Faculty Profiles - OKADA TAKUZO

Information

写真a

OKADA TAKUZO

Organization

Faculty of Mathematics Division of Algebra and Geometry Professor
School of Sciences Department of Mathematics（Joint Appointment）
Graduate School of Mathematics Department of Mathematics（Joint Appointment）
Joint Graduate School of Mathematics for Innovation （Joint Appointment）

Contact information

Profile

I have been working on algebraic geometry. I am interested in rationally connected varieties that are algebraic varieties admitting plenty of rational curves on them, and study them from the viewpoint of birational geometry. My main research topic is rationality problem of algebraic varieties which are classical and important problem in algebraic geometry. I am also interested in explicit analysis of birational properties of Fano 3-folds such as birational Mori fiber space structures and birational automorphism groups.

External link

Degree

Ph. D. in science

Research History

京都大学(2009-2011) 日本学術振興会特別研究員(PD)(2011-2012) 佐賀大学(2012-2023)

Research Interests・Research Keywords

Research theme：I have been working on algebraic geometry. I am interested in rationally connected varieties that are algebraic varieties admitting plenty of rational curves on them, and study them from the viewpoint of birational geometry. My main research topic is rationality problem of algebraic varieties which are classical and important problem in algebraic geometry. I am also interested in explicit analysis of birational properties of Fano 3-folds such as birational Mori fiber space structures and birational automorphism groups.

Keyword：Algebraic Geometry, Birational Geometry, Fano varieties, Mori fiber spaces

Research period： 2023.10

Awards

日本数学会代数学賞

2020.3 日本数学会

Papers

Birational Mori fiber structures of Q-Fano 3-fold weighted complete intersections, III Reviewed International journal

Takuzo Okada

Kyoto J. Math. 60 ( 3 ) 825 - 893 2020.9

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

DOI： 10.1215/21562261-2019-0048

Other Link： https://projecteuclid.org/journals/kyoto-journal-of-mathematics/volume-60/issue-3/Birational-Mori-fiber-structures-of-Q--Fano-3-fold/10.1215/21562261-2019-0048.full
Stable rationality of cyclic covers of projective spaces Reviewed International journal

Takuzo Okada

Proc. Edinb. Math. Soc. (2) 62 ( 3 ) 667 - 682 2019.8

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

DOI： 10.1017/S0013091518000755

Other Link： https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/abs/stable-rationality-of-cyclic-covers-of-projective-spaces/6A5E74AADA1ABC77C980E0D336D3C58C
Stable rationality of orbifold Fano threefold hypersurfaces Reviewed International journal

Takuzo Okada

J. Algebraic Geom. 28 99 - 138 2019.1

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

DOI： https://doi.org/10.1090/jag/712

Other Link： https://www.ams.org/journals/jag/2019-28-01/S1056-3911-2018-00712-X/
Birational Mori fiber structures of Q-Fano 3-fold weighted complete intersections, II Reviewed International journal

Takuzo Okada

J. Reine Angew. Math. 738 73 - 129 2018.5

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

DOI： https://doi.org/10.1515/crelle-2015-0054

Other Link： https://www.degruyter.com/document/doi/10.1515/crelle-2015-0054/html?lang=en
Birationally rigid Pfaffian Fano 3-folds Reviewed International journal

@Hamid Ahmadinezhad, Takuzo Okada

Algebr. Geom. 5 ( 2 ) 160 - 199 2018.3

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

DOI： doi:10.14231/AG-2018-006

Other Link： http://content.algebraicgeometry.nl/2018-2/2018-2-006.pdf
Birational Mori fiber structures of Q-Fano 3-fold weighted complete intersections Reviewed International journal

Takuzo Okada

Proc. Lond. Math. Soc. (3) 109 ( 6 ) 1549 - 1600 2014.12

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

DOI： https://doi.org/10.1112/plms/pdu044

Other Link： https://academic.oup.com/plms/article/109/6/1549/2951248
Stable rationality of index one Fano hypersurfaces containing a linear space Reviewed International journal

Takuzo Okada

Eur. J. Math. 8 ( 3 ) 1158 - 1171 2023.10

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

DOI： https://doi.org/10.1007/s40879-021-00513-5

Other Link： https://link.springer.com/article/10.1007/s40879-021-00513-5
K-stable divisors in P¹*P¹*P² of degree (1,1,2) Reviewed International journal

@Ivan Cheltsov, @Kento Fujita, @Takashi Kishimoto, Takuzo Okada

Nagoya Math. J. 251 686 - 714 2023.9

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

DOI： https://doi.org/10.1017/nmj.2023.5[Opens in a new window]

