Updated on 2021/12/22

写真a

 
UEHARA Takato
 
Organization
Faculty of Natural Science and Technology Associate Professor
Position
Associate Professor
External link

Degree

  • 数理学 ( 九州大学 )

Research Interests

  • Dynamical system

  • Complex dynamical system

  • Entropy

Research Areas

  • Natural Science / Basic analysis  / Analysis

Education

  • Kyushu University   大学院数理学府   数理学専攻博士課程

    2007.4 - 2010.3

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  • Kyushu University   大学院数理学府   数理学専攻修士課程

    2005.4 - 2007.3

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  • Kyushu University   理学部   数学科

    2001.4 - 2005.3

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Research History

  • Okayama University   大学院自然科学研究科   Associate Professor

    2018.9

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  • Saga University   大学院工学系研究科   Associate Professor

    2014.4 - 2018.8

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  • Niigata University   自然科学系   Assistant Professor

    2012.4 - 2014.3

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  • Tohoku University   Graduate School of Science, Department of Mathematics, Geometry   Assistant Professor

    2011.4 - 2012.3

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Professional Memberships

 

Papers

  • Automorphism groups of rational surfaces Reviewed

    Takato Uehara

    Journal of Pure and Applied Algebra   224 ( 1 )   411 - 422   2020.1

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

    DOI: 10.1016/j.jpaa.2019.05.013

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  • On a question of Gromov about the Wirtinger inequalities Reviewed

    T. Kondo, T. Toyoda, T. Uehara

    Geom. Dedicata   195 ( 1 )   203 - 214   2018

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    Language:English   Publishing type:Research paper (scientific journal)  

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  • Rational surface automorphisms preserving cuspidal anticanonical curves Reviewed

    Takato Uehara

    MATHEMATISCHE ANNALEN   365 ( 1-2 )   635 - 659   2016.6

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER HEIDELBERG  

    This article is concerned with automorphisms on rational surfaces. We develop a method for constructing automorphisms in terms of the concept of realization of orbit data, and show that any automorphism preserving a cuspidal anticanonical curve is constructed from a realization of orbit data. Moreover, some properties of automorphisms are discussed.

    DOI: 10.1007/s00208-015-1275-z

    Web of Science

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  • RATIONAL SURFACE AUTOMORPHISMS WITH POSITIVE ENTROPY Reviewed

    Takato Uehara

    ANNALES DE L INSTITUT FOURIER   66 ( 1 )   377 - 432   2016

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ANNALES INST FOURIER  

    The aim of this paper is to construct rational surface automorphisms with positive entropy by means of the concept of orbit data. The concept enables us to introduce some mild and verifiable condition, and to show that if an orbit data satisfies the condition, then there exists an automorphism realizing the orbit data. Applying this result, we describe the set of entropy values of the rational surface automorphisms in terms of Weyl groups.

    Web of Science

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  • Isolated periodic solutions to Painlevé VI equation Reviewed

    K.Iwasaki, T. Uehara

    RIMS Kôkyûroku Bessatsu   B37   69 - 79   2013

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    Language:English  

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  • On the structure of rational surface automorphism groups

    T. Uehara

    RIMS Kôkyûroku   1807   31 - 38   2012

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  • Dynamics on rational surfaces

    T. Uehara

    RIMS Kôkyûroku   1765   137 - 153   2011

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  • Periodic points for area-preserving birational maps of surfaces Reviewed

    Katsunori Iwasaki, Takato Uehara

    MATHEMATISCHE ZEITSCHRIFT   266 ( 2 )   289 - 318   2010.10

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

    It is a basic problem to count the number of periodic points of a surface mapping, since the growth rate of this number as the period tends to infinity is an important dynamical invariant. However, this problem becomes difficult when the map admits curves of periodic points. In this situation we give a precise estimate of the number of isolated periodic points for an area-preserving birational map of a projective complex surface.

    DOI: 10.1007/s00209-009-0570-3

    Web of Science

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  • An ergodic study of Painleve VI Reviewed

    Katsunori Iwasaki, Takato Uehara

    MATHEMATISCHE ANNALEN   338 ( 2 )   295 - 345   2007.6

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

    An ergodic study of Painleve VI is developed. The chaotic nature of its Poincare return map is established for almost all loops. The exponential growth of the numbers of periodic solutions is also shown. Principal ingredients of the arguments are a moduli-theoretical formulation of Painleve VI, a Riemann-Hilbert correspondence, the dynamical system of a birational map on a cubic surface, and the Lefschetz fixed point formula.

