Papers, preprints and notes

Preprints

*Toric Non-archimedean μ-entropy and thermodynamical structure*, arXiv:2303.09090.*Entropies in μ-framework of canonical metrics and K-stability, II -- Non-archimedean aspect: non-archimedean μ-entropy and μK-semistability*, arXiv:2202.12168.*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.

Papers

*Equivariant calculus on μ-character and μK-stability of polarized schemes*, arXiv:2004.06393, accepted by Journal of Symplectic Geometry*Constant μ-scalar curvature Kähler metric - formulation and foundational results*, Journal of Geometric Analysis, 32, Article 145, 2022, available also at arXiv:1902.00664*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.

Thesis

Talks

Symposiums, Conferences & Workshops

*Optimal degeneration of algebraic variety and Perelman entropy*, Moduli spaces and Singularities, CRM, Montreal, June. 20-24, 2024. Slide*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*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*Perelman entropy in Kahler geometry and thermodynamical structure*, Advances in special Kahler metrics, Le Croisic, June, 12-16, 2023. Note*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. )*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*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*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.*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.*Perelman's entropy in Kahler geometry*, The 6th China-Japan Geometry Conference, Chongqing and Osaka (online), Dec. 24-28, 2021. Slide*Perelman's entropy in Kahler geometry and its non-archimedean reflection*, The 27th Symposium on Complex Geometry, Kanazawa (online), Nov. 1-4, 2021. Slide*Canonical metrics and Perelman's entropy in Kahler geometry*, Index Theory and Complex Geometry, Singapore (online), Aug. 16-27, 2021. Video Slide*Perelman's μ-entropy in Kahler geometry (short talk)*, Hayama symposium on complex analysis in several variables, Hayama (online), July 22-25, 2021.Slide*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*μ-cscK metrics, μK-stability and a Lagrangian formalism*, The 26th Symposium on Complex Geometry, Kanazawa (online), Nov. 2-5, 2020.Slide*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.*μ-cscK metric*, NCTS Workshop on Analytic Trends in Complex Geometry and Related Fields, Taipei, June 17-21, 2019. Slide*The moduli space of Fano manifolds admitting Kähler-Ricci solitons*,*Singular metrics in complex Kähler geometry*, CIRM, Marseille, Feb. 4-8 2019.*Kahler-Ricci soliton and moduli space of Fano manifolds*, The 24th Symposium on Complex Geometry, Kanazawa, Nov. 13-16, 2018.*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).*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)*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)*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)*Moduli of Fano manifolds admitting Kähler-Ricci solitons*, Mathsci Freshman Seminar 2018 (Japanese page only), Kyoto University, Kyoto, February 2018.

Seminars

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

I was there

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