Other Link： https://www.cambridge.org/core/journals/nagoya-mathematical-journal/article/kstable-divisors-in-mathbb-p1times-mathbb-p1times-mathbb-p2-of-degree-112/999FB6032A21485AD71CF230CC802E6C
Smooth weighted hypersurfaces that are not stably rational Reviewed International journal

Takuzo Okada

Ann. Inst. Fourier (Grenoble) 71 ( 1 ) 203 - 237 2021.6

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

DOI： 10.5802/aif.3390

Other Link： https://aif.centre-mersenne.org/articles/10.5802/aif.3390/
Alpha invariants of birationally bi-rigid Fano 3-folds I Reviewed International journal

@In-Kyun Kim, @Joonyeong Won, Takuzo Okada

Eur. J. Math. 7 ( 1 ) 272 - 308 2021.3

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

DOI： https://doi.org/10.1007/s40879-020-00441-w

Other Link： https://link.springer.com/article/10.1007/s40879-020-00441-w
Stable rationality of del Pezzo fibrations of low degree over projective spaces Reviewed International journal

@Igor Krylov, Takuzo Okada

Int. Math. Res. Not. 2020 ( 23 ) 9075 - 9119 2020.11

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

DOI： https://doi.org/10.1093/imrn/rny252

Other Link： https://academic.oup.com/imrn/article/2020/23/9075/5144736
On birational rigidity of singular del Pezzo fibrations of degree 1 Reviewed International journal

Takuzo Okada

J. Lond. Math. Soc. (2) 102 1 - 21 2020.8

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

DOI： https://doi.org/10.1112/jlms.12304

Other Link： https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12304
Birationally superrigid Fano 3-folds of codimension 4 Reviewed International journal

Takuzo Okada

Algebra Number Theory 14 ( 1 ) 191 - 212 2020.3

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

DOI： 10.2140/ant.2020.14.191

Other Link： https://msp.org/ant/2020/14-1/p06.xhtml
Stable rationality of higher dimensional conic bundles Reviewed International journal

@Hamid Ahmadinezhad, Takuzo Okada

2 2018.6

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

DOI： https://doi.org/10.46298/epiga.2018.volume2.4266

Other Link： https://epiga.episciences.org/4575
Alpha invariants of birationally rigid Fano three-folds Reviewed International journal

@In-Kyun Kim, Takuzo Okada, @Joonyeong Won

Int. Math. Res. Not. 2018 ( 9 ) 2745 - 2800 2018.5

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

DOI： https://doi.org/10.1093/imrn/rnw310

Other Link： https://academic.oup.com/imrn/article/2018/9/2745/2895553
Q-Fano threefolds with three birational Mori fiber structures Reviewed International journal

Takuzo Okada

Algebraic Varieties and Automorphism Groups, Adv. Stud. Pure Math. 75 393 - 424 2017.12

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

DOI： 10.2969/aspm/07510393

Other Link： https://projecteuclid.org/proceedings/advanced-studies-in-pure-mathematics/Algebraic-Varieties-and-Automorphism-Groups/Chapter/mathbbQ-Fano-threefolds-with-three-birational-Mori-fiber-structures/10.2969/aspm/07510393
Nonrational del Pezzo fibrations admitting an action of the Klein simple group Reviewed International journal

Takuzo Okada

Eur. J. Math. 2 ( 1 ) 319 - 332 2016.3

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

DOI： https://doi.org/10.1007/s40879-015-0080-2

Other Link： https://link.springer.com/article/10.1007/s40879-015-0080-2
Birational superrigidity and slope stability of Fano manifolds Reviewed International journal

@Yuji Odaka, Takuzo Okada

Math. Z. 275 ( 3-4 ) 1109 - 1119 2013.12

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

DOI： https://doi.org/10.1007/s00209-013-1172-7

Other Link： https://link.springer.com/article/10.1007/s00209-013-1172-7
On the birational unboundedness of higher dimensional Q-Fano varieties Reviewed International journal

Takuzo Okada

Math. Ann. 345 ( 1 ) 195 - 212 2009.9

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

DOI： https://doi.org/10.1007/s00208-009-0351-7

Other Link： https://link.springer.com/article/10.1007/s00208-009-0351-7
Nonrational weighted hypersurfaces Reviewed International journal

Takuzo Okada

Nagoya Math. J. 194 1 - 32 2009.6

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

DOI： 10.1017/s0027763000009612

Other Link： https://www.cambridge.org/core/journals/nagoya-mathematical-journal/article/nonrational-weighted-hypersurfaces/CF636DDD97EFFC3DE177262F9F51A7C2