    DOI: 10.1007/s00208-006-0077-8

    Web of Science

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  • Chaos in the sixth Painlevé equation Reviewed

    K.Iwasaki, T. Uehara

    RIMS Kôkyûroku Bessatsu   B2   73 - 88   2007

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    Language:English  

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Presentations

  • A gluing construction of projective K3 surfaces Invited

    Takato Uehara

    Aspects of Complex Dynamics  2021.12.16 

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    Language:English   Presentation type:Oral presentation (general)  

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  • On maximal entropy measures for birational maps on compact complex surfaces Invited

    上原 崇人

    Complex Dynamics and Related Topics  2020.12.10 

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    Language:Japanese   Presentation type:Oral presentation (general)  

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  • Dynamical degrees of birational maps on complex surfaces Invited

    Takato Uehara

    Bifurcation and stability in complex dynamics  2019.12.9 

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    Language:English   Presentation type:Oral presentation (general)  

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  • A gluing construction of K3 surfaces Invited

    Takato Uehara

    Differential Systems: from theory to computer mathematics  2019.12.5 

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    Language:English   Presentation type:Oral presentation (general)  

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  • Siegel disks for rational surface automorphisms with positive entropy Invited

    Takato Uehara

    Geometric Complex Analysis on Foliations and Dynamics  2019.11.26 

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    Language:English   Presentation type:Oral presentation (general)  

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  • 複素曲面上の力学系 Invited

    上原 崇人

    日本数学会2019年度会  2019.3.18 

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    Language:Japanese   Presentation type:Oral presentation (invited, special)  

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  • Dynamical systems on complex surfaces Invited

    Takato Uehara

    Workshop on Complex Analytic and Algebraic Methods in Dynamics  2019.1.15 

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    Language:English   Presentation type:Oral presentation (general)  

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  • K3曲面の構成と力学系への応用 Invited

    上原 崇人

    可積分系理論から見える数理構造とその応用  2018.9.6 

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    Language:Japanese   Presentation type:Oral presentation (general)  

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  • 有理曲面を用いた超越的K3曲面の構成について Invited

    上原 崇人

    複素領域における微分方程式とその周辺  2018.8.29 

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    Language:Japanese   Presentation type:Oral presentation (general)  

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  • A construction of non-projective K3 surfaces from rational surfaces

    UEHARA Takato

    Complex geometry and complex dynamics in higher dimensions  2018.6.27 

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  • A construction of transcendental K3 surfaces

    UEHARA Takato

    The 13th Kagoshima Algebra-Analysis-Geometry Seminar  2018.2.15 

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  • On a construction of non-projective K3 surfaces

    UEHARA Takato

    Line Bundles and Theories on Canonical Kähler Metrics  2018.1.31 

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  • Wirtinger不等式に関するGromovの問題について

    上原 崇人

    測地線及び関連する諸問題  2018.1.6 

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  • 複素曲面のダイナミカルスペクトラム

    上原 崇人

    葉層構造の幾何学とその応用  2017.12.16 

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  • On a construction of transcendental K3 surfaces: application of Arnol’d’s theorem

    UEHARA Takato

    RIMS Workshop on Complex Dynamics 2017  2017.12.13 

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  • Arnol'dの定理を用いた複素K3曲面の構成

    上原 崇人

    第60回函数論シンポジウム  2017.10.7 

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  • 複素K3曲面の構成について

    上原 崇人

    第52回函数論サマーセミナー  2017.9.7 

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  • On automorphisms preserving meromorphic two forms

    UEHARA Takato

    Dynamics and Analysis in Several Complex Variables  2017.3.21 

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  • On automorphisms of rational surfaces with positive entropy

    上原 崇人

    多変数関数論冬セミナー  2016.12.16 

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  • Rigidity of automorphisms on rational surfaces

    UEHARA Takato

    Complex dynamical systems and related topics  2016.12.13 

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  • ジーゲル領域をもつ有理曲面上の自己同型写像

    上原 崇人

    アクセサリー・パラメーター研究会  2016.3.24 

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  • On the topological entropies for automorphisms on rational surfaces

    上原 崇人

    複素領域の微分方程式、漸近解析とその周辺  2016.3.9 

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  • Siegel domains for rational surface automorphisms with positive entropy

    UEHARA Takato

    RIMS Workshop on Complex Dynamics  2015.12.11 

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  • Entropy values of automorphisms on rational surfaces

    UEHARA Takato

    Mini-workshop on moduli spaces and its related topics  2015.5.13 

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  • Isolated periodic points for area-preserving surface mappings

    UEHARA Takato

    Differential and Complex Geometry Seminar  2015.3.30 

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  • Rational Surface Automorphisms with Siegel Disks

    上原 崇人

    複素力学系の総合的研究  2014.12.10 

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  • On rational surface automorphisms with positive entropy

