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: 

Calabi-Yau manifolds, mirror symmetry, moduli space

研究分野: 

複素幾何, シンプレクティック幾何: 

Calabi-Yau多様体, ミラー対称性, モジュライ空間

researchmap   Google Scholar

Publications   (論文概説とコメント)

1. Mirror symmetry and rigid structures of generalized K3 surfaces. arXiv

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

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

4. 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 

5. 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

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

7. 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

8. 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

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

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

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

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

13. 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

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

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

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

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

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

Abstracts & Proceedings

1. 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. 

2. 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.  

3. 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. 

4. 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.

5. 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.

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

2. 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.

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

4. 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)

Organizing Services

1. Aspects of Mirror Symmetry 2024, 2024/?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Research Grants

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.

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 (現 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 (現 大和大学理工学部 講師)