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Presentations

ファノ多様体の双有理的森ファイバー構造の研究と有理性問題への応用 Invited

岡田拓三

日本数学会2020年度年会 2020.3

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Event date： 2024.2

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

Venue：日本大学 Country：Japan
Birationally superrigid Fano 3-folds of codimension 4 Invited International conference

Takuzo Okada

Birational Geometry and Fano Varieties 2019.6

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Event date： 2024.2

Language：English Presentation type：Oral presentation (general)

Country：Russian Federation
Birationally solid Fano 3-fold hypersurfaces Invited International conference

Takuzo Okada

2023 Clay Research Workshop: K-stability and Birational Geometry 2023.9

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Event date： 2023.9

Language：English Presentation type：Oral presentation (general)

Country：United Kingdom

Other Link： https://www.claymath.org/events/k-stability-and-binational-geometry/
Birationally solid Fano 3-folds Invited

2024.2

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Event date： 2024.2

Language：Japanese Presentation type：Oral presentation (general)

Country：Japan
Birationally solid Fano 3-fold hypersurfaces Invited International conference

Takuzo Okada

Fano varieties, their Geometry and Moduli 2023.10

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Event date： 2024.2

Language：English Presentation type：Oral presentation (general)

Country：Korea, Republic of
On K-stability of birationally superrigid Fano 3-folds Invited International conference

Takuzo Okada

Birational Geometry, Kahler-Einstein metrics and Degenerations 2019.4

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Event date： 2024.2

Language：English Presentation type：Oral presentation (general)

Country：Russian Federation
Birationally superrigid Fano 3-folds of codimension 4 Invited International conference

Takuzo Okada

Akgebraic Geometry International Conference 2019.6

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Event date： 2024.2

Language：English Presentation type：Oral presentation (general)

Country：Korea, Republic of
Birationally superrigid Fano threefolds of codimension 4 Invited International conference

Takuzo Okada

Kinosaki Algebraic Geometry Symposium 2019 2019.10

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Event date： 2024.2

Language：English Presentation type：Oral presentation (general)

Country：Japan
Birationally superrigid Fano 3-folds of codimension 4 Invited

2019.11

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Event date： 2024.2

Language：Japanese Presentation type：Oral presentation (general)

Country：Japan
On the degree of irrationality of quartic 3-folds Invited International conference

Takuzo Okada

Birational Geometry, Kahler-Einstein metrics and Degenerations 2019.11

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Event date： 2024.2

Language：English Presentation type：Oral presentation (general)

Country：Korea, Republic of
3次元4次超曲面の非有理次数について Invited

岡田拓三

湯布院代数幾何ワークショップ 2019.12

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Event date： 2024.2

Language：Japanese Presentation type：Oral presentation (general)

Venue：日本文理大学湯布院研修所 Country：Japan
正標数還元手法による非安定有理性の証明について Invited

岡田拓三

新潟代数セミナー 2020.2

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Event date： 2024.2

Language：Japanese Presentation type：Oral presentation (general)

Venue：新潟大学 Country：Japan
代数多様体の（安定）有理性問題の概観 Invited

岡田拓三

新潟代数セミナー 2020.2

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Event date： 2024.2

Language：Japanese Presentation type：Oral presentation (general)

Venue：新潟大学 Country：Japan
On K-stability of birationally superrigid Fano 3-folds Invited

2020.7

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Event date： 2024.2

Language：Japanese Presentation type：Oral presentation (general)

Country：Japan
K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces Invited International conference

Takuzo Okada

Zoom Algebraic Geometry Seminar 2020.12

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Event date： 2024.2

Language：English Presentation type：Oral presentation (general)

Country：Japan
Birational geometry of Fano 3-fold WCIs Invited International conference

Takuzo Okada

Fao varieties and Birational Geometry (online) 2021.2

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Event date： 2024.2

Language：English Presentation type：Oral presentation (general)

Country：United Kingdom
Birational geometry of Fano 3-fold weighted complete intersections Invited International conference

Takuzo Okada

The 19th Affine Algebraic Geometry Meeting (online) 2021.3

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Event date： 2024.2

Language：English Presentation type：Oral presentation (general)

Country：Japan
代数多様体の有理性の問題 Invited

岡田拓三

複素幾何学の諸問題Ⅱ 2021.9

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Event date： 2024.2

Language：Japanese Presentation type：Oral presentation (general)

Venue：Online Country：Japan
Birational geometry of sextic double solids with cA points Invited International conference

