SATO KENTA
Organization
Faculty of Mathematics Division of Algebra and Geometry Assistant Professor
School of Sciences Department of Mathematics（Joint Appointment）
Graduate School of Mathematics Department of Mathematics（Joint Appointment）
Title
Assistant Professor
Contact information
Profile
I am studying algebraic geometry. In particular, I am interested in algebraic varieties in positive characteristic. In algebraic geometry of positive characteristic, techniques such as resolution of singularities and vanishing of cohomologies cannot be used, so there are many difficulties compared to characteristic 0. I am conducting research with the goal of solving such difficulties by developing a method specific to positive characteristic using Frobenius morphism. So far, I have mainly studied singularities in positive characteristic. Recently, I am also interested in studying global objects such as Fano varieties from the viewpoint of positive characteristic.
Research History
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理化学研究所数理創造プログラム・基礎科学特別研究員：2019年4月～2020年9月 東京大学大学院数理科学研究科・学術振興会特別研究員PD：2018年10月～2019年3月
Research Interests・Research Keywords
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Research theme：Boundedness of projective varieties in positive characteristic
Keyword：Algebraic geometry, Positive characteristic, Fano varieties, Globally F regular, Boundedness
Research period： 2020.4
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Research theme：Singularities in positive characteristic
Keyword：Algebraic geometry, Positive characteristic, F-singularity, MMP, F-pure threshold
Research period： 2017.4
Awards
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東京大学数理科学研究科長賞
2018.9 東京大学数理科学研究科
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東京大学数理科学研究科長賞
2016.3 東京大学数理科学研究科
Papers
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Deformations of log terminal and semi log canonical singularities Reviewed International journal
@Kenta Sato, @Shunsuke Takagi
Forum Math. Sigma 11 ( e35 ) 1 - 34 2023.5
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On accumulation points of $F$-pure thresholds on regular local rings Reviewed International journal
@Kenta Sato
J. Algebra 622 614 - 635 2023.5
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Ascending chain condition for $F$-pure thresholds with fixed embedding dimension Reviewed International journal
@Kenta Sato
Int. Math. Res. Not. 2021 ( 10 ) 7205 - 7223 2021.5
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General hyperplane sections of threefolds in positive characteristic Reviewed International journal
@Kenta Sato, @Shunsuke Takagi
J. Inst. Math. Jussieu. 19 ( 2 ) 647 - 661 2020.3
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Ascending chain condition for $F$-pure thresholds on a fixed strongly $F$-regular germ Reviewed International journal
@Kenta Sato
Compos. Math. 155 ( 6 ) 1194 - 1223 2019.6
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Stability of test ideals of divisors with small multiplicity Reviewed International journal
@Kenta Sato
Math. Z. 288 ( 3-4 ) 783 - 802 2018.8
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Weak Akizuki-Nakano vanishing theorem for singular globally $F$-split 3-folds Reviewed International journal
@Kenta Sato
Manuscr. Math. 1900
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Arithmetic and geometric deformations of $F$-pure and $F$-regular singularities Reviewed International journal
@Kenta Sato, @Shunsuke Takagi
to appear in Amer. J. Math. 1900
Presentations
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正標数3次元多様体におけるBertiniの定理 Invited
@佐藤謙太
正標数の可換環論とその周辺2024 in 淡路島 2024.3
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代数多様体の超平面切断と特異点 Invited
@佐藤謙太
第7回数理新人セミナー 2024.2
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Geometrically log canonicity of log canonical surface singularity in positive characteristic Invited
2024.1
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On boundedness of Fano threefolds with fixed Gorenstein index in positive characteristic Invited International conference
Young Perspectives on Algebraic Geometry 2023.12
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General hyperplane section of log canonical threefolds in positive characteristic Invited International conference
2023.10
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On boundedness of Fano threefolds in positive characteristic Invited International conference
International workshop on Birational Geometry 2023.10
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正標数3次元Fano多様体の有界性について Invited
@佐藤謙太
代数幾何学とその周辺の話題 2023.9
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基礎体の非分離拡大に対する特異点の振る舞いについて Invited
@佐藤謙太
第5回情報数理セミナー 2023.6
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General hyperplane section of log canonical threefolds in positive characteristic Invited International conference
Workshop on Commutative Algebra and Algebraic Geometry in Prime Characteristics 2023.5
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General hyperplane section of log canonical threefolds in positive characteristic Invited International conference
Algebraic Geometry and Singularities in Positive and Mixed Characteristic 2023.5
