HANIHARA NORIHIRO
Organization
Faculty of Mathematics Division of Algebra and Geometry Assistant Professor
School of Sciences Department of Mathematics（Concurrent）
Graduate School of Mathematics Department of Mathematics（Concurrent）
Title
Assistant Professor
Contact information
Profile
My research subject is representation theory of algebras. Given a ring (like a quiver or a commutative ring), its representation theory is about the study of categories (primarily the module category) and various related structures. I am particularly interested in homological structures appearing in Cohen-Macaulay representation theory of finite dimensional algebras or of commutative Gorenstein rings. I am mainly studying tilting theory linking their representation theories and also the theory of cluster tilting objects (or non-commutative resolutions) for these rings, through triangulated categories like derived categories, singularity categories, and cluster categories, and their enhancements by differential graded categories.
Research Areas
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Natural Science / Algebra
Degree
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Doctor of Philosophy (Mathematical Science)
Research History
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2021年4月--2022年3月 日本学術振興会特別研究員PD 名古屋大学多元数理科学研究科 2022年4月--2024年3月 日本学術振興会特別研究員PD 東京大学カブリ数物連携宇宙研究機構
Research Interests・Research Keywords
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Research theme： Non-commutative resolutions in triangulated categories and their enhancements
Keyword： non-commutative resolution, derived category, dg enhancement, Cohen-Macaulay representation theory
Research period： 2025.4 - 2028.3
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Research theme： Calabi-Yau structures on differential graded categories
Keyword： dg category, Calabi-Yau structure, singularity category, cluster category
Research period： 2022.4 - 2025.3
Awards
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建部賢弘奨励賞
2024.9 日本数学会
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多元数理論文賞
2019.3 名古屋大学多元数理科学研究科
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理学部学修奨励賞
2017.3 東京大学理学部
Papers
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Non-commutative resolutions for Segre products and Cohen-Macaulay rings of hereditary representation type Reviewed
Norihiro Hanihara
Trans. Amer. Math. Soc. 378 ( 4 ) 2429 - 2475 2025
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Morita theorem for hereditary Calabi-Yau categories Reviewed International journal
Norihiro Hanihara
Adv. Math. 2022
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Yoneda algebras and their singularity categories Reviewed International journal
Norihiro Hanihara
Proc. Lond. Math. Soc. 2022
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Cluster categories of formal dg algebras Reviewed International journal
Norihiro Hanihara
Forum Math. Sigma 2022
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Auslander correspondence for triangulated categories Reviewed International journal
Norihiro Hanihara
Algebra & Number Theory 14 ( 8 ) 2037 - 2058 2020
MISC
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形式的dg代数のクラスター圏とその森田型定理
埴原 紀宏
第66回代数学シンポジウム報告集 2021.12
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Cluster tilting for Segre products
Norihiro Hanihara
Oberwolfach Reports 1900
Professional Memberships
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The Mathematical Society of Japan
Research Projects
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Grant number：25K17233 2025.4 - 2028.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Early-Career Scientists
埴原 紀宏
Grant type：Scientific research funding
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微分次数付き圏のカラビ・ヤウ構造と多元環の表現論
Grant number：JP22J00649, 22KJ0737 2022 - 2024
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows
Authorship：Principal investigator Grant type：Scientific research funding
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三角圏のAuslander対応と団傾理論
Grant number：JP19J21165 2019 - 2021
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows
Authorship：Principal investigator Grant type：Scientific research funding