Starting from Sept 2025, I am a research fellow (post-doc) at IGP/IMFP under the mentorship of Mingchen Xia .
From September 2022 to July 2025, I was PhD student at Institut Fourier under the supervision of Gérard Besson and Hervé Gaussier.
From September 2021 to June 2022, I was a master's student at Institut Fourier under the supervision of Gérard Besson.
| E-mail: | zhsha at imfp dot org dot cn |
| zhsha0251 at gmail dot com |
Address: USTC Shanghai Institute for Advanced Studies, 99 Xiupu Road, Pudong New Area, Shanghai, China
My research area is complex geometry and geometric analysis.
I am interested in problems related to scalar curvature, complex Monge-Ampère equations, and canonical Kähler metrics.
[5] In progress...
The statement in Thm 1.2 is a little bit misleading. It can be understood that: Thm 1.2 (1) means if you start from $\mathbb{P}^2$ and consider its blowup, the maximized model will be $\mathbb{P}^2$ itself, with value $\min_X S(\omega) \cdot \operatorname{sys}_2 = 12\pi$. Meanwhile, Thm 1.2 (2) means if you start from a Hirzebruch surface $F_e$ and consider its blowup, the maximized model will be $F_0 \cong \mathbb{P}^1 \times \mathbb{P}^1$, with value $8\pi$.
[4] The 2-systole on compact Kähler surfaces with positive scalar curvature, arXiv:2601.02901, latest version, 2026
We adapt the level set method in Kähler setting and prove a systolic inequality for non-rational ruled surface. This paper has been merged into [4].
[3] A 2-systolic inequality on non-rational compact Kähler surfaces with positive scalar curvature, arXiv:2510.13353, latest version, 2025
...
[2] Rigidity of complete Kähler-Einstein metrics under cscK perturbations, arXiv:2510.13278, latest version, 2025
There are some typos in the arXiv version and the proof of Proposition 3.1 is incorrect, while the statement that the soliton is expanding is still true by our assumption. Please see the revised version in the above link.
[1] The Kähler-Ricci soliton on bounded pseudoconvex domains, arXiv:2412.03345, latest version, 2024
• Pluripotential theory on Kähler manifolds (To be updated...)
• Blowing up a point as a connected sum
• Computing the canonical bundle of a blow-up via short exact sequences
• Métriques kählériennes canoniques sur les domaines pseudoconvexes bornés, PhD thesis, online version, 2025
• Scalar curvature and $S^1$-valued harmonic maps on 3-manifolds, Master thesis, unrevised, 2022
• Peking-Westlake Geometric Analysis Seminar, online seminar, The 2-systole on compact Kähler surfaces with positive scalar curvature, 26 Dec 2025
• Geometry/Topology Young Researcher Workshop, Academy of Mathematics and Systems Sciences, CAS, The 2-systole on compact Kähler surfaces with positive scalar curvature, 18 Dec 2025
• The 4th Milan-Grenoble-Turin meeting in geometry and topology, Institut Fourier, Rigidity of complete Kähler--Einstein metrics under cscK perturbations, 18 Sept 2025
• The 5th Korea-France Conference in Mathematics, Institut de Mathématique de Bordeaux, The Kähler-Ricci soliton on bounded pseudoconvex domains, 16 July 2025
• Seminar talk, IGP-USTC, Canonical Kähler metric on bounded pseudoconvex domains, 9 Jul 2025
• Flows and Singular Spaces, Henri Lebesgue Center, The cscK metric on bounded pseudoconvex domains, 24 Jun 2025
• Curvature and Geometric Analysis in Rome, Sapienza Università di Roma, (Poster session) Kähler-Ricci solitons on bounded pseudoconvex domains, 12 Nov 2024
• Séminaire Compréhensible, Institut Fourier, Calabi conjecture and Kähler-Einstein metrics, 18 Jan 2024
• Journées des doctorants, Institut Fourier, Gradient Kähler-Ricci solitons on strictly pseudoconvex domains, 25 Oct 2023
Please feel free to contact me if you would like to visit Shanghai, and give a talk here.
"It seems entirely plausible that, with all the tremendously clever people working so hard on mathematics, there is nothing left for someone such as myself (who would be the first to admit they do not have any special talent in the field) to do. Perhaps my value would be to act more like cannon fodder? Since just sending in enough men in will surely break through some barrier."
• arXiv:DG
• arXiv:CV
• zbMATH
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