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Takayuki Koike
小池 貴之

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  • I uploaded a new preprint (A gluing construction of K3 surfaces, arXiv:1903.01444, j.w. T. Uehara).

Takayuki Koike

    I am a lecturer of Department of Mathematics, Graduate School of Science, Osaka City University.

Email : tkoike [at] sci.osaka-cu.ac.jp
Research field : Complex geometry, The theory of functions of several complex variables.
Research interests : (Singular) Hermitian metrics on a line bundle on a complex manifold, The theory of functions of several complex variables on a neighborhood of a complex submanifold.

I am interested in singular Hermitian metrics of a (nef) line bundle L over a complex manifold,
especially in minimal singular metrics of L, metrics of L with the mildest singularities among singular Hermitian metrics of L whose local weights are plurisubharmonic.
I am also interested in complex analysis on neighborhoods of compact analytic subvarieties, especially in Ueda theory.

Papers & Preprints

Papers

  1. T. Koike, Minimal singular metrics of a line bundle admitting no Zariski-decomposition, Tohoku Math. J. (2) Volume 67, Number 2 (2015), 297--321, arXiv:1304.1289.
  2. T. Koike, On minimal singular metrics of certain class of line bundles whose section ring is not finitely generated, Ann. Inst. Fourier (Grenoble) Volume 65, Number 5 (2015), 1953--1967, arXiv:1312.6402.
  3. T. Koike, On the minimality of canonically attached singular Hermitian metrics on certain nef line bundles, Kyoto J. Math., Volume 55, Number 3 (2015), 607--616, arXiv:1405.4698.
  4. Y. Tanizaki, T. Koike, Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling, Ann. Physics 351 (2014), 250--274, arXiv:1406.2386.
  5. T. Koike, Toward a higher codimensional Ueda theory, Math. Z., Volume 281, Issue 3 (2015), 967--991, arXiv:1412.2354, correction.
  6. T. Koike, Ueda theory for compact curves with nodes, Indiana U. Math. J, Volume 66, Number 3 (2017), 845--876, arXiv:1507.00109.
  7. T. Koike, N. Ogawa, Local criteria for non embeddability of Levi-flat manifolds, J. Geom. Anal Volume 28, Number 2 (2018), 1052--1077, arXiv:1603.09692.
  8. G. Hosono, T. Koike, On minimal singular metrics of line bundles whose stable base loci admit holomorphic tubular neighborhoods, to appear in Ann. Fac. Sci. Toulouse Math. (6), arXiv:1612.08212.
  9. T. Koike, Higher codimensional Ueda theory for a compact submanifold with unitary flat normal bundle, to appear in Nagoya Math. J., arXiv:1606.01837.

Preprints

  1. T. Koike, On a neighborhood of a torus leaf of a certain class of holomorphic foliations on complex surfaces, arXiv:1510.02287.
  2. T. Koike, Arnol'd's type theorem on a neighborhood of a cycle of rational curves, arXiv:1805.05326.
  3. T. Koike, N. Ogawa, On the neighborhood of a torus leaf and dynamics of holomorphic foliations, arXiv:1808.10219.
  4. T. Koike, T. Uehara, A gluing construction of K3 surfaces, arXiv:1903.01444.

論文/プレプリント

論文

  1. T. Koike, Minimal singular metrics of a line bundle admitting no Zariski-decomposition, Tohoku Math. J. (2) Volume 67, Number 2 (2015), 297--321, arXiv:1304.1289.
  2. T. Koike, On minimal singular metrics of certain class of line bundles whose section ring is not finitely generated, Ann. Inst. Fourier (Grenoble) Volume 65, Number 5 (2015), 1953--1967, arXiv:1312.6402.
  3. T. Koike, On the minimality of canonically attached singular Hermitian metrics on certain nef line bundles, Kyoto J. Math., Volume 55, Number 3 (2015), 607--616, arXiv:1405.4698.
  4. Y. Tanizaki, T. Koike, Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling, Ann. Physics 351 (2014), 250--274, arXiv:1406.2386.
  5. T. Koike, Toward a higher codimensional Ueda theory, Math. Z., Volume 281, Issue 3 (2015), 967--991, arXiv:1412.2354, correction.
  6. T. Koike, Ueda theory for compact curves with nodes, Indiana U. Math. J, Volume 66, Number 3 (2017), 845--876, arXiv:1507.00109.
  7. T. Koike, N. Ogawa, Local criteria for non embeddability of Levi-flat manifolds, J. Geom. Anal Volume 28, Number 2 (2018), 1052--1077, arXiv:1603.09692.
  8. G. Hosono, T. Koike, On minimal singular metrics of line bundles whose stable base loci admit holomorphic tubular neighborhoods, to appear in Ann. Fac. Sci. Toulouse Math. (6), arXiv:1612.08212.
  9. T. Koike, Higher codimensional Ueda theory for a compact submanifold with unitary flat normal bundle, to appear in Nagoya Math. J., arXiv:1606.01837.