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Toward the boundedness of Fano varieties in positive characteristic Invited International conference
Algebraic Geometry and Singularities in Positive and Mixed Characteristic 2023.5
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正標数の3次元多様体におけるBertiniの定理 Invited
@佐藤謙太
杉本代数セミナー 2023.4
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正標数の3次元射影多様体におけるBertiniの定理について Invited
@佐藤謙太
正標数体上の代数多様体、および連接層の導来圏に関するワークショップ 2023.3
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Geometrically log canonicity of log canonical surfaces in positive characteristic Invited International conference
Mini Workshop on singularities 2023.3
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General hyperplane section of log canonical threefolds in positive characteristic Invited International conference
The 1st Algebraic geometry Atami symposium 2023.2
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General hyperplane section of log canonical threefolds in positive characteristic Invited International conference
Korea-Japan Conference in Algebraic Geometry 2023.2
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General hyperplane section of log canonical threefolds in positive characteristic
2022.11
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Arithmetic and deformations of F-singularities Invited International conference
Advances in Mixed Characteristic Commutative Algebra and Geometric Connections 2022.5
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Deformation of klt singularities Invited International conference
Fellowship of Rings(MSRI) 2022.4
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Deformation of klt or lc singularities
2021.11
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klt及びlc特異点の変形理論
@佐藤謙太
日本数学会 2021.9
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Deformations of klt or F-regular singularities Invited
2021.8
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Deformation of log canonical singularities Invited
2021.5
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商特異点の混標数局所環上の変形理論 Invited
@佐藤謙太
九大代数学セミナー 2021.4
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Arithmetic and geometric deformations of $F$-singularities Invited
2021.4
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Arithmetic and geometric deformations of $F$-singularities Invited International conference
Birational geometry meeting 2021.3
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Strongly $F$-regular singularities deform to klt singularities
2020.11
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Toward classification of algebraic varieties
iTHEMS Coffee Meeting 2020.10
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An algebraic approach to the four color theorem
2020.9
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$F$純閾値の極限 Invited
@佐藤謙太
2020年度代数学シンポジウム 2020.9
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On accumulation points of $F$-pure thresholds on regular local rings Invited
2020.8
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On accumulation points of $F$-pure thresholds on regular local rings International conference
Commutative algebra seminar 2020.2
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Akizuki-Nakano vanishing on globally $F$-split 3-folds and its application International conference
Algebraic geometry seminar 2020.2
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Akizuki-Nakano vanishing on globally $F$-split 3-folds and its application
2020.1
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On the accumulation points of $F$-pure thresholds International conference
2019.11
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Akizuki-Nakano vanishing on globally $F$-split 3-folds and its application Invited
2019.11
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$F$純閾値の昇鎖条件
@佐藤謙太
日本数学会 2019.9
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A pathology on the accumulation points of $F$-pure thresholds Invited
2019.7
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正標数の特異点
@佐藤謙太
RIKEN iTHEMSのアウトリーチについての研究集会2019 2019.6
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Ascending chain condition for $F$-pure thresholds Invited
2019.5
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Introduction to singularity theory in algebraic geometry
iTHEMS Math Seminar 2019.5
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Ascending chain condition for $F$-pure thresholds Invited
2018.8
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$F$純閾値の昇鎖条件 Invited
@佐藤謙太
新潟代数セミナー 2018.6
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On the ascending chain condition for $F$-pure thresholds Invited International conference
London-Tokyo Workshop in birational geometry 2018.5
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Ascending chain condition for $F$-pure threshold Invited International conference
Commutative Algebra Seminar 2018.5
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Ascending chain condition for $F$-pure threshold Invited International conference
Algebraic Geometry Seminar 2018.5
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$F$純閾値の昇鎖条件
@佐藤謙太
