Zehao Sha 沙泽浩

Starting from September 2025, I am a research fellow (postdoc) at IMFP under the mentorship of Mingchen Xia.

From September 2022 to July 2025, I was a PhD student at Institut Fourier under the supervision of Gérard Besson and Hervé Gaussier.

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

Research interests

I am interested in various kinds of geometry, particularly problems concerning scalar curvature.

Currently, I am studying birational geometry. DG is sucked by AI now.

IMFP–IGP Seminar, 2026–2027

I am organizing this seminar for the academic year 2026–2027. Please feel free to contact me if you would like to visit Shanghai and give a talk here.

(Pre-)Publications

[7]PSC Kähler cones of minimal Kähler surfaces and a birational obstructionPreprintarXiv submission on hold2026PDF

[6]Scalar curvature on Kähler blow-ups and systolic inequalitieswith Jian WangPreprint2026arXiv:2608.27433

[5]Positive scalar curvature Kähler metrics and shifted $K$-stabilityPreprint2026arXiv:2608.20030

[4]A variational characterization of positive scalar curvature Kähler metricsPreprint2026arXiv:2608.20023

[3]The 2-systole on compact Kähler surfaces with positive scalar curvaturePreprint2026arXiv:2601.02901

[2]Rigidity of complete Kähler–Einstein metrics under cscK perturbationsPreprint2025arXiv:2510.13278

[1]The Kähler–Ricci soliton on bounded pseudoconvex domainsPreprint2024arXiv:2412.03345 revised PDF

Update. The current arXiv version was largely extracted from my thesis, and some parts of the exposition are more detailed or redundant than necessary. I have substantially rewritten the paper while keeping the main results unchanged. The revised version has a clearer main line and a more streamlined presentation; please use the updated PDF linked above.

Notes and theses

NoteBlowing up a point as a connected sum
NoteComputing the canonical bundle of a blow-up via short exact sequences
Short noteA 2-systolic inequality on non-rational compact Kähler surfaces with positive scalar curvaturearXiv:2510.13353, 2025. Uses the level-set method in the Kähler setting; this manuscript was merged into [4].
PhD thesisMétriques kählériennes canoniques sur les domaines pseudoconvexes bornésOnline version, 2025
Master thesisScalar curvature and $S^1$-valued harmonic maps on 3-manifoldsUnrevised, 2022

Talks

2 Apr 2026IMFP–IGP Seminar, USTC Shanghai Institute for Advanced StudiesThe 2-systole on compact Kähler surfaces with positive scalar curvature

26 Dec 2025Peking–Westlake Geometric Analysis Seminar, onlineThe 2-systole on compact Kähler surfaces with positive scalar curvature

18 Dec 2025Geometry/Topology Young Researcher Workshop, Academy of Mathematics and Systems Sciences, CASThe 2-systole on compact Kähler surfaces with positive scalar curvature

18 Sep 2025The 4th Milan–Grenoble–Turin Meeting in Geometry and Topology, Institut FourierRigidity of complete Kähler–Einstein metrics under cscK perturbations

16 Jul 2025The 5th Korea–France Conference in Mathematics, Institut de Mathématique de BordeauxThe Kähler–Ricci soliton on bounded pseudoconvex domains

9 Jul 2025Seminar talk, IGP–USTCCanonical Kähler metric on bounded pseudoconvex domains

24 Jun 2025Flows and Singular Spaces, Henri Lebesgue CenterThe cscK metric on bounded pseudoconvex domains

18 Jan 2024Séminaire Compréhensible, Institut FourierCalabi conjecture and Kähler–Einstein metrics

25 Oct 2023Journées des doctorants, Institut FourierGradient Kähler–Ricci solitons on strictly pseudoconvex domains

Elsewhere

Mathematics Genealogy What's a mathematician to do?

“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.”
From the MathOverflow discussion linked above

Useful links

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