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I am currently an associate professor at Department of Mathematics, Osaka Metropolitan University.
My research area is in complex differential and algebraic geometry. I am particularly interested in canonical metrics in Kähler geometry and its relationship to algebro-geometric stability in the sense of Geometric Invariant Theory.
Brief CV
Brief CV
Education
Education
University College London (UK), 2013-2015, PhD student, supervised by Jason Lotay and Michael Singer. Link to my thesis.
University of Edinburgh (UK), 2011-2012, PhD student (transferred to the University College London in January 2013).
University of Cambridge (UK), 2010-2011, Part III Mathematical Tripos, MMath with distinction.
University of Cambridge (UK), 2008-2010, BA (Hons) in Mathematics (Class 1).
University of Tokyo (Japan), 2004-2008, BA in Cognitive Behavioral Science.
Employment
Employment
Osaka Metropolitan University (Japan), 2022-current, associate professor.
Tokyo Institute of Technology (Japan), 2018-2022, assistant professor.
Università degli Studi di Firenze (Italy), 2018, postdoc in memory of Paolo de Bartolomeis. Mentor: Fiammetta Battaglia.
Université d'Aix-Marseille (France), 2017-2018, postdoc. Mentor: Julien Keller.
Data4CS K.K. (Japan), 2016-2017, data analyst.
Visits
Visits
CRM-Simons Scholar, Centre de Recherche Mathématique, Montréal (Canada), June 2024.
ShanghaiTech University (China), Institute of Mathematical Sciences, from September 2019 to January 2020.
Publications
Publications
Papers
Papers
On uniform log K-stability for constant scalar curvature Kähler cone metrics, with Takahiro Aoi and Kai Zheng, Comm. Anal. Geom. 33, (2025) n.3, 701--767 (arXiv:2110.02518).
A variational approach to the Hermitian--Einstein metrics and the Quot-scheme limit of Fubini--Study metrics, with Julien Keller, Geom Dedicata 219, 50 (2025) (arXiv:1907.05770); link to the view-only version.
Uniform L^2-estimates for flat nontrivial line bundles on compact complex manifolds, with Takayuki Koike and Shin-ichi Matsumura, Complex Manifolds, 12(2025), n. 1, 2025, pp. 20240009, to appear in the topical issue on "COMPLEX GEOMETRY AND LIE GROUPS" (arXiv:2409.05300).
Balanced metrics for extremal Kähler metrics and Fano manifolds, In: Hirachi, K., Ohsawa, T., Takayama, S., Kamimoto, J. (eds) The Bergman Kernel and Related Topics. HSSCV 2022. Springer Proceedings in Mathematics & Statistics, vol 447 (arXiv:2311.11612).
Anticanonically balanced metrics and the Hilbert--Mumford criterion for the delta_m-invariant of Fujita--Odaka, Ann. Global Anal. Geom., 64, (2023) n. 8. (arXiv:2104.12346); link to the view-only version.
Quot-scheme limit of Fubini--Study metrics and its applications to balanced metrics, with Julien Keller, In: Cheltsov, I., Chen, X., Katzarkov, L., Park, J. (eds) Birational Geometry, Kähler–Einstein Metrics and Degenerations. Springer Proceedings in Mathematics & Statistics, vol 409 (arXiv:2101.00996).
Expected centre of mass of the random Kodaira embedding, J. Geom. Anal., 32, 122 (2022), (arXiv:2009.06201); link to the view-only version.
Quot-scheme limit of Fubini--Study metrics and Donaldson's functional for vector bundles, with Julien Keller, Épijournal de Géométrie Algébrique, 5 (2021), n.21 (arXiv:1809.08425).
Quantisation of extremal Kähler metrics, J. Geom. Anal., 31 (2021), n.3, 2970--3028. (arXiv: 1508.02643); link to the view-only version.
Mapping properties of the Hilbert and Fubini--Study maps in Kähler geometry, Ann. Fac. Sci. Toulouse Math. Série 6, Tome 29 (2020) no. 2, 371--389. (arXiv: 1705.11025, with erratum, see also arXiv:2502.08038 for corrections).
Existence of twisted constant scalar curvature Kähler metrics with a large twist, Math. Z., 292 (2019), n. 3-4, 791--803. (arXiv: 1508.00513); link to the view-only version.
Relative stability associated to quantised extremal Kähler metrics, J. Math. Soc. Japan, 71 (2019), n. 3, 861--880. (arXiv: 1705.11018).
Scalar curvature and Futaki invariant of Kähler metrics with cone singularities along a divisor, Ann. Inst. Fourier, 69 (2019) n.2, 591--652. (arXiv: 1508.02640).
About J-flow, J-balanced metrics, uniform J-stability and K-stability, with Julien Keller, Asian J. Math., 22 (2018), n. 3, 391--412. (arXiv: 1705.02000).