第23回代数若手研究会 2018.3
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Berkovich log discrepancies in positive characteristic (after E. Canton)
2018.1
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Ascending chain condition for $F$-pure thresholds on fixed strongly $F$-regular germ Invited
2017.12
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Ascending chain condition for $F$-pure thresholds International conference
2017.11
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On Ascending chain condition for $F$-pure thresholds Invited
2017.11
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Ascending chain condition for $F$-pure thresholds on fixed strongly $F$-regular germ Invited International conference
2017.10
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General hyperplane sections of 3-folds in positive characteristic International conference
Algebraic Geometry Seminar 2017.4
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General hyperplane sections of threefolds in positive characteristic Invited
2017.3
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General hyperplane sections of 3-folds in positive characteristic Invited International conference
The 2-nd Higher dimensional algebraic geometry Echigo Yuzawa symposium 2017.2
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Stability of multiplier ideals of divisors with small multiplicity Invited
2017.1
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Bertini theorems for canonical or klt 3-folds in positive characteristic (ポスター) International conference
@佐藤謙太
代数幾何学城崎シンポジウム2016 2016.10
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On the fitting ideals in free resolutionの紹介
@佐藤謙太
第13回可換環論サマースクール 2016.10
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On the non-nef loci in positive characteristic (Short Communication)
2016.7
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On the non-nef loci of divisors on singular varieties in positive characteristic Invited
2016.7
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Stability of test ideals of divisors with small multiplicity (ポスター) International conference
@佐藤謙太
2016.7
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Stability of test ideals of divisors with small multiplicity (ポスター) International conference
@佐藤謙太
2016.6
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On the non-nef loci of divisors on singular varieties in positive characteristic Invited
2016.3
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正標数の代数多様体におけるnon-nef locusについて
@佐藤謙太
第13回城崎新人セミナー 2016.2
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On the stability of test ideals of divisors with small multiplicity Invited
2015.11
Professional Memberships
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日本数学会
Academic Activities
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Screening of academic papers
Role(s)： Peer review
2021
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世話人
第24回代数学若手研究会 （ 東京大学 ） 2019.2 - Present
Research Projects
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大域的F正則多様体の一様有界性
Grant number：20K14303 2020 - 2023
日本学術振興会 科学研究費助成事業 若手研究
Authorship：Principal investigator Grant type：Scientific research funding
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F純閾値の昇鎖条件について
2017 - 2018
日本学術振興会 特別研究員
Grant type：Joint research
Class subject
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代数学Ⅱ・演習
2024.10 - 2025.3 Second semester
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代数学Ⅱ・演習
2023.10 - 2024.3 Second semester
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代数学I・演習
2023.4 - 2023.9 First semester
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代数学Ⅱ・演習
2022.10 - 2023.3 Second semester
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数学演習Ｂ
2022.4 - 2022.9 First semester
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代数学Ⅰ・演習
2022.4 - 2022.9 First semester
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代数学Ⅱ・演習
2021.10 - 2022.3 Second semester
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数学概論Ⅰ・演習
2021.4 - 2021.9 First semester
Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.
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2023 理化学研究所（数理創造プログラム) Classification:Affiliate faculty Domestic/International Classification:Japan
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2022 理化学研究所（数理創造プログラム) Classification:Affiliate faculty Domestic/International Classification:Japan
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2021 理化学研究所（数理創造プログラム) Classification:Affiliate faculty Domestic/International Classification:Japan
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2020 理化学研究所（数理創造プログラム) Classification:Affiliate faculty Domestic/International Classification:Japan
Participation in international educational events, etc.
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2022.5
ICTP (International Centre for Theoretical Physics)
A virtual International Graduate Course on Tight closure and its applications
Venue：イタリア(オンライン)
Number of participants：80
Social Activities
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RIKEN iTHEMS のアウトリーチについての研究会 2019に参加し、「正標数の特異点」について講演
理化学研究所数理創造プログラム 東京大学 玉原国際セミナーハウス 2019.6