Genki Hosono

I am a postdoctral researcher in Mathematical Institute, Tohoku University.

I am interested in several complex variables and complex geometry.
In particular, I am interested in pluripotential theoretic properties of (quasi-)plurisubharmonic functions and singular Hermitian metrics.
I am also studying the Ohsawa-Takegoshi L^2 extension theorem.

• Approximations and examples of singular Hermitian metrics on vector bundles, Arkiv för Matematik, Vol. 55, No. 1 (2017), pp. 131–153. arXiv:1505.02396
• Local geodesics between toric plurisubharmonic functions with infinite energy, Annales Polonici Mathematici, Vol. 120, No. 1 (2017), pp. 33–40. arXiv:1606.05235
• On minimal singular metrics of line bundles whose stable base loci admit holomorphic tubular neighborhoods (with Takayuki Koike), to appear in Annales de la Faculté des Sciences de Toulouse. arXiv:1612.08212
• The optimal jet L^2 extension of Ohsawa-Takegoshi type, arXiv:1706.08725, to appear in Nagoya Mathematical Journal.
• On sharper estimates of Ohsawa-Takegoshi L^2-extension theorem, arXiv:1708.08269.
• A suggestion of peripheral curves on hard contact lenses (with Yukimi Goto, Tatsuya Miura and Hiroki Kodama, in Japanese), Suurikagaku Jissenkenkyu Letter 2018, LMSR 2018-1. Article link
• Subharmonic variation of Azukawa pseudometrics for balanced domains, arXiv:1811.07154.
• A converse of Hörmander's L^2-estimate and new positivity notions for vector bundles (with Takahiro Inayama), arXiv:1901.02223.
• On projective manifolds with pseudo-effective tangent bundle (with Masataka Iwai and Shin-ichi Matsumura), arXiv:1908.06421.
• A simplified proof of optimal L^2-extension theorem and extensions from non-reduced subvarieties, arXiv:1910.05782.

• Approximations and examples of singular Hermitian metrics on vector bundles, 2015 Seoul Workshop on Complex Geometry and Analysis, Seoul National University, Seoul, July 2015.
• Approximations and examples of singular Hermitian metrics on vector bundles, MSJ Autumn Meeting 2015, Kyoto Sangyo University, Kyoto, September 2015.
• Converegnce along geodesics between toric plurisubharmonic functions, MSJ Autumn Meeting 2016, Kansai University, Osaka, September 2016.
• On convergence along geodesics between plurisubharmonic functions, The 22nd Symposium on Complex Geometry, Shiinoki Cultural Complex, Kanazawa, November 2016.
• On convergence along geodesics between plurisubharmonic functions, Young Mathematicians Workshop on Several Complex Variables 2016 , The University of Tokyo, Tokyo, November 2016.
• On geodesics between toric plurisubharmonic functions, East Asian Core Doctoral Forum on Mathematics, Seoul National University, Seoul, January 2017.
• On minimal singular metrics of line bundles whose stable base loci admits holomorphic tubular neighborhoods, MSJ Spring Meeting 2017, Tokyo Metropolitan University, Hachioji, March 2017.
• The optimal jet L^2 extension of Ohsawa-Takegoshi type, The 23rd Symposium on Complex Geometry, Ishikawa Prefectural bunkyo hall, Kanazawa, November 2017.
• On recent topics on L^2 extension theorems, Topology of pseudoconvex domains and analysis of reproducing kernels, Kyoto University, Kyoto, November 2017.
• On recent topics on L^2 extension theorems, Winter seminar on several complex variables, Tokyo University of Science, Noda, December 2017.
• On recent topics on L^2 extension theorems, Positivity Concepts on Holomorphic Line Bundles and Theories on Canonical Kähler Metrics, Osaka City University, Osaka, January 2018.
• On recent topics on L^2 extension theorems, MSJ Spring Meeting 2018, University of Tokyo, Tokyo, March 2018.
• Variational theories in complex analysis of several variables, The 61st symposium on complex analysis, Hirosima University, Hirosima, November 2018.
• Twisted Hörmander condition and plurisubharmonicity, and new positivity notions, Workshop on Holomorphic Maps, Pluripotentials and Complex Geometry, Shizuoka Prefecture Gender Equality Center "Azalea", Sizuoka, March 2019.
• Variation theory and a converse of Hormander's L^2 estimate, Young Mathematicians Workshop on Several Complex Variables 2019, Osaka, September 2019
• Hironaka's example on deformation of Kahler manifolds and recent development, Kodaira's Theory on Complex Manifolds and its Development, Osaka, December 2019
• L^2 theoretic conditions for plurisubharmonicity and positivity of vector bundles, Winter seminar on several complex variables, online, December 2020.
• Variational theories in L^2 and pluripotential theories, Grauert theory and recent complex geometry, online, February 2021.

