Invited]Yoko UmetaRecent topics in algebraic analysis 2022/02
- On the Stokes geometry of a unified family of PJ-hierarchies (J=I,II,IV,34) [Invited]UMETA YokoFormal and Analytic Solutions of Partial Differential Equations FASPDE18 2018/06 Padova University
- On the Stokes geometry of a unified family of PJ-hierarchies (J=I,II,IV,34) [Invited]梅田 陽子Workshop on Algebraic analysis and Asymptotic analysis 2018/05
- An introduction to exact WKB analysis [Not invited]梅田 陽子Bilateral Mini-Workshop of NTNU and Yamaguchi University of Mathematics and its Applications 2017/12
- 完全WKB解析による高階パンルヴェ方程式の研究 [Not invited]梅田 陽子山口複素解析セミナー 2017/12
- Lax pairをもつ非線形方程式の完全WKB解析 [Invited]梅田 陽子第1回岡潔女性数学者セミナー 2017/12
- Stokes geometry for a unified family of some Painleve hierarchies [Not invited]梅田 陽子Algebraic Analysis in Yamaguchi - D-module, microlocal analysis, summability- 2017/11
- 4つのPainleve階層を含むシステムのストークス幾何 [Not invited]梅田 陽子Workshop on Accessory Parameters 2017/10
- 4つのPainleve階層を含むシステムのストークス幾何 [Not invited]梅田陽子東京理科大学理工学部数学科談話会 2017/01 東京理科大学理工学部数学科 東京理科大学理工学部数学科
- ４つのPainleve階層を含むシステムのストークス幾何 [Not invited]梅田 陽子複素解析セミナー 広島大学 2016/12
- 4つのPainleve階層を含むシステムのストークス幾何 [Not invited]梅田陽子代数解析奈良研究集会 2016/11 奈良女子大学 森藤伸哉, 岡田靖則, 本多尚文, 山崎晋
- Stokes geometry for a unified family of some Painleve hierarchies [Not invited]Yoko UmetaNew development of microlocal analysis and singular perturbation theory 2016/10 RIMS Naofumi Honda
- 完全WKB解析とインスタントン解 [Not invited]梅田 陽子岡山大学CORセミナー 2016/01
- ストークス曲線同士の接触の縮退について [Not invited]梅田 陽子金沢山口数学合同研究集会 2015/12
- Instanton-type solutions for a unified family of (P_J)_m(J=I,II,IV,34) [Not invited]Yoko UmetaAlgebraic analysis methods in complex partial differential equations 2015/12 京都大学数理解析研究所 岡田靖則
- Multiple-scale analysis for some class of systems of non-linear differential equations [Not invited]梅田 陽子広島複素解析セミナー 2015/11
- 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 [Not invited]梅田 陽子山口大学数理科学談話会 2015/11
- Multiple-scale analysis for a unified family of (P_J)_m (J=I,II,IV,34) [Not invited]Yoko UmetaAlgebraic Analysis and Related Topics 2015/10 北海道大学 本多尚文
- 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 [Not invited]梅田 陽子, 田島慎一日本数学会 2015/03
- 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 [Not invited]梅田陽子, 田島慎一超幾何研究会2015 2015/01
- On the monodromy structure of holonomic D-modules associated with simple line singularities [Not invited]梅田 陽子, 田島慎一Several aspects of microlocal analysis 2014/10
- PI階層のインスタントン解構成法 [Not invited]梅田 陽子関数方程式セミナー 山形大学 2014/09
- ニュートン非退化孤立特異点と局所コホモロジー類 [Not invited]梅田 陽子, 田島慎一数式処理研究の新たな発展 2014/08
- ニュートン非退化孤立特異点と局所コホモロジー類 [Not invited]梅田 陽子, 田島慎一微分方程式談話会 芝浦工業大学 2014/08
- (PI)mのインスタントン解構成に関する諸問題 [Not invited]梅田 陽子代数解析学と局所凸空間 2014/02
- Multiple-scale analysis for Painleve hierarchies with a large parameter [Not invited]梅田 陽子微分方程式の総合的研究 東京大学 2013/12
- 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 [Not invited]梅田 陽子つくば大学解析セミナー 2013/12
- Multiple-scale analysis for Painleve hierarchies with a large parameter [Invited]梅田 陽子Recent progress in the domain of Painleve equations: algebraic, asymptotic and topological aspects 2013/11 ストラスブール大学
- Instanton-type solutions of Painleve hierarchies (PJ)m J=I,II,IV,34 [Not invited]梅田 陽子微分方程式の指数解析とその周辺 2013/10
- On a construction of general formal solutions for the first Painleve hierarchy with a large parameter [Not invited]梅田 陽子Various Aspects on the Painleve Equations 2012/11