    UEHARA Takato

    Symmetries of Kähler manifolds, dynamics and moduli spaces  2014.9.25 

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  • On rational surface automorphisms preserving cuspidal anticanonical curves

    UEHARA Takato

    Moduli spaces and self-maps  2014.3.4 

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  • パンルヴェ第6方程式の力学系について

    上原 崇人

    第7回佐賀大学数学研究交流会  2014.2.6 

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  • On automorphism groups of rational surfaces

    上原 崇人

    第三回若手代数複素幾何研究集会  2014.1.8 

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  • On rational surface automorphisms

    上原 崇人

    射影多様体の幾何とその周辺2013  2013.11.2 

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  • Siegel disks on rational surfaces

    UEHARA Takato

    New Developments in Complex Dynamical Systems  2012.12.13 

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  • The entropy values of automorphisms on rational surfaces

    UEHARA Takato

    Various Aspects on the Painlevé Equations  2012.11.30 

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  • Construction of automorphisms on rational surfaces

    上原 崇人

    第10回アフィン代数幾何学研究集会  2012.9.6 

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  • On automorphisms of rational surfaces

    UEHARA Takato

    Korea-Japan Joint Conference in Algebraic Geometry  2012.8.20 

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  • Constructing automorphisms of rational surfaces

    UEHARA Takato

    Interactions between continuous and discrete holomorphic dynamical systems  2012.7.10 

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  • Rational surface の自己同型写像について

    上原 崇人

    九州代数幾何若手勉強会  2012.3.14 

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  • Ergodic theory of Painlevé VI

    UEHARA Takato

    The 4th International GCOE symposium on "Weaving Science Web beyond Particle-Matter Hierarchy"  2012.2.21 

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  • On rational surface automorphisms

    上原 崇人

    複素力学系の総合的研究  2012.1.25 

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  • Rational surface automorphisms preserving cuspidal anticanonical curves

    UEHARA Takato

    Automorphisms of algebraic varieties - Dynamics and Arithmetic  2011.12.20 

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  • Rational surface automorphisms with positive entropy

    可積分系数理の多様性  2010.8.20 

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  • Construction of rational surface automorphisms with positive entropy

    上原 崇人

    複素力学系とその関連分野の総合的研究  2009.12.18 

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  • 有理曲面上の複素力学系

    上原 崇人

    有理曲面上の複素力学系  2009.8.10 

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  • 有理曲面上の自己同型写像の構成について

    上原 崇人

    2009函数方程式論サマーセミナー  2009.8.1 

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  • 正のエントロピーをもつ有理曲面上の自己同型写像

    上原 崇人

    2008函数方程式論サマーセミナー  2008.8.7 

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  • 面積保存写像の孤立周期点について

    上原 崇人

    玉原特殊多様体研究集会  2008.7.22 

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  • Ergodic theory of Painlevé VI equation

    UEHARA Takato

    The 1st GN Workshop on Differential Galois Theory for Hamiltonian Systems and Related Topics  2008.6.5 

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  • Isolated periodic points in area-preserving surface dynamics

    上原 崇人

    完全WKB解析と超局所解析  2008.5.26 

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  • Periodic solutions to Painlevé VI and S. Saito's fixed point formula

    上原 崇人

    超幾何方程式研究会2008  2008.1.7 

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  • Area-preserving surface dynamics and S. Saito's fixed point formula

    UEHARA Takato

    Complex Dynamics and Related Topics  2007.9.3 

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  • Area-preserving surface dynamics and S. Saito's fixed point formula

    上原 崇人

    2007函数方程式論サマーセミナー  2007.8.6 

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Research Projects

  • 有理曲面を用いたK3曲面上の力学系の解析

    Grant number:19K03544  2019.04 - 2023.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    上原 崇人

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    Grant amount:\4290000 ( Direct expense: \3300000 、 Indirect expense:\990000 )

    本研究の研究対象は,コンパクト複素曲面上の双正則もしくは双有理自己同型写像による高次元の複素力学系である.
    まず,以前の研究において示した,有理曲面上の双正則自己同型写像による力学系に対するエントロピー値の結果を,今年度は双有理自己同型写像に拡張した.具体的には,あるワイル群の任意の元に対応するスペクトル半径の対数は,適当な有理曲面上の双有理写像のエントロピーとして実現されることを示した.本結果は,豊富に存在することが知られている値に対してそれをエントロピー値として実現する力学系が存在すること,つまり,力学系が豊富に存在することを述べており,今後の研究に大きな影響を与えるものと期待している.
    また,以前に構成したK3曲面を別の角度から考察した.以前の研究では,複素射影平面上で楕円曲線内の9点ブローアップで得られる2つの有理曲面を用意して,楕円曲線の正則管状近傍をのりしろとして2つの有理曲面を貼り合わせることでK3曲面が構成されることを示した.この構成により得られるものは,いわゆるK3曲面のII型退化の近傍を記述した曲面となっている.今年度は,K3曲面のIII型退化の近傍に対応する構成として,2次元射影空間の6点ブローアップで記述される4つの3次曲面を用意して,無限遠3直線の近傍をのりしろとして貼り合わされる曲面について,コホモロジー群がどのようにして得られるかを検証した.この計算は,K3曲面構成へ重要なステップであると考えている.