プレプリント

  1. T. Koike, On a neighborhood of a torus leaf of a certain class of holomorphic foliations on complex surfaces, arXiv:1510.02287.
  2. T. Koike, Arnol'd's type theorem on a neighborhood of a cycle of rational curves, arXiv:1805.05326.
  3. T. Koike, N. Ogawa, On the neighborhood of a torus leaf and dynamics of holomorphic foliations, arXiv:1808.10219.
  4. T. Koike, T. Uehara, A gluing construction of K3 surfaces, arXiv:1903.01444.

Organizing

  1. Potential Theoretical Aspects of Complex Analytic Geometry, The University of Tokyo, Tokyo, February 12-14, 2016 (with G. Hosono and R. Nomura).
  2. Positivity Concepts on Holomorphic Line Bundles and Theories on Canonical Kähler Metrics, Osaka City University, Osaka, January 28-31, 2018.
  3. Workshop on Complex Analytic and Algebraic Methods in Dynamics, Osaka City University, Osaka, January 15-18, 2019.

オーガナイズした集会等

  1. 複素解析幾何学のポテンシャル論的諸相, 東京大学, 2016/2/12-14 (細野元気氏, 野村亮介氏と共同で).
  2. Positivity Concepts on Holomorphic Line Bundles and Theories on Canonical Kähler Metrics, 大阪市立大学, 2018/1/28-31.
  3. Workshop on Complex Analytic and Algebraic Methods in Dynamics, 大阪市立大学, 2019/1/15-18.

Curriculum Vitae

Education

Mar. 2011 B.S. in Mathematics, the University of Tokyo.
Mar. 2013 M.S. in Mathematical Sciences, the University of Tokyo.
Mar. 2015 Ph.D. in Mathematical Sciences, the University of Tokyo.
    Dissertation: Studies on singular Hermitian metrics with minimal singularities on numerically effective line bundles
    Advised by Professor Shigeharu Takayama.

Employment & Fellowships

Nov. 2012--Mar. 2015 FMSP course student, Leading Graduate Course for Frontiers of Mathematical Sciences and Physics.
Apr. 2013--Mar. 2015 JSPS Research Fellow (DC1, 25-2869).
Apr. 2015--Mar. 2016 JSPS Research Fellow (PD, 25-2869).
Apr. 2016--Dec. 2017 JSPS Research Fellow (PD, 28-4196).
Jan. 2018-- Lecturer of Department of Mathematics, Graduate School of Science, Osaka City University, Leading Initiative for Excellent Young Researchers(LEADER, No. J171000201).

Professional Societies

Teaching

Winter 2011 Mathematics IB (Calculus) (Lecturer: Shigeharu Takayama)*
Summer 2012 Mathematics IB (Calculus) (Lecturer: Shigeharu Takayama)*
Summer 2013 Algebra I (Lecturer: Atsushi Shiho)**
Summer 2014 Computing for Mathematicians I (Lecturer: Shingo Ichii)**
Winter 2014 Computing for Mathematicians II (Lecturer: Shingo Ichii)**

Awards

プロフィール

学歴

平成19年3月 麻布高等学校卒業.
平成23年3月 東京大学理学部数学科卒業.
平成25年3月 東京大学大学院数理科学研究科数理科学専攻修士課程修了.
平成27年3月 東京大学大学院数理科学研究科数理科学専攻博士課程修了.
    博士 (数理科学), 2015年3月24日授与
    博士論文題目:Studies on singular Hermitian metrics with minimal singularities on numerically effective line bundles
              (数値的半正な正則直線束の極小特異エルミート計量に関する研究)
    指導教員:高山 茂晴教授

職歴/フェローシップ

平成24年11月--平成27年3月 FMSPコース生, Leading Graduate Course for Frontiers of Mathematical Sciences and Physics.
平成25年4月--平成27年3月 日本学術振興会特別研究員(DC1, 25-2869).
平成27年4月--平成28年3月 日本学術振興会特別研究員(PD, 25-2869).
平成28年4月--平成29年12月 日本学術振興会特別研究員(PD, 28-4196).
平成30年1月-- 大阪市立大学 大学院理学研究科 数学教室の講師・卓越研究員 (No. J171000201).

所属学会

教育経験

平成23年度冬学期 数学IB (微積分入門) 演習 (担当:高山茂晴先生)*
平成24年度夏学期 数学IB (微積分入門) 演習 (担当:高山茂晴先生)*
平成25年度夏学期 代数学特別演習I (担当:志甫淳先生)**
平成26年度夏学期 計算数学I (担当:一井信吾先生)**
平成26年度冬学期 計算数学II (担当:一井信吾先生)**

受賞



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Updated on March 14, 2019.

Takayuki KOIKE (tkoike [at] sci.osaka-cu.ac.jp), Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku Osaka, 558-8585 Japan.

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最終更新日:2019年3月14日.

小池 貴之 (tkoike [at] sci.osaka-cu.ac.jp), 〒558-8585 大阪市住吉区杉本3-3-138 大阪市立大学 大学院理学研究科 数学教室.