Slope instability of projective spaces blown up along a line, Ann. Global Anal. Geom., 53 (2018), n. 2, 251--264. (arXiv: 1508.02637); link to the view-only version.
Ueda's lemma via uniform Hörmander estimates for flat line bundles, with Takayuki Koike, arXiv:2212.01360, to appear in Kyoto J. Math.
Preprints
Preprints
GIT stability and biquotients of SU(3), with Hiroaki Ishida and Hisashi Kasuya, arXiv:2509.20254.
Relative uniform K-stability over models implies existence of extremal metrics, arXiv:2506.02360, submitted.
Quantitative injectivity of the Fubini--Study map, arXiv:2502.08038.
On the coupled Ding stability and the Yau--Tian--Donaldson correspondence for Fano manifolds, with Kento Fujita, arXiv:2412.04028, submitted.
A Hilbert--Mumford criterion for nilsolitons, arXiv:2311.12469, submitted.
Link to the list of my papers on arXiv.
Publications in Japanese
Publications in Japanese
See my page in Japanese.
Other notes
Other notes
An Introduction to the Kempf--Ness Theorem; lecture notes for the postgraduate courses (Advanced topics in Geometry E and F) at Tokyo Institute of Technology, and Advanced Geometry D (Lectures on Geometry I) at Osaka Metropolitan University.
Lecture notes for the intensive course at Kyoto University.
Lecture notes for the postgraduate course (Mathematical Sciences B) at Osaka Metropolitan University.
Talks
Talks
The 10th China-Japan Geometry Conference, Nanjing University of Science and Technology (China), 22-28/Sep/2025.
Purdue Geometry and Geometric Analysis Seminar, Purdue University (US), online, 27/Oct/2025.
Differential Geometry Seminar, Fukuoka University (Japan), 6/Nov/2025.
Workshop on Algebraic Geometry and Complex Geometry in Osaka, Osaka (Japan), 26-30/Jan/2026.
Conferences
Conferences
The 10th China-Japan Geometry Conference, Nanjing University of Science and Technology (China), 22-28/Sep/2025.
The 31th Symposium on Complex Geometry, Kanazawa (Japan), 1-4/Dec/2025.
Workshop on Algebraic Geometry and Complex Geometry in Osaka, Osaka (Japan), 26-30/Jan/2026.
Grants
Grants
Principal Investigator
JSPS KAKENHI (Grant-in-Aid for Scientific Research (C)), 2023-2027, Grant Number JP23K03120.
JSPS KAKENHI (Grant-in-Aid for Early-Career Scientists), 2019-2023, Grant Number JP19K14524.
Co-Investigator
JSPS KAKENHI (Grant-in-Aid for Scientific Research (B)), 2024-2029, Grant Number JP24K00524. Principal Investigator: Hisashi Kasuya.
Organisation of events
Organisation of events
OCAMI Differential Geometry Seminar (website in Japanese) and OCAMI Complex Analysis Seminar (in Japanese); organiser 2022-current.
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」, the second meeting, the third meeting, the fourth meeting, the fifth meeting, and the sixth meeting, co-organised with Nobuhiro Honda, Satoshi Nakamura, Naoto Yotsutani, and Takahiro Aoi.
Mini-workshop on Higgs bundles, co-organised with Masataka Iwai, Hisashi Kasuya, and Natsuo Miyatake.
New developments in Kobayashi–Hitchin correspondence and Higgs bundles, co-organised with Masataka Iwai, Hisashi Kasuya, and Natsuo Miyatake.
Workshop on Dynamics in Arithmetic and Complex Geometry and its applications; list of organisers.
Non-archimedean and tropical geometry from complex and algebraic geometry and dynamics; list of organisers.
Symplectic and complex geometry days in Osaka, co-organised with Masahiro Futaki and Yohsuke Imagi.
Geometry seminar at Tokyo Institute of Technology; organiser 2020-21.
Groupe de Travail - Métriques à courbure spéciale (géométrie complexe); a work group at the Institut de Mathématiques de Marseille, organised by Julien Keller and myself.
UCL Junior geometry seminar; organiser 2013-14. Link to the current website.
Links
Links
Home Page of the GeCo GeDi (Geometria Complessa e Geometria Differenziale) project.
Titech complex geometry seminar; a seminar held intermittently at Tokyo Institute of Technology.
Contact Details
Contact Details
Email : yhashimoto_AT_omu.ac.jp (please replace _AT_ by @)
Email : yhashimoto_AT_omu.ac.jp (please replace _AT_ by @)
Postal address :
Postal address :
Department of Mathematics, Graduate School of Science/School of Science,
Osaka Metropolitan University,
3-3-138, Sugimoto, Sumiyoshi-ku, Osaka,
558-8585,
JAPAN.
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