- Instanton-type solutions of (P34)m and (PIV)m with a large parameter [Not invited]梅田 陽子Recent development of microlocal analysis and asymptotic analysis 2012/10
- Construction of general formal solutions for equations of the second Painleve hierarchy [Not invited]梅田 陽子関数方程式分科会, 日本数学会 2012/09
- On a construction of instanton-type solutions for the second Painleve hierarchy [Not invited]梅田 陽子Recent development of microlocal analysis for the theory of asymptotic analysis 2011/11
- On the exact WKB analysis and instanton-type solutions [Not invited]梅田 陽子GF2011 International Conference on Generalized Functions 2011/04
- An introduction to WKB analysis I - IV [Not invited]梅田 陽子Workshops, GTAnalysis WKB et D-modules 2010/11
- Multiple-scale analysis for Painleve hierarchies with a large parameter [Not invited]梅田 陽子Recent Developments in Resurgence Theory and Related Topics 2010/07
- Multiple-scale analysis for Painleve hierarchies with a large parameter [Not invited]梅田 陽子第11回北東数学解析研究集会 2010/02
- A construction of instanton-type solutions for Painleve hierarchy by using multiple-scale analysis [Not invited]梅田 陽子Microlocal Analysis and Related Topics 2009/10
- On a consturction of instanton-type solutions for Painleve hierarchy from a view point of multiple scale analysis [Not invited]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 2009/09
- Multiple-scale analysis for the first Painleve hierarchy [Not invited]梅田 陽子New Development of Asymptotic Analysis and Dynamical Systems 2009/06
- On the solid or dotted line condition for degenerate Stokes geometry [Not invited]梅田 陽子Foundations of exact WKB analysis and resurgence theory 2008/12
- On the solid or dotted line condition for degenerate Stokes geometry [Not invited]梅田 陽子Workshop on New approach to analytic equations-transformation theory, singular solutions and Stokes problem 2008/09
- 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 [Not invited]梅田 陽子稚内表現論セミナー/ 数理科学系談話会 2008/07
- On the number of the turning points of the second kind of the Noumi-Yamada system [Not invited]梅田 陽子完全WKB解析と超局所解析 2008/05
- 野海山田方程式のStokes幾何について [Not invited]梅田 陽子PDEセミナー 北海道大学 2008/04
- 野海山田方程式NY奇数系のなす代数多様体について [Not invited]梅田 陽子関数方程式分科会, 日本数学会 2008/03
- On the solid or dotted line condition for the degenerate Stokes geometry [Not invited]梅田 陽子関数方程式分科会, 日本数学会 2008/03
- On the turning point of the second kind of the Noumi-Yamada system NY_(2m+1) [Not invited]梅田 陽子第9回北東数学解析研究集会 2008/02
- 野海山田方程式NY奇数系の第2種変わり点について [Not invited]梅田 陽子COE Conference for Young Researchers 2008/02
Research Projects
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2022/04 -2027/03Author : 田島 慎一, 小原 功任, 鍋島 克輔, 渋田 敬史, 梅田 陽子
- 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日本学術振興会：科学研究費助成事業Date (from‐to) : 2020/04 -2024/03Author : 梅田陽子
- Japan Society for the Promotion of Science：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2018/04 -2022/03Author : Tajima ShinichiBy 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：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2015/04 -2018/03Author : Tajima Shinichi, Oaku Toshinori, Shibuta Takafumi, Umeta YokoBased 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：Grants-in-Aid for Scientific ResearchDate (from‐to) : 2014/04 -2018/03Author : AOKI TAKASHI, HONDA Naofumi, KAWAI Takahiro, TAKEI Yoshitsugu, YAMAZAKI Susumu, KOIKE Tatsuya, UMETA YokoIntroducing 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.
- パンルヴェ階層の完全WKB解析若手研究BDate (from‐to) : 2015/04 -2018/03Author : 梅田 陽子