Takuzo Okada

Seminar of Algebraic Geometry of East Asia (online) 2021.9

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Event date： 2024.2

Language：English Presentation type：Oral presentation (general)

Country：Japan
Birational geometry of sextic double solids with cA points Invited International conference

Takuzo Okada

Algebraic Geometry Seminar (Online) 2021.10

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Event date： 2024.2

Language：English Presentation type：Oral presentation (general)

Country：Korea, Republic of
On birationally solid Fano 3-fold hypersurfaces Invited International conference

Takuzo Okada

Algebraic Geometry Seminar 2022.10

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Event date： 2024.2

Language：English Presentation type：Oral presentation (general)

Country：Korea, Republic of
On birationally solid Fano 3-folds Invited International conference

Takuzo Okada

Rationality, Moduli, and Related Topics 2022.11

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Event date： 2024.2

Language：English

Country：Japan
Birational rigidity of certain singular Fano 3-folds Invited International conference

Takuzo Okada

The 21st Affine Algebraic Geometry Meeting 2023.3

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Event date： 2024.2

Language：English

Country：Japan
Birationally solid Fano 3-folds

2024.1

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Event date： 2024.1

Language：Japanese Presentation type：Oral presentation (general)

Country：Japan
代数多様体の有理性問題とファノ多様体の双有理幾何

岡田拓三

数理談話会（九州大学） 2024.1

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Event date： 2024.1

Language：Japanese Presentation type：Oral presentation (general)

Venue：九州大学 Country：Japan
Birational Mori fiber space structures of Fano varieties and rationality problem

2023.11

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Event date： 2023.11

Language：Japanese

Country：Japan
Birationally solid Fano 3-folds

2023.4

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Event date： 2023.4

Language：Japanese Presentation type：Public lecture, seminar, tutorial, course, or other speech

Country：Japan

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MISC

代数多様体の有理性問題(複素幾何学の諸問題Ⅱ)

岡田拓三

数理解析研究所講究録 No. 2211 pp. 207-222 2022.1

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Language：Japanese Publishing type：Article, review, commentary, editorial, etc. (scientific journal)
森ファイバー空間の双有理剛性 Reviewed

岡田拓三

日本数学会『数学』 73巻3号 pp.225-246 2021.7

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Language：Japanese Publishing type：Article, review, commentary, editorial, etc. (scientific journal)
Birationally superrigid Fano threefolds of codimension 4

2020.2

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Language：Japanese Publishing type：Article, review, commentary, editorial, etc. (scientific journal)
Stable rationality of orbifold Fano 3-fold hypersurfaces

Takuzo Okada

2017.2

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Language：English Publishing type：Article, review, commentary, editorial, etc. (scientific journal)
Nonrational weighted hypersurfaces

Takuzo Okada

2008.2

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Language：English Publishing type：Article, review, commentary, editorial, etc. (scientific journal)

Professional Memberships

The Mathematical Society of Japan

Academic Activities

主催者

新潟代数シンポジウム（新潟大学） 2023.12

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Type：Competition, symposium, etc.
主催者

阿蘇代数幾何学研究集会（休暇村南阿蘇（阿蘇市）） 2023.9

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Type：Competition, symposium, etc.
Screening of academic papers

Role(s)： Peer review

2023

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：4

Number of peer-reviewed articles in Japanese journals：1
プログラム責任者

第67回代数学シンポジウム（京都大学数理解析研究所） 2022.8 - 2022.9

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Type：Competition, symposium, etc.
座長

第67回代数学シンポジウム（京都大学数理解析研究所） 2022.8 - 2022.9

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Type：Competition, symposium, etc.
数学（日本数学会）

2022.7 - 2026.6

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Type：Academic society, research group, etc.
Screening of academic papers

Role(s)： Peer review

2022

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：4
座長

日本数学会秋季総合分科会（千葉大学） 2021.9

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Type：Competition, symposium, etc.
Screening of academic papers

Role(s)： Peer review

2021

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：8
Screening of academic papers

Role(s)： Peer review

2020

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：3
Screening of academic papers

Role(s)： Peer review

2019

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：5
Screening of academic papers

Role(s)： Peer review

2018

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：5
世話人 International contribution

城崎代数幾何学シンポジウム2017 （城崎国際アートセンター（豊岡市）） 2017.10

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Type：Competition, symposium, etc.
Screening of academic papers

Role(s)： Peer review

2017

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：4
主催者 International contribution

第四回若手複素代数幾何研究集会（Younger Generations in Algebraic and Complex Geometry, IV） 2016.1 - 2023.1

