Papers & Talks

1. Toric Non-archimedean μ-entropy and thermodynamical structure, arXiv:2303.09090.
2. Entropies in μ-framework of canonical metrics and K-stability, II -- Non-archimedean aspect: non-archimedean μ-entropy and μK-semistability, arXiv:2202.12168.
3. Entropies in μ-framework of canonical metrics and K-stability, I -- Archimedean aspect: Perelmna's W-entropy and μ-cscK metrics, preprint arXiv:2101.11197.

1. Equivariant calculus on μ-character and μK-stability of polarized schemes, arXiv:2004.06393, accepted by Journal of Symplectic Geometry
2. Constant μ-scalar curvature Kähler metric - formulation and foundational results, Journal of Geometric Analysis, 32, Article 145, 2022, available also at arXiv:1902.00664
3. The moduli space of Fano manifolds with Kähler-Ricci solitons, Advances in Math., Volume 357, Article 106841, 1 Dec. 2019, available also at arXiv:1802.08128.

Theory on Kähler metrics with constant exponentially weighted scalar curvature and exponentially weighted K-stability including Kähler-Ricci solitons, Aug. 2020, PDF.

1. Optimal degeneration of algebraic variety and Perelman entropy, Moduli spaces and Singularities, CRM, Montreal, June. 20-24, 2024. Slide
2. Distortion and Moment measure of L-psh function over trivially valued field, K-stability and moment maps, Isaac Newton Institute, Cambridge, May. 13-17, 2024. Slide
3. Recent developments of Kahler-Ricci flow on Fano manifolds, Workshop on Dynamics in Arithmetic and Complex Geometry and its applications, Osaka, Jan. 16-19, 2024
4. Perelman entropy in Kahler geometry and thermodynamical structure, Advances in special Kahler metrics, Le Croisic, June, 12-16, 2023. Note
5. A Thermodynamical formalism for Optimal degeneration in Kahler geometry, iTHEMS now and next, March 29, 2023, RIKEN. Slide (Designed mainly for physicists, though I'm not sure if it succeeded. )
6. An overview of non-archimedean pluripotential theory and its outlook, 多変数関数論冬セミナー, University of Tokyo, Dec. 17-19, 2022. Slide
7. A sketch of the future of $\mu$-cscK metrics and $\mu K$-stability, The 28th Symposium on Complex Geometry, Kanazawa, Nov. 7-11, 2022. Slide
8. 代数多様体の最適退化, 専門家向け勉強会「ケーラー多様体上の標準計量とその周辺3」, Tokyo Institute of Technology, Aug. 22-23, 2022.
9. I forgot the title, but I gave a short talk on Perelman's entropy in night session. , Hayama symposium on complex analysis in several variables, Hayama, July 23-26, 2022.
10. Perelman's entropy in Kahler geometry, The 6th China-Japan Geometry Conference, Chongqing and Osaka (online), Dec. 24-28, 2021. Slide
11. Perelman's entropy in Kahler geometry and its non-archimedean reflection, The 27th Symposium on Complex Geometry, Kanazawa (online), Nov. 1-4, 2021. Slide
12. Canonical metrics and Perelman's entropy in Kahler geometry, Index Theory and Complex Geometry, Singapore (online), Aug. 16-27, 2021. Video Slide
13. Perelman's μ-entropy in Kahler geometry (short talk), Hayama symposium on complex analysis in several variables, Hayama (online), July 22-25, 2021.Slide
14. Perelman's μ-entropy in Kahler geometry and μ-cscK metrics, 第22回 多様体上の微分方程式, Kanazawa (online), Nov. 26-27, 2020.Slide
15. μ-cscK metrics, μK-stability and a Lagrangian formalism, The 26th Symposium on Complex Geometry, Kanazawa (online), Nov. 2-5, 2020.Slide
16. μ-cscK metrics and μK-stability, 専門家向け勉強会「ケーラー多様体の標準軽量とその周辺」, Tokyo Institute of Technology, Feb. 20-22, 2020.
17. μ-cscK metric, NCTS Workshop on Analytic Trends in Complex Geometry and Related Fields, Taipei, June 17-21, 2019. Slide
18. The moduli space of Fano manifolds admitting Kähler-Ricci solitons, Singular metrics in complex Kähler geometry, CIRM, Marseille, Feb. 4-8 2019.
19. Kahler-Ricci soliton and moduli space of Fano manifolds, The 24th Symposium on Complex Geometry, Kanazawa, Nov. 13-16, 2018.
20. Moduli space of Fano manifolds admitting Kähler-Ricci solitons, The 65th Geometry Symposium (Japanese page only), Sendai, Aug. 28-31, 2018 (Extended version of Slide B).
21. Kähler-Ricci soliton and K-stability, beyond Kähler-Einstein, Younger generations in Algebraic and Complex geometry V, Hakodate community plaza, Hakodate, Aug. 6-9, 2018. Draft (more AG flavor)
22. Moduli space of Fano manifolds admitting Kähler-Ricci solitons, HAYAMA Symposium on Complex Analysis in Several Variables XX & Pacific Rim Complex-Symplectic Geometry Conference, Shonan Village Center, Hayama, July 13-17, 2018. Slide B (more DG flavor)
23. On complex analytic moduli space of Fano manifolds admitting Kähelr-Ricci solitons, The 2nd Symposium in Geometry and Differental Equations, ShanghaiTech University, Shanghai, June 11-15, 2018. Slide A (a blend of DG and AG)
24. Moduli of Fano manifolds admitting Kähler-Ricci solitons, Mathsci Freshman Seminar 2018 (Japanese page only), Kyoto University, Kyoto, February 2018.

