Research

数学, 数理物理の周辺分野に幅広く興味を持っています.

Research Fields: 

complex geometry, symplectic geometry, mathematical physics: 

Calabi-Yau manifolds, mirror symmetry

研究分野: 

複素幾何, シンプレクティック幾何, 数理物理: 

Calabi-Yau多様体, ミラー対称性

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Publications   (論文概説とコメント)

1. Mirror symmetry and rigid structures of generalized K3 surfaces, Advances in Mathematics, Vol. 460  (2025) 110050. arXiv

2. K3 differential operators for genus zero groups Γ_0(n)_+, with Shonobu Hosono, - addendum to “BCOV cusp forms of lattice polarized K3 surfaces”-, arXiv

3. BCOV cusp forms of lattice polarized K3 surfaces, with Shinobu Hosono, Advances in Mathematics, Vol. 434 (2023) 109328. arXiv

4. Attractor mechanisms of moduli spaces of Calabi-Yau 3-folds, with Yu-Wei Fan, Journal of Geometry and Physics, Vol. 185 (2023) 104724. arXiv

5. Degenerating Hodge structure of one-parameter family of Calabi-Yau threefolds, with Tatsuki Hayama, Asian Journal of Mathematics, Vol. 25, No. 1, (2021), 31–42. arXiv 

6. Weil-Petersson geometry on the space of Bridgeland stability conditions, with Yu-Wei Fan and Shing-Tung Yau, Communication in Analysis and Geometry, Vol. 29, No. 3, 681-706, 2021. arXiv

7. Geometric transitions and SYZ mirror symmetry, with Siu-Cheong Lau, Pacific Journal of Mathematics, 301-2 (2019), 489-517. arXiv

8. Local Calabi-Yau manifolds of affine type A via SYZ mirror symmetry, with Siu-Cheong Lau, Journal of Geometry and Physics 139 (2019) 103-138. arXiv

9. Degenerations and Lagrangian fibrations of Calabi-Yau manifolds, Handbook for Mirror Symmetries of Calabi-Yau and Fano Manifolds, Advanced Lectures in Mathematics, Vol. 47 (2019) 149-204. arXiv

10. Doran-Harder-Thompson conjecture via SYZ mirror symmetry: elliptic curves, Symmetry, Integrability and Geometry: Methods and Applications, 13 (2017), 024. arXiv

11. Calabi-Yau threefolds of type K (I): Classification, with Kenji Hashimoto, International Mathematics Research Notices, 2017; Issue 21 (1) 6654-6693. arXiv

12. Calabi-Yau threefolds of type K (II): Mirror Symmetry, with Kenji Hashimoto, Communication in Number Theory and Physics, 2016;10 (2) 157-192. arXiv

13. Calabi-Yau threefolds with infinite fundamental group, Calabi-Yau Manifolds and their Moduli 2014, Proceedings of Symposia in Pure Mathematics, 2016; 93, 331-338.

14. Lectures on BCOV holomorphic anomaly equations, with Jie Zhou, Calabi-Yau Varieties; Arithmetic, Geometry and Physics, Fields Institute Monograph Series, 2015; 34 (1) :445-473. arXiv

15. Non-commutative projective Calabi-Yau schemes, Journal of Pure and Applied Algebra, 2015; 219 (7) 2771-2780. arXiv

16. L^p-convergence of the Laplace-Beltrami eigenfunction expansions, Comptes Rendus Mathématiques de l'Académie des Sciences Canada, 2015; 37 (2) 76-80.

17. Trilinear forms and Chern classes of Calabi-Yau threefolds, with Pelham Wilson, Osaka Journal of Mathematics, 2014; 51 (1) 203-213. arXiv

18. On the minimal volume of simplices enclosing a convex body, Archiv der Mathematik, 2014; 102 (5) 489-492.

19. Pfaffian Calabi-Yau threefolds and mirror symmetry, Communication in Number Theory and Physics, 2012; 6 (3) 661-696. arXiv

Abstracts & Proceedings

1. Mirror symmetry for generalized K3 surfaces: Oberwolfach Reports (MFO-RIMS Tandem Workshop: Algebraιc Geometry and Noncommutative Projective Varieties), 2024, 29-31. 

2. 一般化K3曲面のミラー対称性, 第69回幾何学シンポジウム予稿集 (東京理科大学, 2022), 57-61. 

3. Mirror symmetry and rigid structures of generalized K3 surfaces, Proceeding of the 3rd Japan-Taiwan Joint Conference on Differential Geometry, OCAMI Reports 2022, 26-36.  