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  • Analysis of automorphisms on rational surfaces based on entorpy

    Grant number:16K17617  2016.04 - 2020.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)  Grant-in-Aid for Young Scientists (B)

    Uehara Takato

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    Grant amount:\4030000 ( Direct expense: \3100000 、 Indirect expense:\930000 )

    We construct a family of K3 surfaces in terms of rational surfaces. More precisely, by using two rational surfaces obtained from the blowups of nine points on elliptic curves on projective spaces, we show that a family of K3 surfaces is given by patching two surfaces that are the complements of appropriate tubular neighborhoods of elliptic curves in the rational surfaces. The family contains non-projective K3 surfaces, which enables us to establish the basis for the study of dynamical systems on K3 surfaces.

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  • Construction and application of a theory of dynamical systems on complex surfaces

    Grant number:24740096  2012.04 - 2016.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)  Grant-in-Aid for Young Scientists (B)

    Uehara Takato

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    Grant amount:\4420000 ( Direct expense: \3400000 、 Indirect expense:\1020000 )

    We study dynamical systems of biholomorphic automorphisms on rational surfaces with positive topological entropy. We determine explicitly the determinant values, which are defined for automorphisms preserving anticanonical curves, and show the existence of an abundance of rational surface automorphisms with positive entropy. Moreover, we show the existence of automorphisms on complex surfaces with positive entropy having a given number of Siegel domains, which are observed around fixed points.

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Class subject in charge

  • Calculus II (2021academic year) 3rd and 4th semester  - 水1,水2

  • Calculus II (2021academic year) 3rd and 4th semester  - 水1~2

  • Calculus IIa (2021academic year) Third semester  - 水1,水2

  • Calculus IIb (2021academic year) Fourth semester  - 水1,水2

  • Applied Analysis (2021academic year) Late  - その他

  • Advanced topics in applied analysis (2021academic year) Prophase  - 月5,月6

  • Excercises in Basic Analysis a (2021academic year) 1st semester  - 木7,木8

  • Excercises in Basic Analysis b (2021academic year) Second semester  - 木7,木8

  • Excercises in Basic Analysis (2021academic year) 1st and 2nd semester  - 木7,木8

  • Basic Analysis B (2021academic year) 1st and 2nd semester  - 木5,木6

  • Basic Analysis Ba (2021academic year) 1st semester  - 木5,木6

  • Basic Analysis Bb (2021academic year) Second semester  - 木5,木6

  • Seminar in Analysis (2021academic year) Year-round  - その他

  • Analysis II (2021academic year) 3rd and 4th semester  - 木3,木4

  • Analysis IIa (2021academic year) Third semester  - 木3,木4

  • Analysis IIb (2021academic year) Fourth semester  - 木3,木4

  • A Basic Course in Calculus II (2020academic year) 3rd and 4th semester  - 水1,水2

  • Basic Course in Calculus IIa (2020academic year) Third semester  - 水1,水2

  • Basic Course in Calculus IIb (2020academic year) Fourth semester  - 水1,水2

  • Basic Course in Calculus IIa (2020academic year) Third semester  - 水1,水2

  • Basic Course in Calculus IIb (2020academic year) Fourth semester  - 水1,水2

  • Applied Analysis (2020academic year) special  - その他

  • Advanced topics in applied analysis (2020academic year) Prophase  - 月5,月6

  • Excercises in Basic Analysis a (2020academic year) 1st semester  - 木7,木8

  • Excercises in Basic Analysis b (2020academic year) Second semester  - 木7,木8

  • Excercises in Basic Analysis (2020academic year) 1st and 2nd semester  - 木7,木8

  • Basic Analysis B (2020academic year) 1st and 2nd semester  - 木5,木6

  • Basic Analysis Ba (2020academic year) 1st semester  - 木5,木6

  • Basic Analysis Bb (2020academic year) Second semester  - 木5,木6

  • Seminar in Analysis (2020academic year) Year-round  - その他

  • Analysis II (2020academic year) 3rd and 4th semester  - 木3,木4

  • Analysis IIa (2020academic year) Third semester  - 木3,木4

  • Analysis IIb (2020academic year) Fourth semester  - 木3,木4

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