1. Introduction to optimal degeneration problems, Complex Analysis and Geometry Seminar, Rutgers University, NewBrunswick, Sep 8, 2023. Slide
2. Non-archimedean μ-entropy and moment measure, Seminaire de geometrie algebrique, Sorbonne University, Jussieu, June 22, 2023. Note
3. Non-archimedean pluripotential theory on μ-entropy, 代数幾何セミナー, Kyoto University, May, 15, 2023.
4. Optimal degeneration of polarized variety and toric μ-entropy, 代数幾何セミナー, Osaka University, May, 8, 2023.
5. The non-archimedean μ-entropy in toric case, 複素解析幾何セミナー, University of Tokyo, Oct. 31, 2022.
6. Perelman's entropy and optimal degeneration, ZAG seminar (online), July 20, 2021. YouTube, Slide
7. `Phase transition' in Kahler geometry (short talk), iTHEMS coffee meeting, RIKEN, Wako (online), June 18, 2021. Slide
8. Geometry of canonical metrics on Kahler manifolds, iTHEMS Math seminar, RIKEN, Wako (online), May 14, 2021. Note
9. μ-cscK metrics and μK-stability of polarized manifolds, Seminar on Geometric Complex Analysis (online), University of Tokyo, Tokyo, July 13, 2020. Slide
10. μ-cscK metrics and μK-stability of polarized manifolds, Séminaire du CIRGET / Géométrie et Topologie (online), UQAM (online), Montreal (online), June 12, 2020. YouTube, Slide
11. μ-cscK metric, Differential topology seminar, Kyoto University, Kyoto, June 4, 2019.
12. Canonical metrics on compact Kähler manifolds and moduli spaces of complex structures, Geometry seminar, Nagoya University, Nagoya, Nov. 6, 2018.
13. Kähler-Ricci soliton and torus equivariant K-stability (very short talk), Summer School on Algebraic Geometry, Tambara Institute of Mathematical Sciences, Tambara, July 2018.
14. Kähler-Ricci soliton, K-stability and moduli space of Fano manifolds, Seminar on Geometric Complex Analysis, University of Tokyo, Tokyo, May 2018.

1. July 23-26, 2022, Hayama, Hayama Symposium on Complex Analysis in Several Variables XXIII.
2. Sep. 28- Oct. 2, 2020, Online, Simons conferences on K-stability.
3. Nov., 11-14, 2019, Kanazawa, The 25th Symposium on Complex Geometry.
4. July, 13-16, 2019, Hayama, Hayama Symposium on Complex Analysis in Several Variables XXI.
5. June, 24-28, 2019, Beijing, Trends in Modern Geometry 2019.
6. Feb, 17-22, 2018, Kyoto, Fukaya 60, Geometry and Everything.
7. May, 14-16, 2018, IHP, Paris, Workshop on degenerations of Calabi-Yau manifolds.