4. Calabi-Yau多様体のアトラクター機構とその周辺, 日本数学会2021年度秋季総合分科会予稿集(代数学分科会特別講演, 千葉大学(Zoom), 2021), 75-85. 

5. Kahlerモジュライ空間と三角圏の安定性条件, 日本数学会2020年度年会予稿集 (幾何学分科会特別講演, 熊本大学(Zoom), 2020), 87-97.

6. Calabi-Yau多様体の退化とLagrangeファイブレーション, 第65回幾何学シンポジウム報告集 (基調講演, 東北大学, 2018), 104-114.

7. Toward Weil-Petersson geometry of Kahler moduli spaces, 城崎代数幾何シンポジウム2017報告集, 15-25.

Expository Articles

1. モジュライ空間とミラー対称性, Close Up, 早稲田大学 基幹理工学部・研究科, 2024. 記事

2. 数学と総合政策学, SFC総合政策学シリーズ(第5巻) -総合政策学の方法論的展開-, 87-103, 2023.

3. 鉛をかじる数学者, Researcher’s Eye, 三田評論, 2022年12月号. ONLINE

4. 京都大学ガロア祭 -問題と解説(有限幾何)-, 数学セミナー2018年12月号, 42-44.

5. 代数幾何とカラビ・ヤウ多様体, 数理科学2018年10月号, 22-28.

6. 代数幾何とシンプレクティック幾何の双対性, 研究ピックアップ, 京都大学白眉ニュースレター Vol.14, p14, 2017.

Editing Services

1. 城崎代数幾何学シンポジウム2018報告集, KURENAI紅 (上原北斗, 渡邉究, 金沢篤)

Postdoctoral Fellows

1. 三田史彦 (特別研究員: 深谷圏と量子コホモロジーの研究), 京都大学, 2020/4-2021/3 (-> 学習院大学理学部 助教)

2. 川谷康太郎 (特別研究員: 射の圏の安定性条件の研究), 京都大学, 2019/10-2020/3 (-> 大和大学理工学部 講師 -> 和歌山県立医科大学医学部 講師)

Organizing Services

1. Calabi-Yau Varieties and Related Topics, 2026/?, Tokyo Metropolitan University. 

2. Aspects of Mirror Symmetry 2025, 2025/9/22-23, Chiba University. 

3. Calabi-Yau Varieties and Related Topics, 2025/7/5-6, Tsuda University. 

4. Aspects of Mirror Symmetry 2024, 2024/8/19-21, Chiba University. 

5. Aspects of Mirror Symmetry 2023, 2023/9/4-6, Chiba University. 

6. Aspects of Mirror Symmetry 2022, 2022/9/5-7, Chiba University. 

7. Calabi-Yau Manifolds and Mirror Symmetry - Past, Present, and Future -, 2022/8/8-12, Gakushuin University. 

8. 第66回代数学シンポジウム, 2021/8/31-9/3, 早稲田大学. 

9. Aspects of Mirror Symmetry 2021, 2021/8/18-20. (Zoom online)

10. Online workshop on mirror symmetry and related topics, 2020/12/7-11. (Zoom online)

11. ミラー対称性の諸相 2020, 2020/9/16-17. (Zoom online)

12. The 5th KTGU Mathematics Workshop for Young Researchers, 2020/2/7, Kyoto University. 

13. Mirror Symmetry and Related Topics 2019, 2019/12/9-13, Kyoto University. 

14. Aspects of Mirror Symmetry 2019, 2019/7/10-11, Chiba University.

15. Kinosaki Algebraic Geometry Symposium, 2018/10/22-26, Kinosaki International Art Center.

16. ミラー対称性の諸相 2018, 2018/9/25-26, 京都大学.

17. Complex Geometry and Symplectic Geometry at Crossroads, 2017/9/25-26, Kyoto University. 

18. ミラー対称性の諸相 2017, 2017/6/21-23, 京都大学. 

19. Current Topics in Complex and Symplectic Geometry, 2017/3/6-10, Kyoto University. 

Research Grants (KAKEN)

1. 基盤研究(A) 23H00083 (Martin Guest 代表), Differential Geometry and Integrable Systems: Exploiting New Links, 2023-2027.

2. 基盤研究(C) 22K03296, ミラー対称性の幾何学, 2022-2026. 

3. 卓越研究費, 複素代数幾何とシンプレクティック幾何の双対性, 2019-2024. 

4. 若手研究(B) 17K17817, モジュライ理論から見たCalabi-Yau多様体とFano多様体のミラー対称性, 2017-2022. 

5. 白眉研究費, Calabi-Yau多様体とミラー対称性の研究, 2016-2019.