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Type：Competition, symposium, etc.
Screening of academic papers

Role(s)： Peer review

2016

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：3
Screening of academic papers

Role(s)： Peer review

2015

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：3
主催者

代数多様体とその周辺（琉球大学） 2014.9 - 2014.10

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Type：Competition, symposium, etc.
主催者

第三回若手複素代数幾何研究集会（松藤プラザ　駅前「いきいき」ひろば（長崎市）） 2014.1

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Type：Competition, symposium, etc.
Screening of academic papers

Role(s)： Peer review

2014

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：2
主催者 International contribution

第二回若手複素代数幾何研究集会（佐賀大学） 2012.12

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Type：Competition, symposium, etc.
Screening of academic papers

Role(s)： Peer review

2012

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：1
主催者

複素幾何と代数幾何の若手研究集会（熊本大学） 2010.2

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Type：Competition, symposium, etc.

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Research Projects

ファノ多様体の双有理幾何

Grant number：22H01118 2022 - 2026

日本学術振興会科学研究費助成事業基盤研究(B)

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Authorship：Principal investigator Grant type：Scientific research funding
代数多様体の有理性とその周辺に関する研究

Grant number：18K03216 2018 - 2022

日本学術振興会科学研究費助成事業基盤研究(C)

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Authorship：Principal investigator Grant type：Scientific research funding
ファノ多様体の双有理的森ファイバー構造の研究と有理性問題への応用

Grant number：26800019 2014 - 2017

科学研究費助成事業若手研究(B)

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Authorship：Principal investigator Grant type：Scientific research funding
Stanley-Reisner イデアルの算術階数とそのベキの射影次元

Grant number：26400049 2014 - 2016

日本学術振興会科学研究費助成事業基盤研究(C)

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Authorship：Coinvestigator(s) Grant type：Scientific research funding
Qファノ多様体と有理連結多様体の双有理幾何学的研究

Grant number：24840034 2012 - 2013

日本学術振興会科学研究費助成事業研究活動スタート支援

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Authorship：Principal investigator Grant type：Scientific research funding
高次元Qファノ多様体と有理連結多様体の双有理幾何学的研究

Grant number：11J02053 2011

日本学術振興会科学研究費助成事業特別研究員奨励費

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Authorship：Principal investigator Grant type：Scientific research funding
高次元Qファノ多様体と有理連結多様体の双有理幾何学的研究

2011

日本学術振興会特別研究員

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Authorship：Principal investigator Grant type：Joint research
射影多様体のカステルヌボー・マンフォード量とその周辺の話題についての研究

Grant number：21540044 2009 - 2013

日本学術振興会科学研究費助成事業基盤研究(C)

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Authorship：Coinvestigator(s) Grant type：Scientific research funding
非有理的有理連結多様体の双有理幾何学的研究

Grant number：21840032 2009 - 2010

科学研究費助成事業若手研究(スタートアップ)

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Authorship：Principal investigator Grant type：Scientific research funding
有理的でない有理連結多様体の研究

Grant number：06J52622 2006 - 2007

日本学術振興会科学研究費助成事業特別研究員奨励費

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Authorship：Principal investigator Grant type：Scientific research funding
有理的でない有理連結多様体の研究

2006 - 2007

日本学術振興会特別研究員

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Grant type：Joint research

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Class subject

微分積分学Ⅱ

2024.10 - 2025.3 Second semester
線形代数学Ⅱ

2024.10 - 2025.3 Second semester
線形代数学Ⅰ

2024.4 - 2024.9 First semester
代数幾何学基礎・演習

2024.4 - 2024.9 First semester
微分積分学Ⅰ

2024.4 - 2024.9 First semester

Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.

2023 佐賀大学理工学部 Classification:Part-time lecturer Domestic/International Classification:Japan

Semester, Day Time or Duration：後学期金曜2限、3限
2023 埼玉大学 Classification:Intensive course Domestic/International Classification:Japan

Semester, Day Time or Duration：2024年1月29日〜2月2日

Acceptance of Foreign Researchers, etc.

Korea Institute for Advanced Study

Acceptance period： 2024.1 （Period）：Less than 2 weeks

Nationality：Italy

Business entity：Japan Society for the Promotion of Science

Travel Abroad

2023.10 - 2023.11

Staying countory name 1：Korea, Republic of Staying institution name 1：Korea Institute for Advanced Study
2023.9

Staying countory name 1：United Kingdom Staying institution name 1：Clay Mathematical Institute
2022.10

Staying countory name 1：Korea, Republic of Staying institution name 1：Institute for Basic Science, Center for Geometry and Physics