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Takayuki Koike
小池 貴之

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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.

講義関連 (For students)

講義関連のページはこちらから.

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.
  10. T. Koike, Plurisubharmonic functions on a neighborhood of a torus leaf of a certain class of foliations, to appear in Forum Math., arXiv:1510.02287.

Preprints

  1. T. Koike, Arnol'd's type theorem on a neighborhood of a cycle of rational curves, arXiv:1805.05326.
  2. T. Koike, N. Ogawa, On the neighborhood of a torus leaf and dynamics of holomorphic foliations, arXiv:1808.10219.
  3. T. Koike, T. Uehara, A gluing construction of K3 surfaces, arXiv:1903.01444.
  4. T. Koike, Hermitian metrics on the anti-canonical bundle of the blow-up of the projective plane at nine points, arXiv:1909.06827.

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. Complex geometry and complex dynamics in higher dimension, Osaka City University, Osaka, June 27, 2018 (as a local organizer, with Y. Okuyama).
  4. Several Complex Variables Winter Seminar, Osaka City University, Osaka, December 21-23, 2018 (as a local organizer, with S. Hamano).
  5. Workshop on Complex Analytic and Algebraic Methods in Dynamics, Osaka City University, Osaka, January 15-18, 2019 (with Y. Nakamura).
  6. Young mathematicians workshop on algebraic, geometric, and analytic aspects of K theory and vector bundles, University of the Ryukyus, Okinawa, August 20-23, 2019 (with T. Matsushita).
  7. "Young Mathematicians Workshop on Several Complex Variables 2019", Osaka City University, Osaka, September 7-9, 2019 (with M. Adachi and A. Yamamori).
  8. Geometric Complex Analysis on Foliations and Dynamics, RIMS, Kyoto, November 25-27, 2019 (with T. Ohsawa).
  9. Kodaira's Theory on Complex Manifolds and its Development, Osaka City University, Osaka, December 8-9, 2019 (with T. Ohsawa).
  10. Studies on Pseudoconvexity of General Order, Osaka City University, Osaka, March 8-10, 2020 (with T. Ohsawa).

Curriculum Vitae

  • Lecturer of Department of Mathematics, Graduate School of Science, Osaka City University, Leading Initiative for Excellent Young Researchers(LEADER).
  • Born on July 5, 1988 in Tokyo and grew up in Tokyo.

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).
Oct. 2018-- JSPS Grant-in-Aid for Research Activity start-up (H18H05834, K19K21024).

Professional Societies

  • The Mathematical Society of Japan (Member #11163).

Teaching

  • Complex AnalysisII (Winter semester, 2019)
  • Complex AnalysisI, Ordinary Differential Equation (Summer semester, 2019)
  • Mathematical Science C (Winter semester, 2018)
  • Teaching Assistants at College of Arts and Sciences* and Department of Mathematics**, The University of Tokyo.
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

  • Mar. 2015 Dean's Award, Graduate School of Mathematical Sciences, The University of Tokyo.
  • Sep. 2018 MSJ Takebe Katahiro Prize for Encouragement of Young Researchers, The Mathematical Society of Japan.


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Updated on October 1, 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10月1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.