• On the convergence along geodesics between plurisubharmonic functions, Seminar in Analytic Geometry, Nagoya University, Nagoya, October 2016
• On the convergence along geodesics between plurisubharmonic functions, Tohoku Complex Analysis Seminar, Tohoku University, Sendai, December 2016
• On the proof of the optimal L2 extension theorem by Berndtsson-Lempert and related results, Seminar on Geometric Complex Analysis, Tokyo, November 2017.
• On the proof of the optimal L2 extension theorem by Berndtsson-Lempert and related results, Seminar in Analytic Geometry, Nagoya, Febrary 2018.
• On recent improvements on estimates of $L^2$ extension theorems , Seminar on Complex Analysis, Osaka, Febrary 2018.
• Variational theories in complex analysis of several variables, Seminar on Geometric Complex Analysis, Tokyo, December 2018.
• Variational theories in complex analysis of several variables, Complex Analysis seminar, Osaka, December 2018.
• Recent development on the Ohsawa-Takegoshi L^2 extension theorem, Colloquium in Mathematical Institute of Tohoku University, Sendai, April 2019
• H"ormander's L^2 estimate, L^2 extension theorems, and positivity notions of Hermitian metrics, Tohoku Complex Analysis Seminar, Tohoku University, Sendai, April 2019
• Optimal L^2 extension theorem and variation theory, Seminar in Geometry, Tohoku University, Sendai, May 2019
• Variations of Bergman kernels and Ohsawa-Takegoshi L^2 extension theorems, Differential Topology Seminar, Kyoto University, Kyoto, July 2019
• Simplification of the proof of optimal L^2 extension theorems and its application, Seminar in Analytic Geometry, Nagoya, October 2019
• A simplified proof of the optimal L^2 extension theorem and its application, Seminar on Geometric Complex Analysis, University of Tokyo, Tokyo, December 2019

• On local geodesics between toric plurisubharmonic functions (short communications), HAYAMA Symposium on Complex Analysis in Several Variables XVIII, Shonan Village Center, Hayama, July 2016.
• The optimal jet L^2 extension of Ohsawa-Takegoshi type (short communications), HAYAMA Symposium on Complex Analysis in Several Variables XIX, Shonan Village Center, Hayama, July 2017.
• On sharper estimates of L^2 extension theorems (short communications), HAYAMA Symposium on Complex Analysis in Several Variables XX, Shonan Village Center, Hayama, July 2018.

Mar. 2013 B.S. in Mathematics, the University of Tokyo.
Mar. 2015 M.S. in Mathematical Sciences, the University of Tokyo.
Mar. 2018 Ph.D. in Mathematical Sciences, the University of Tokyo.

Oct. 2013--Mar. 2018 FMSP course student, Leading Graduate Course for Frontiers of Mathematical Sciences and Physics.
Apr. 2015--Mar. 2018 JSPS Research Fellow (DC1), Japan Society for the Promotion of Science.
Apr. 2018-- Project Researcher, Graduate School of Mathematical Sciences, The University of Tokyo.

Teaching Assistants:
Summer 2013 Mathematics II (Linear Algebra) (College of Arts and Sciences, The University of Tokyo. Lecturer: Akihiro Shimomura)
Winter 2013 Mathematics IB (Calculus) (College of Arts and Sciences, The University of Tokyo. Lecturer: Shigeharu Takayama)
Summer 2014 Complex Analysis II (Department of Mathematics, The University of Tokyo. Lecturer: Shigeharu Takayama)
Summer 2016 Complex Analysis II (Department of Mathematics, The University of Tokyo. Lecturer: Kengo Hirachi)
Winter 2016 Set and Topology (Department of Mathematics, The University of Tokyo. Lecturer: Masahiko Kanai)

Takahiro Inayama
Eiji Inoue
Masataka Iwai
Takayuki Koike
Tatsuya Miura